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Transcript of Energy Level Structure and Transition Probabilities
jANL-78-XX-95
Energy Level Structure and Transition Probabilities
in the Spectra of the Trivalent Lanthanides in LaF-
W. T. Carnal!Chemistry Division
Argonne National Laboratory
Hannah Crosswhite and H. M. CrosswhiteDepartment of Physics
The Johns Hopkins University
- N O T I C E -
Thi* report w u prepared u an account of worksponsored by the United Slates Covemment. Neither theUnited State* nor ih* United States Department ofEnergy, nor any of their employees, nor *ny of theircontractors, nbcontradon, or their employees, mikesany wininty, expreis ot implied, or aitumei any legalliability or responsibility for the accuracy, completeneaor tisefulrten of any information, apparatus, product orprocen disclosed, or represent! that its tat would notinfringe privately owned rights.
filSTBlBimoN OF THIS DOCUMENT Ig UNJ4MIXS&
BLANK PAGE
CONTENTSPage
I. Introduction 2
II. Physical and Crystal!ographic Properties of LaF., 5
Fig. 1. LaF3 Structure Viewed Down the C-axis 6
III. Treatment of Experimental Data 8
Fig. 2. Crystal-field Parameters for Ln3+:LaCl3 and Ln3+:LaF3 13
IV. Energy Level Correlations - Survey of Experimental Data 14
1. f2(f12) 14
2. f3(f]1) 14
3. fV°) 16
4. f5(f9) 16
5. f6(f8) 17
6. f7 17
V. Theoretical Interpretation of Excited State Relaxation 19
A. Theoretical Treatment of Absorption Spectra 19
1. General Concepts 19
2. Induced Electric-Dipole Transitions 21
3. Magnetic Dipole Transitions 23
4. Comparison of Calculated and Observed TransitionProbabilities 24
B. Relaxation of Excited States 24
1. General Considerations 24
2. Radiative Relaxation 253+
Fig. 3. Energy-level diagrams of Ln :LaCl, 273. Non-radiative Relaxation 28
4. Comparison of Computed Excited State Lifetimes with
Those Observed Experimentally 30
5. Comments on the Use of the Tables 31
Acknowledgements 33
References 34
APPENDIX Ii.
Fig. 1. Variation of the Slater Parameter F with Lanthanide Atomic Number.
Fig. 2. Variation of the Spin-Orbit Constant with Lanthanide Atomic Number.
Table 1. Parameters for Ln3+:LaCl,. **
Table 2. Relativistic Hartree-Fock Integrals for 4fN(IV).
APPENDIX II3+
Table 1. Atomic Parameters for Ln :LaF3-
Table 2. Crystal-Field Parameters for Ln rLaFj.
APPENDIX III
Table 1. Experimental and Calculated Energy Levels for Pr :LaF,.
Table 2. Matrix Elements of [U ( A*] 2 for Selected 4f2-transitions.
APPENDIX IV3+ N
Table 1. Experimental and Calculated Energy Levels for Nd :LaF,.
Table 2. Matrix Elements of [ U ^ ] 2 for Selected 4 f 3 - t rans i t ions . •*
Figs. 1-21. Tlie Absorption Spectrum of Nd :LaF, in the Region -\4000-50000 cm"
recorded at A K.
APPENDIX V
Table 1. Computed Energy Levels for Pm :LaF,.
Table 2. Matrix Elements of [l/ x*] 2 for Selected 4f4-transitions.
APPENDIX VI
Table 1. Experimental and Calculated Energy Levels for Sm :LaFg.
Table i. Matrix Elements of [irX*]2 for Selected 4f5-transitions.APPENDIX VII
3+Table 1. Computed Energy Levels for Eu :LaFg. '•'
Table 2. Matrix Elements of [U ( X , ] 2 for Selected 4f6-transitions.
4-*
APPENDIX VIII
Table 1. Experimental and Calculated Energy Levels for Gd :LaF,.
Table 2. Matrix Elements of [ U ^ ] 2 for Selected 4f7-transitions.
APPENDIX IX
Table 1. Experimental and Calculated Energy Levels for Tb3+:LaF .
Table 2. Matrix Elements of [U ( X )] 2 for Selected 4f8-transitions.
APPENDIX X
Table 1. Experimental and Calculated Energy Levels for Dy :LaF .
Table 2. Matrix Elements of [U*X']2 for Selected 4f9-transitions.
APPENDIX XI3+Table 1. Experimental and Calculated Energy Levels for Ho :LaF3.
Table 2. Matrix Elements of [U ( X*] 2 for Selected 4f10-transitions.
APPENDIX XII.3+Table 1. Experimental and Calculated Energy Levels for Er :LaF,.
Table 2. Matrix Elements of [U ( X )] 2 for Selected 4fn-transitions.
-3+.,
APPENDIX X I I I .
Table 1. Experimental and Calculated Energy Levels for TmOT:LaF3
Table 2. Matrix Elements of [U ( X* ] 2 for Selected 4f12-transitions.
APPENDIX XIV
Table 1. Calculated Values of Qx for Ln3+:LaF3-
Table 2. Observed and Calculated Excited State Lifetimes for Ln3+:LaF,
Table 3. Partial Lifetimes and Branching Ratios in the Relaxation of
Excited States in Tb3+:LaFo.
FOREWORD
The spectroscopic investigations of lanthanide doped LaF^ crystals
and their theoretical interpretation reported here are the result of an
extensive joint effort of the Argonne National Laboratory and The Johns
Hopkins University over the last decade. It had its roots in similar
studies at both laboratories of other crystal hosts, particularly LaCl3>
for which a summary is also given in an appendix to this report. This
work was supported at Argonne by the United States Atomic Energy
Commission and the United States Energy Research and Development
Administration, and at Hopkins by the United States Army Research Office
and the National Science Foundation. An identical report is being
issued under separate cover by each institution.
-2-
I. Introduction
The low-temperature absorption spectra of trivalent lanthanide compounds
reveal the sharp-line structure characteristic of transitions between states
within the 4f -configuration, induced by the ionic environment. These transi-
tions can be directly represented as upper-state energy levels. In some cases,
notably ions in LaC13 host crystals, the empirical levels have been interpreted
in terns of a model which exhibits in detail the structure of the 4f elec-
tronic configuration itself. The atomic parameters derived from these studies
vary slowly and systematically across the lanthanide series and in fact are
depressed from corresponding values derived from atomic and ionic vapor
spectra.
G. H. Dieke has given a definitive review of the spectra of lanthanides
in crystals including a comprehensive summary of the data in LaCl3 host crys-
tals, Dieke (1968). The early interpretive papers concentrated on analysis of
the crystal-field parameters. More recently, the emphasis has been on devel-
oping models which include structural details of the 4fN configurations them-
selves with simultaneous diagonalization of the complete Hamiltonian rather
than a perturbation-theory treatment. The most recent analyses have been
given in a series of papers, Crosswhite et al. (1976), Carnall et al. (1976),
Crosswhite et al. (1977). These include effective two-body and three-body
operators approximating the electrostatic effects of configuration-mixing
interactions, plus two-body double-vector effective operators which allow for
the variation of spin-orbit interactions with spectroscopic term and for the
spin-other-orbit corrections for relativistic effects. The present analysis
of spectroscopic data for the lanthanides in single-crystal U F ~ employs the
most recent model.
'•&',
-3-
As a crystal matrix in which to study the absorption spectra of lantha-
nide ions, laFg has several advantageous features. In addition to being a „ >
transparent host over a wide region of the spectrum, it is chemically inert
so that the crystals can be handled in air. Thus even though the site SJW- **
metry of the metal ion is low, the commercial availability of the crystals in
a wide range of dopings has encouraged extensive experimental studies.
We report here two types of correlation with experimental results. For
even-f-electron systems we have computed a center of gravity based on the en-
ergies of the observed states, and calculated optimized sets of atomic energy
level parameters. For odd-electron systems we have performed complete crystal-
field calculations in which the parameters of both the atomic and crystal-
field parts of the interaction have been adjusted to experimental data. Trends >
in the free-ion parameters over the series have been examined and in some cases y
further restrictions on their values are set, based on observed parametric reg- f
ularities across the periodic series. The crystal field parameters for the I
odd-f-electron ions have also been compared and regularities over the series >
are noted. The end result of this effort is a set of eigenvectors for all of
the ionic states in each configuration. We then turn to the interpretation of
intensities of absorption bands and develop the basis for computing transition
probabilities using a semi-empirical theory of induced electric dipole transi-
tions. Finally, we apply the results of the analysis of absorption spectra at
\ „ room temperature to the related process of excited state relaxation, and pro-
' vide the basis for computing the radiative lifetime for any given state in any
!> •'->-,• member of the series.
Spectroscopic results for all lanthanides doped into LaF, (Ln :LaF,)
' ",,, > except Pm3+ and Eu3+ are reported. Since the crystals were obtained from
S;- commercial sources, the fact that the only isotope of Pm available in macro
-4-
amounts is ' Pm which is g"-unstable with a relatively short half-life, ex-
cluded it from consideration. The tendency of EuF3 to reduce to EuF2 at high
temperatures even in the presence of F., vapors, and the very strong broad band2+structure associated with Eu in the visible and ultraviolet range due to
4f -+ 4f 5d transitions, made it impossible to obtain the requisite experi-3+
mental data for the Eu-system. The energy level schemes for Pm :LaFo and
Eu :LaF_ were therefore calculated using parameters obtained by interpolation.
Some of the experimental results utilized in the analyses represent as
yet unpublished work done over a period of years in the Chemistry Division of
Argonne National Laboratory with the help of senior thesis students and guest
scientists. These results were obtained using several different instruments.
Spectra in the range ^OOO-ieOOO cm" were recorded using a Cary Model 14R
(crystal-grating- 0.5 meter) recording spectrophotometer. In the region
15000-50000 c m , both a 1-meter Hilger-Engis Model 1000 spectrograph equipped
with an EMI 9558 Q photomultiplier, and the Argonne 30' Paschen-Runge spectro-
graph (in second order) were used. Observations were made at ^298, 77, and
4 K. Crystals of LaF, doped with selected lanthanides in various concentra-
tions were obtained from Optovac Inc., North Brookfield, Mass. 01535.
There continues to be a wide interest in lanthanide-doped crystals and
glasses as laser materials. In some cases quantitative intensity calculations
have been carried out and related to the fluorescing properties in a given
host. The most extensive calculations have been limited to the f (f ) and3 11
f (f ) members of the series since the matrix elements of the tensor opera-
tors connecting the states of interest required ir the intensity analysis formore complex systems have not been published. We report here a consistent set
of the matrix elements for all 4f -configurations based on the systematic atomic
parameters generated in this work.
-5-
II. Physical and Crystal!ographic Properties of LaF-
There have been conflicting reports suggesting both C2V, Oftedal (1929,
1931) and D 3 h, Schlyter (1953), site symmetries of the La3+ ions in LaFy
More recent studies, Mansmann (1964, 1965), Zalkin et al. (1966), Lowndes
et al. (1969), indicate that the nine nearest-neighbor F" ions present a suf-
ficiently distorted environment so that the symmetry is D 3 d (P3cl) with a C2
site symmetry, Fig. 1. A recent powder neutron-diffraction study of LaF, and
CeF,, Cheetham et al. (1976), provided additional confirmation of the latter
structure. Isostructural members of the series are LaF-, CeF,, PrF,, and
NdF,; SmFo and the heavier trifluorides are dimorphic. They also crystallize
in the orthorhombic YF3 lattice where each Y3 + has 8-F" at 2.3 A and one at
2.6 A, Zalkin and Templeton (1953).
The crystallographic evidence for a low site symmetry in LaF3 is con-
sistent with the results of an early spectroscopic study of PrF, in which
Sayre and Freed (1955) pointed out that the number of lines observed at low
temperature for electronic transitions associated with several excited states
excluded a site symmetry higher than C2y. The Raman spectrum of LaF, has been
interpreted in terms of a C2 site symmetry of the La , but these results also
emphasize that the deviation of the symmetry from more symmetric models is
small indeed, Bauman and Porto (1967). Spectroscopic evidence for hidden3+selection rules in the polarized spectrum of Nd :LaF3 is also suggestive of
an approach to a symmetry higher than C2> Wong et al. (1963b), Kumar et al.
(1976).
A recant investigation of the normal and vacuum ultraviolet absorption
bands of trivalent lanthanides doped into LaF3 has provided evidence that LaF3o
is transparent down to the normal ultraviolet limit of ^000 A, Heaps et al.
(1976).
Fig. 1
LoF3 STRUCTURE VIEWED DOWN THE c-AXIS
FK08)
0 I 2A
oo = 7.185 ± O.OOI A
c0 = 7.351 ± 0.001 A
A. Zalkin, D. H. Templeton, J.E.HopkinsInorg. Chem. 5, 1466 (1966)
Space Group0jd-P3ClSite symmetry C2
- 7 -
Refractive index (n) measurements using films of LaF3> CeF,, and NdF,,
Haas et al. (1959), provided the following values in the 0.25-2.0 p range:
x(u)2.0
1.2
0.8
0.6
n__
1.57
1.575
1.58
1.585
0.45
0.40
0.30
0.27
n
1.60
1.61
1.625
1.65
For single-crystal LaF_, the expression obtained for the variation of the re-
fractive index (ordinary ray) with wavelength in the visible-near ultraviolet,
Wirich (1966), was
n = 1.57376 + 1 5 3 - 1 3 7
0 X(A) - 686.2
2536.5 1.65587 1.65652
3131.5 - 1.63639
3663.3 - 1.62520
4046.5 1.61797 1.61933
4358.3 1.61664 1.61546
5460.7 1.60597 1.60583
The M.P. of LaF3 is 1493°C and its density is 5.94 gm/cm3, Brown (1958).
-8-
III. Treatment of Experimental Data
In recent years there have been numerous reports of the spectroscopic
properties of different lanthanides in host LaF,, and many of these investiga-
tions have included low-temperature spectra. Consequently, the energies of
the crystal-field components associated with many of the free-ion states have
been recorded. The extensive data available led us to begin a systematic
theoretical analysis of the 4f energy level structures over the series.
Part of the motivation to undertake a systematic analysis of the data
stemmed from the results described in two papers by Onopko (1968a,b) in which
he pointed out that the energies of crystal-field components of several of the
lowest-lying free-ion states in Nd3+:LaF3 and Er3+:LaF3 could be computed in
reasonably good agreement with experiment by assuming that the site symmetry
approaches D,.. The approximation also appeared to be justified in treating
the crystal-field levels in Gd :LaF3, Schwiesow and Crosswhite (1969). We
had already developed computer programs that allow a complete diagonalization
of the atomic and crystal-field Hamiltonian for the 4f3(4f11) case in D 3 h~
symmetry. We had also determined the atomic parameters for both Nd :NdF33+
and Er :LaF3. We therefore extended the analysis using Onopko's crystal-
field parameters. The initial results confirmed the validity of Onopko's
analysis by providing a computed set of crystal-field levels that were in
reasonably good agreement with experiment throughout the spectral range to
^50,000 c m .
The analysis was extended by assigning the experimentally observed en-
ergy to those crystal-field states identified by the initial computation.
This permitted a least-squares adjustment of the original crystal-field param-
eters. Additional assignments were made based entirely on the correlation
-9-
between the optimized crystal-field parameter calculations and observed levels.
We then proceeded to perform a similar crystal-field calculation for other Ian-
than ides using the optimized values for Nd and Er' as the basis for beginning
the analysis.
For odd-electron systems the crystal field will split a level into J +
1/2 separate components in all site symmetries except cubic and octahedral.
The number of possible components therefore is the same for C2 and D 3 h, and
because D ^ appears to be a good approximation to the actual one, it is not
difficult to correlate the experimental and computed levels.3+ 2
On the contrary, in even-electron systems such as Pr (4f ), crystal-
field calculations based on D~u symmetry do not remove the degeneracy of the
vi = ±1, ±2 states. It has been pointed out that the number of lines observed
in the spectrum of Pr :LaF, implies a low site symmetry consistent with the
complete removal of symmetry-related degeneracy in the indicated levels. Sayre
and Freed (1955), Carnall et al. (1969). This leads to ambiguities in making
the necessary crystal-field correlations. We have therefore attempted complete
crystal-field analyses only for odd-electron systems. For the even-electron
cases we have made the approximation of fitting the centers of the crystal
groups to the free-ion Hamiltonian only.
The basic theory used to interpret the structure observed experimentally
in lanthanide crystal spectra has been considerably refined in recent years.
A semi-empirical approach has been employed in which the attempt is made to
identify those effective interactions operating within the f -configuration
that reproduce the observed structure. Judd (1963), Wybourne (1965), Judd et
al. (1968), Crosswhite et al. (1968). Based on this method of interpretation,
the total Hamiltonian of the system can be written:• A
glSTBlBUTlON OF XHiS JJOQUMJSNT Ig UHU«££gR
-10-
E " EF + ECF
where Ep is the atomic part of the interaction:
k=0.2,4,6Fk(nf,nf)f.
k aL(L+l) YF(R7)
1=2,3,4,6,7,8Mkm.
kk=0,2,4 k=2,4,6
kThe F , i k k-j., a, 3, y, T , M and P are parameters and their associated terms
are the corresponding operators. E C F represents the crystal-field interaction.
Following Onopko (1968a,b) we assumed that the symmetry of the lanthanide site
in LaF3 was approximately hexagonal (Dou)> that is, that the hexagonal terms
in the crystal-field expansion are dominant.
ECF B kC ( k ) = B 2C { 2 ) + B 4C ( 4 ) + B 6C ( 6 ) + B 6rC ( 6 ) + C { 6 )
W B 0 l 0 B0L0 + B0l0 B6lL6 C -6
The above interactions which constitute the model used in this investigation
are discussed in detail in Appendix I with reference to the similar treatment
of the more extensive data for Ln +:Lado-
For odd-f-electron systems the total Hamiltonian can be separated into
three submatrices and all three of them diagonal!zed simultaneously. The
methods of truncating the very large matrices that occur for ions in the mid-
dle of the series have been discussed previously, Carnall et al. (1976). The
results of the diagonalizations—which eventually included variation of most
of the parameters in the systems, are given in Appendix II.
Onopko (1968a,b) quoted his original results in the Stevens operator3+(g. ) normalization and subsequently extended the analysis to Er :LaF,,
• > -
-11-
Onopko (1969). The corresponding crystal-field parameters in the tensor opera-i,
tor normalization (B*) used in the present study, Wybourne (1965), are given
below:
3 2 0 =
3 6 Q =
666 =
Nd3+:
138 cm"1
176
100
645
LaF3
-8-BJ =
4-4-
276 cm"1
1408
1600
679
3 2 0 =
1*40 =
Er3+:
141 cm"1
145
48.3
430
LaF3
4-•4-
4-4-
282 cm"1
1160
773
453
The crystal-field parameters obtained from the Nd :LaF3 data in this investi-
gation are compared with those for Nd :LaCl3, Crosswhite et ai. (1976), where
the symmetry is hexagonal, below:
Nd3+:LaF3
(D3h Approximation)
BQ = 216 cm"1
BJ = 1225BQ = 1506
B5 = 7700
a = 1 7 cm"
139 levels fitted
Nd3+:LaCl3
(C3h Symmetry)
BQ = 163 cm"1
B« = -336
B0 = "713
B«=462
a = 8.1 cm"
101 levels fiti
It has been demonstrated that ab initio calculations of crystal-field
parameters based on an ionic model are not able to reproduce the values ob-
tained semi-empirically. However, serious efforts are being made to develop
suitable models for the LaF crystal, Newman and Curtis (1969), Stedman and
Newman (1971), and attempts have also been made to treat the low-symmetry LaF3
lattice case by actually using the appropriate number of terms in the poten-
tial, Matthies and Weisch (1975).
-12-
The experimental results of the present efforts should provide a useful
testing ground for further theoretical treatments. Systematic trends in the
values of the crystal field parameters for Ln3+:LaF3 are compared with those3+
for Ln :LaCl3 which are much better established experimentally, in Fig. 2.
i- . >
200-
100-
1000
500
1000-
500-
1
r2
0
i
1
o
1
1 1 1
1 1 1
1 1
_ 2o
1 1
1
o Lα«
• Lα!i
i i
.0 SL
1 I
1
I
I I 1 1 1 1
1
1
1
— — •
-flu
1
1
1
1
"TS—•
-flu
1
1
•
o
1
1 1
o
1 1
1
- 9 .
1
1 1
T-
"°—o-
i i
i
i
N2 3 4 5 6 7 8 9 10 I! 12Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm
Fig. 2. Crystal-f ie ld Parameters forLn3 +:LaCl3 and Ln3 +:LaF3.
-14-
IV. Energy Level Correlations - Survey of Experimental Data
The energy level structure in Pr :LaF, has been examined experimentally
in moderate to high resolution by several groups. Wong et al. (1963a), Yen
et al. (1964), Caspers et al. (1965a), Carnal! et al. (1969). Free-ion level
energies are recorded in Appendix III together with the corresponding computed
levels using parameters given in Appendix II. The weak point in the theoret-
ical analysis is the assumption of a center of gravity for the Ig and for the
3r transitions.
,3+.,Most of the possible crystal-field components in the spectrum of Tin :I-«»F-
have been observed, Carnall et al. (1970), and the centers of gravity of these
groups are compared to the calculated free-ion levels in Appendix XIII.
2. 4f3(f]1)
There are extensive published reports, Wong et al. (1963b), Caspers et
al. (1965b), of the structure observed in the low-temperature absorption and
3+fluorescence spectra of Nd :LaF^. These data have been extended by previously
unpublished work at ANL to provide as complete a set of crystal-field compo-
nents as possible. Of the 182 levels in the f configurations, 139 have been
assigned. The results are included in Appendix IV, and can be compared to
those obtained in the recent extensive investigation of the spectrum of3+
Nd :LaCI3, Crosswhite et al. (1976). Kumar et al. (1976) have examined the
absorption and fluorescence spectra of Nd +:LaF, at 77 K, the latter excitedo
using the 3371 A line of a Np-laser. They reported several transitions not
observed in previous investigations. Some of these are consistent with band
energies observed in the present study but there are discrepancies. In gen-
eral, there is a small shift in energy between observations at 77 K and those
?•••*
-15-
reported here which refer to 4 K. The assignments made to the fluorescence
spectrum serve to further establish the energies of the lower-lying states
which had been reported earlier. The components of the I-IR/O state reported
by Voron'ko et al. (1973) from observations made at 77 K are in good agreement
with the unpublished results recorded in Table 1, Appendix IV.
The present theory of intensities of f -»• f transitions treats the compos-
ite free-ion states rather than transitions between individual crystal-field
components (see Section V). A number of investigators are presently concerned
with extending the theory to the crystal-field case. In order to provide a
basis for testing the results of such calculations we include in Figs. 3-22,
Appendix IV, a set of absorption spectra of Nd3+:LaF3 taken at -\4 K covering
most of the levels observed in the f -configuration. No attempt was made to
preserve a constant resolution since two different instruments were used, and
several different crystals of varying concentrations and path lengths were em-
ployed. However, in any one group, the relative intensities of the components
are clearly evident.
The absorption and fluorescence spectra of Er :LaFg measured at 77 K and
including levels up to -v/39500 cm" were reported by Krupke and Gruber (1963,
1964, 1965). Several higher-energy transitions were also tentatively identi-
fied. A subsequent investigation, Carnall et al. (1972), included measurements
at %4 K in the range 6000-50000 c m . Additional spectroscopic measurements at
low temperature have been made, so that the levels recorded in Appendix XII
represent a composite and in a number of cases a revaluation of results ap-
pearing in the literature. In addition to a discrepancy in the calibration
standards applied to a number of groups originally reported by Carnal! et al.
(1972), the comparison of experimental energies with those computed based on
-16-
the crystal-field interpretation used here suggested a possible vibronic origin
for some of the states previously identified as crystal-field components.
3. 4f4( f1 0)
The absorption spectrum of Pm :LaF3 has not been reported, but an exten-
sive investigation of the absorption and fluorescence spectra of Pm :LaCl, has
been published, Carnail et al. (1976). We have therefore used the regularities3+in the energy level parameters for Ln :LaF- as the basis for interpolation and
3+
assignment of approximate parameters for Pm :LaFj. The corresponding computed
free-ion levels are given in Appendix V. The chemical shifts observed on com-
paring free-ion levels in Nd3+:LaF3 and Nd3+:LaCl3 are similar to those found
in comparing the computed results for Pm :LaF3 with the experimental states of
Pm3+:LaCl3.
An extensive investigation of the absorption and fluorescence spectra of
Ho :LaF3 has been reported by Caspers et al. (1970). Additional experiments
have been conducted at ANL, but only minor additions or modifications of the
published data were indicated. In many cases, the number of observed components
of free-ion groups is less than allowed theoretically based on C« site symmetry,
but the centers of gravity of these levels appear to provide the basis for cal-
culation of a consistent set of energy level parameters, as recorded in Appen-
dix XI.
4. 4f5(f9) », /<y
The observation and analysis of the absorption and fluorescence spectra \
of Sm3+:LaF3 in the range 0-11000 cm was reported by Rast et al. (1967), and . ';>• •^'•j
the line list was extended to 2000 cm in a tabulation given in Dieke (1968). ;
The number of observed lines was further extended in the present investigation,
and a composite tabulation based primarily on recent work at ANL is given in \- :
Appendix VI.
-17-
Absorption and fluorescence spectra of Dy3+:LaF- including levels up to
^32000 cm" have been reported in the literature by Fry et al. (1968). A num-
ber of new levels including groups at higher energies were recorded in the
course of the present investigation. The results are presented in Appendix X.
5- 4f6(f8)
Crystals of LaF3 doped with EuF. are found to contain some Eu2+ which
3+
makes it difficult to observe the Eu transitions in absorption in the near-
ultraviolet. Weber (1967a) observed fluorescence in Eu3+:LaF3 from the excited
states DQ, DJ, 5D 2. and D3 using pulsed selective excitation. The energy
level scheme for the low-lying D and F states that can be deduced from these
measurements shows the expected red shift with respect to the corresponding
levels observed in Eu :LaCl-, Dieke (1968), and is consistent with the results
given in Appendix VII. The latter were computed based on energy level param-
eters deduced from systematic trends over the series.
T*K; energy levels of Tb 3 + in single-crystal TbFj have been studied in
absorption and fluorescence by Krupka and Guggenheim (1960). From this data
the centers of gravity of the D- and the ground term F multiplet components
could be determined. The results are in agreement with the moderately exten-3+sive study of the low-temperature absorption spectrum of Tb :LaF, which was
3+part of the present investigation. The free-ion levels of Tb :LaF, are given
in Appendix IX.
6. 4flc c ox
The energy levels of the P and I groups in Gd :LaF3 were reported by
Schwiesow and Crosswhite (1969) who also performed a crystal-field analysis
assuming an approximate hexagonal site symmetry. The experimental results were
subsequently extended to include the 6D states in the 40000-50,000 cm range,
-18-
Carnall et al. (1971). The data recorded in Appendix VIII are a composite of
the indicated published results.
i>:
' : ' • • • • '
;3
&,
BLANK PAGE
-19-
V. Theoretical Interpretation of Excited State Relaxation
A. Theoretical Treatment of Absorption Spectra
1. General Concepts
The quantitative treatment of the intensities of trivalent lanthanide ab-
sorption bands relates an experimentally determined quantity, a normalized band
envelope, PEXpT, to a theoretical model based on the mechanisms by which radia-
tion can be absorbed, fhe terms oscillator strength or transition probability
are applied interchangeably to the symbol P. There is some magnetic dipole
character in a few transitions (P*. p ), but an induced electric-dipole mecha-
nism (Pc p ) must be invoked to account for the intensities of most lanthanide
absorption bands. The term induced or forced electric dipole is used to empha-
size that true electric dipole transitions require the initial and final states
to be of different parity, whereas no parity change is involved in transitions
within a configuration. In contrast, magnetic dipole transitions within a con-
figuration are (parity) allowed. The weak intra-f transitions are accounted
for by assuming that a small amount of the character of higher-lying opposite-
N
parity configurations is mixed into the f states via the odd terms in the
potential due to the ligand field, Wybourne (1965). We neglect higher multi-
pole mechanisms, (electric quadrupole, etc.), and write:
PEXPT = PE.D. + PM.D.
In expressing Pr n in terms of a theoretical model, Judd (1962) and Ofelt
(1962) summed over the intensities of the individual crystal-field components
of a given state. As a consequence, the model applies to spectra observed at •.'
room temperature or above since it is assumed that all of the crystal-field
-20-
components of the ground state are equally populated. Some attempts have been
made to avoid this summation and thus treat the intensities of transitions be-
tween the lowest crystal-field level of the ground state and excited crystal-
field states, Axe (1963). However, the intensity calculations reported in the
present summary deal only with composite levels. Thus the appropriate expres-
sion for I'exPT' which represents the number of classical oscillators in one ion,
more commonly referred to as the probability for absorption of radiant energy,
Hoogschagen (1946), is:
2P = 2303 mc /e.(a)da = 4.32 x 10"9 feAo)iotxP1 me* 1 n
where e. is the molar absorptivity of a band at the energy a. (cm" ), and the
other symbols have their usual meaning. P is here a dimensioniess quantity.
The molar absorptivity at a given energy is computed from the Beer-Lambert law:
E = l o g l o / I (l)
3where c is the concentration of the lanthanide ion in moles/1000 cm , S, is the
light path in the crystal (cm), and log IQ/I is the absorptivity or optical
density. The expression for Pc^pj is identical to that for f defined by Krupke
(1966) in his treatment of lanthanide spectra in LaF3-
In view of our interest in both absorption and fluorescence processes,
there is an advantage in pointing out the basic role of the Einstein coefficient
in expressing the transition probability due to dipole radiation:
2 (2)
where i and f signify the initial and final states, A is the (spontaneous)
transition probability per unit time, a(cm" ) is the energy difference between
-21-
the states, and D is the dipole operator, Condon and Shortley (1957).
In addressing the problem of the absorption of energy, Broer et al. (1945)
expressed eq. (2) in terms of oscillator strength using the relationship P =2 2 2
Amc/frr a e . The factor 2J + 1 was added since the matrix elements of D are
summed over all components of the initial state i. A refractive index correc-
tion x was also included giving:
(3)
n p
where F and M represent the matrix elements of the electric dipole and mag-
netic dipole operators, respectively, joining an initial state J to the final
fn + J>i
state J,, x - — g _ ' , and n is the refractive index of the medium.
2. Induced Electric-Dipole Transitions
Oudd (1962) and Ofelt (1962) independently derived expressions for theN
oscillator strength of induced electric dipole transitions within the f con-
figuration. Since their results are similar, and were published simultaneously,
the basic theory has become known as the Judd-Ofelt theory. However, Judd's
expression, eq. (4), was cast in a form that could be directly related to oscil-
lator strengths derived from lanthanide absorption spectra taken at 25°C or
above:
PE n " H Tv(^j|U
(X)||,J.'J')
2 (4)
t,u' X=2,4,6
A
where v(sec ) is the mean frequency of the transition ipj •* <|/'J', IΓ ' is a
unit tensor operator of rank X, the sum running over the three values X = 2,4,6,
and the T^ are three parameters which can be evaluated from experimental data.
These parameters involve the radial parts of the 4f wave functions, the wave
functions of perturbing configurations such as 4f 5d, and the interaction
Si*
-22-
between the central ion and the immediate environment.
Typically, several excited states are encompassed by a single complex
absorption envelope, and the matrix elements of u' ' are summed over these
states. The energy in this case becomes that of the center of gravity of
the envelope. Those investigators who have studied lanthanide intensities
in crystals have followed an alternate parametrization, Axe (1963), Krupke
(1966), which has clear advantages in describing both the absorption and
fluorescence processes in terms of a single set of adjustable parameters.
The expression for T given by Judd in eq. (4) was:A
(5)
Substituting v = cc? and eq. (5) into eq. (4) gives
9 n X=2,4,6E.D. 3h(2J+l (6)
where ft. = (2X+l)Z(2t+l)B+52(t,X), Axe (1963), and in terms of F2, eq. (3),
A x v
(7)
The matrix elements of eq. (6) are calculated in the SL basis using the
relation:
'S'L'J ,) = 6(S,S'J(-1)S+L '+J+Xt(2J+lJ(2J'+1(fNaSLJ
£,£'£} (fNaSL||U(A)||fNa'SL') (8)
Selection rules imposed by the nature of the mechanism assumed are discussed
by Ofalt (1962). The reduced matrix elements on the right side of eq. (8)
have been tabulated by Nielson and Koster (1963). The matrix elements as
-23-
computed must be transformed from the SL basis to intermediate coupling before
being squared and substituted into eq. (6).
The intermediate-coupling eigenvectors, |f i/>J>, are expressed in terms of
SL basis states, |fNaSLJ>, by:
|fN*J> = c(a,S,L)|fNaSLJ>
where c(a,S,L) are the numerical coefficients resulting from the simultaneous
diagonalization of the atomic parts of the Hamiltonian. The matrix elements
of U , eq. (8), have been calculated for transitions between various excited
states as well as between the ground and excited states of the whole series of
lanthanide ions using the energy level parameters given in Appendix II. The
results are tabulated in Appendices III-XII.
3. Magnetic Pipole Transitions
Following the results of Condon and Shortly (1957), the magnetic dipole
operator is given as M = -e/2mc £(L^+2S 4). The matrix elements of the opera-
(9)
tor FT in eq. (3) can then be wri t ten,
FT2 = e2/4m2c2(tf<J| |L+2S| |tfi'J' )2
The non-zero matrix elements w i l l be those diagonal in the quantum numbers a,
S, and L. The selection rule on J , &J = 0,± l , restr icts consideration to
three cases:
1) J'=J («SLJ||L+2S|jaSLJ,) = gfi [J(J+l)(2J+l)]1 /2 (10)
where a = 1 + J ( J + 1 ) + SiS+1? " L ( L + 1 )where g - l + 2J(J+1)
2) J'=J-1
(aSU||L+2S||aSU-l) = 1 i [
-24-
3) J'=J+1
(aSLJl |L+2S| laSLJ-t-IJ (12)
The matrix elements calculated in eqs. (10)-(12) must be transformed into
the intermediate coupling scheme before computation of the magnetic dipole con-
tribution represented by eq. (9).
Values of the quantity P, > 0.015 x 10"8 where PM D B P'n and n is the
refractive index of the medium, have been tabulated for transitions of the tri-
valent lanthanide ions between the ground states and all excited free-ion
states, Carnal 1 et al. (1968a).
4. Comparison of Calculated and Observed Transition Probabilities
A number of authors have determined the ft, intensity parameters from a
least squares fitting procedure using band envelopes for Ln :LaF, observed at
^25°C and available sets of the matrix elements of IP . Krupke (1966) was the
first to show that transition probabilities in good agreement with experiment
could be computed for Pr :LaF3 a"d Nd : L a l V A summary of parameter values,
3+Sly for Ln :LaF3 is presented in Table 1, Appendix XIV. The parameters for3+ 3+ 3+
Sm :LaF , Dy :LaF3, and Tm :LaF were checked against results obtained inthe present investigation, and those for Dy3+ and Tm were modified from the
values originally reported. While the values of the matrix elements of
given in Appendices III-XIII differ slightly from those in the literature, these
differences are not sufficient to affect the reported values of fi,.
B. Relaxation of Excited States
1. General Considerations
A great deal of progress has been made in analyzing the mechanisms of
excited state relaxation of lanthanides in crystal hosts. Two modes of
! • * - •
-25-
relaxation can be recognized: radiative and non-radiative processes. Axe (1963)
addressed the problem of expressing the radiative process in quantitative terms
using the Judd-Ofelt theory. Non-radiative relaxation was already being formu-
lated in terms of multiphonon processes in the early 1960's. Barasch and Dieke
(1965), Riseberg and Moos (1967,1968). Such processes become, less probable as
the energy gap between an excited state and the next lower energy state increases.
2. Radiative Relaxation
In treating the fluorescence process, the Einstein coefficient, eq. (2)
is used directly to express the rate of relaxation of an excited state (ifiJ) to a
particular final state (i|»'J'). Following Axe (1963), the counterpart of eq. (3)
becomesA Q
jl IX'F2 + n3M2] (13)
where a(cm ) represents the energy gap between states (IJIJ) and (i|>'J'), x, =2 22 2q > ana" n 1S tne refractive index of the medium. As in the absorptionq
process, there is an implicit assumption that all crystal-field components of
the initial state are equally populated. In principal, if fluorescence can be
detected, the lifetime of the state is long compared to the rate at which it is
populated in the excitation process, so thermal equilibrium at the temperature
of the system can be achieved prior to emission.
The matrix elements of the electric and magnetic dipole operators, r
and FT , are identical to those in eq. (7) and eq. (9), respectively. However,
the form of the refractive index correction in eq. (13) is not the same as for
the absorption process, eq. (3). Equation (13) can be evaluated using param-
eters & established from measurement of the absorption spectrum of the lan-
thanide ion in a crystal lattice identical to that studied in fluorescence.
' • $ '•• •
-26-
Since excited state relaxation generally involves transitions to several
lower-lying states, we define a total radiative relaxation rate, Ay(^J)
£ ,*,J,) (14)
where the sum runs over all states lower in energy than the fluorescing state.
It is useful to define in addition the radiative branching ratio, 3R,
from the relaxing state (ijjJ) to a particular final state (ij/'J,)
and the radiative lifetime of a state
1 (16)
The principal fluorescing states of the lanthanides in crystal hosts are
indicated in Fig. 3. However, fluorescence from many of these levels is only
observed at low temperatures since rapid relaxation of an excited state by non-
radiative processes competes strongly with the radiative mode unless the energy
gap to the next lower level is large, as discussed in the next section.
Since the parameters Q^ have been determined for a number of the lantha-
nides in LaF, host, Table 1, Appendix XIV, we can compute the radiative life-
time of any excited state using eqs. 13, 14 and 16. For those states with
large energy gaps to the next lower level, the observed and computed radiative
lifetimes would be expected to be in approximate agreement. Weber (1967b) has
pointed out that such agreement is observed for excited states in Er :LaF,
where the energy gaps are in excess of 3000 cm" :
i'?-'
4<
3
3
34
32
30
Sβ
26
24
22
20
Iβ
16
14
12
10
8
6
4
2
•lO'cm-i",
=i ,— — *^%
I » —
» %
»-^%
I^*
• '.
-\ —
, t
S!_ I—i'
-%
..-Ss- r y
is —
Ce Pr N-d Pm Sm Eu Gd Tb Dy Ho Er Tm Yb
Fig. 3. Energy Level Diagrams for Ln 3 + :LaCl 3 .
y
'r
/V*;-".:.i<";-
U.I t
1
-28-
Transition4 I - 4 I!13/2 M5/2
rn/2 *2PF3/2
3. Non-radiative
TR(msec)
10.9
11.6
0.43
Relaxation
Observed Lifetime(msec)
13
11
0.29
Following the excitation of a lanthanide ion in a crystal lattice, the
relaxation of excited states may occur by a purely radiative process, or more
generally, may occur by the transfer of some energy to lattice vibrations. It
was known experimentally for a number of years before any quantitative theory
of non-radiative processes was developed that fluorescence was not observed at
25°C from Ln :LaCl, if the energy gap between the excited state and that next
lower in energy was < 1000 cm" , Barasch and Dieke (1965). In a systematic
investigation of multiphonon orbit-lattice relaxation of lanthanide excited
states, Riseberg and Moos (1968) have given an explicit expression for the
temperature dependent transition rate in LaF,, LaCl, and LaBr,. The energy-gap
dependence of the multiphonon process is treated phenomenologically by assuming
that the appropriate phonon energy is that corresponding to the cut-off in the
phonon states. For LaF, this is 350 cm" , while for LaCl, it is 260 cm" .
In terms of the ^1000 cm energy gap cited earlier, it is apparent that a 3-4
phonon emission process is a relatively efficient mode of relaxation at 25°C.
However, as the gap increases, demanding the simultaneous emission of a large
number of phonons, the process rapidly decreases in probability such that radia-
tive decay can efficiently compete as a relaxation mechanism.
Since in the usual case both radiative and non-radiative processes operate
to relax an excited state, we can express the total fluorescence lifetime of the
-29-
state as
(17)
where AT is the radiative rate and WT(ij>J) is the sum of the rates of the various
non-radiative processes.
The dependence of the relaxation rate on energy gap alone, W(o) can be
expressed as a simple exponential, Moos (1970),
W(o) = Ce a A E
where C and a are parameters characteristic of the host material, not of the
lanthanide ion. For LaF3, C = 6.6 x 108 (sec-1) and a = -5.6 x 10"3, Riseberg
and Weber (1976).
Adding the temperature dependence, Riseberg and Moos (1967,1968), results
in the expression
= W(o) { [ e f ( V k T - I ] " 1 + l}AE/ f i a ) i
which can be rewritten
W(«J) = CeaAE[l - e " f i V k T r A E / f i a , i (18)
-1where Hia). is the maximum phonon energy, taken as 350 cm" for LaF,, Riseberg
and Weber (1976). Since k = 0.695, kT = 207 cm at room temperature and the
corresponding expression is:
= CeaAE(.8155)-AE/35°
For example, the radiative lifetime of the Ig/o state of Er :LaF, at
a/l?oon cm" has been computed to be 20.7 msec but observed to be M).15 msec,
Weber (1967b). Since AE between Ig/2 and the next lower I-j-j/g state 1S
'.'•%
-30-
1- 1 4 - 1 <
2000 cm , W(i|d) = -lO sec . Thus the non-radiative lifetime of 'vO.l msec
is rate determining.
4. Comparison of Computed Excited-State Lifetimes with Those Observed
Experimentally
Experimental measurements of excited-state lifetimes for a number of
lanthanides in LaF3 have been reported, and in many instances these values have
been compared to those computed using eq. (13), (17) and (18). Although the
results of the computations were reported, the availability of the relevant
matrix elements of U* ' interconnecting the excited states in the various con-
figurations is very limited. The only tabulation that includes all members of
the series is restricted to matrix elements that join excited states to the
ground state, Carnall et al. (1968b). As a consequence, the results presented
in Appendices III-XIII represent the first systematic effort to make intercon-
necting matrix elements of lr ' available for the whole series and thus enable
calculation of a wide range of lifetimes. Some minor corrections to values re-
ported in the earlier tables have also been made. Calculated radiative life-
times and observed lifetimes for some of the prominent fluorescing states in
Ln :LaF- are given in Table 2, Appendix XIV. An example of the complete cal-
culation of the lifetimes associated with the radiative relaxation of two
states in Tb , showing branching ratios to all lower-lying states, is given
in Table 3, Appendix XIV. The strong radiative coupling of the D4 to the D3
state is clearly indicated. Recently Page et al. (l>76) reported lifetimes in', 5 3 + '
v the 100 psec range for the D. state in Tb :LaF3 at 300 K, with little change,
!,> v, as expected, on cooling to 77 K. However, these values are a factor of ten,v . v shorter than would have been predicted, see Table 2, Appendix XIV, and must be'*' • 3+ 5
. i>. regarded as questionable. In Tb :LaCl, at 300 K the lifetimes of the D 3
:V ; 1 states were 570 and 1220 psec, respectively, in good agreement with the calcu-
< lated values for the LaF 3 host, Barasch and Dieke (1965).
-31-
•>£/
5. Comments on the Use of the Tables
(A) Atomic (free-ion) states
As discussed in the introduction, detailed crystal-field calculations
were only carried out for odd-f-electron systems. For the even-f-electron
systems a center of gravity was computed from the experimentally observed
crystal-field components of each state. These "free-ion" states are recorded
in the appendices and were used as the basis for computing the energy level
parameters. Similar tabulations of the free-ion state energies have been
included for the odd-f-electron systems in order to facilitate use of the
tables of U(K)*2. In these latter cases the computation was made using the
atomic parameter values given in Appendix I with the crystal-field parameters
set equal to zero. In all the tabulations of free-ion levels the state
designation corresponds to the largest component of the eigenvector.
(B) Tables of ( U ^ ) 2
The entries in these tables are arranged in order of increasing J-value
for the initial state. Entries are not repeated. For example, the matrix
element between an initial J = 9/2 and a final J = 3/2 state is identical
to the J = 3/2 -»• J = 9/2 entry. Only the latter is given. If the entry is
missing from the table, the matrix elements are zero. The following partial3+
tabulation of matrix elements of U(K)*2 for Nd :LaF3 joining the ground( I9/2) state with several excited states taken from Appendix IV serves as
3+
an illustration and may be compared with results given for Nd (aquo) in
Carnall et al. (1968b).
-32-
State
41
41
41
41
4F
4F
2H
M9
11
13
15
3
5
9
Eton"1)
235
2114
4098
6148
11621
12660
12768
.0194
0
0
0
.0006
.0095
.1072
.0135
0
.2283
.2337
.0082
1.1639
.4549
.0452
.0554
.3983
.1195
-33-
Acknowledgements
Several individuals contributed substantially to the experimental inves-
tigation and/or interpretation of important segments of the data presented in
this report, and their assistance is gratefully acknowledged:
Dr. Katheryn Rajnak, Kalamazoo College, Kalamazoo, Michigan
Prof. R. Sarup, College of the Holy Cross, Worcester, Massachusetts
Dr. H. Kramer (ne'e LSmmermann)
and the following senior thesis students:
E. A. Flom, St. Olaf College, Northfield, Minnesota
D. W. Mehaffy, Coe College, Cedar Rapids, Iowa
J. F. Pophanken, Houston Baptist College, Houston, Texas
G. A. Robbins, Stamford University, Birmingham, Alabama
BLANK PAGE
-34-
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Stedman, G. E. and D. J. Newman (1971), J. Phys. Chem. Solids 32., 109.
Trees, R. E. (1951), Phys. Rev. 83, 756.
Trees, R. E. (1952), Phys. Rev. 85, 382.
Trees, R. E. (1964), J. Opt. Soc. Am. 54, 651.
Voron'ko, Y. K., V. V. Osiko, N. V. Savost'yanova, V. S. Fedorov and I. A.
Shcherbakov (1973), Soviet Phys. Solid State 1£, 2294.
Weber, M. J. (1967a), in Optical Properties of Ions in Crystals, H. M. Crosswhite
and H. W. Moos, eds., Wiley Interscience, New York, p. 467.
Weber, M. J. (1967b), Phys. Rev. 157, 262.
Weber, M. J. (1967c), Final Report to Research and Development Procurement
Office, U.S. Army Engineering R&D Laboratories, Ft. Belvoir, Virginia,
Contract DA44-009-AMC-1727(E).
Weber, M. J. (1968), J. Chem. Phys. 48, 4774.
-38-
Weber, M. J., B. H. Matsinger, V. L. Donlan and G. T. Surratt (1972), J. Chem.
Phys. 57, 562.
Wirich, M. P. (1966), App1. Optics 5_, 1966.
Wong, E. Y., 0. M. Stafsudd and D. R. Johnson (1963a), J. Chem. Phys. 39, 786.
Wong, E. Y., 0. M. Stafsudd and D. R. Johnson (1963b), Phys. Rev. 131, " ° -
Wybourne, B. G. (1965), Spectroscopic Properties of Rare Earths, Wiley, N. Y.
Yen, W. M., W. C. Scott and A. L. Schawlow (1964), Phys. Rev. 136, A271.
Zalkin, A. and D. H. Templeton (1953), J. Am. Chem. Soc. 75, 2453.
Zalkin, A., D. H. Templeton and J. E. Hopkins (1966), Inorg. Chem. 5_, 1466.
APPENDIX I
-1-
Appendix I
As a result of the correspondence between the energy levels of lantha-
nides in LaCl, and LaF,, it is convenient to summarize the present status of
the theory applied to the host LaClg in order to facilitate the LaF, discus-
sion. The basic experimental work on trivalent lanthanide spectra in LaCl,
crystals has been described by G. H. Dieke, Dieke (1968), who also gave a
comprehensive historical review and a brief discussion of early efforts at
theoretical analysis. Most of the subsequent extensions of the latter have
been based on the same data, and no attempt will be made to reproduce them
here.
The effect of the crystalline neighborhood on the electronic orbitals of
the rare earth ion is appreciable, but is nevertheless small compared with the
atomic electron interactions, and to a large extent can be treated in terms of
a model whose basis states are the free-ion orbitals themselves, without need
for specific structural detail of the electronic involvement with ligand ions.
Because of the dominance of the atomic forces it is important to have an atomic
Hamilton!an which is detailed enough to accurately describe the observed crystal
level groupings. In the process we have incidently learned much about the
structure of the atomic energy levels themselves.
In a pure 4f configuration the only interactions to be evaluated would
be the four Slater integrals F 0 , 2 ' 4 , 6 and the spin-orbit integral, s, plus rela-
tivistic correction terms representing spin-other-orbit and spin-spin inter-
actions. Ab initio evaluations for each of these can be carried out; however,
the latter values are not quite in agreement with experimental ones. This is
not because they are inaccurate in themselves but because there are additional
contributions due to ignored inter-configuration interactions which have the
-2-
same angular dependence and are therefore lumped with the former in any empirical
fitting. The experimental values are therefore only effective ones, although
we conventionally continue to give them the original names. These same inter-
actions will in addition produce completely new effective-Hamiltonian operators,
namely: ctL(L+l), Trees (1951, 1952, 1964); &G(G2) and Y G ( R ? ) , Racah (1949) and
Rajnak and Wybourne (1963); T^., the three-body electrostatic effective opera-
tors discussed by Rajnak and Wybourne (1963), Rajnak (1965), Judd (1966,1972)
and Crosswhite et al. (1968); and A-z., the generalized two-body double-vector
operators, Judd et al. (1968) and Crosswhite and Judd (1970).
Fortunately, not all of the theoretically possible operators are needed
in the analysis, and those that are (including the Fk and t, corrections) a-e
all either constant or slowly varying functions of the atomic number Z. For
instance, of the fourteen possible T^., only those six which have non-zero
matrix elements in second-order perturbation theory are retained. Furthermore,
these results are in good agreement with ab initio calculations, Newman and
Taylor (1971,1972), Balasubramanian et al. (1975). A review of the whole ques-
tion of crystal energy level parametrization was given by Newman (1971).
There are thirteen generalized two-body double-vector operators, eight
having rank one in each of the spin and orbital angular momentum spaces. (An
additional one has matrix elements exactly proportional to those of the spin-
orbit interaction and can be ignored). Five have rank two in each of the
spaces. The principal contribution to the latter comes from the spin-spin
interaction and can be estimated by ab initio calculations of the Marvin inte-
grals M 0 , 2' 4, Marvin (1947). The former appears to be dominated by spin-other-
orbit effects, parametrized by the same Marvin integrals, and another effect
arising from the fact that there are spin-orbit matrix elements connecting 4f
-3-
with configurations of the type 4f n'f. Rajnak and Wybourne (1964) have
called these "electrostatically-correlated spin-orbit" effects. Matrix ele-
ments have been given by Judd et al. (1968). Their essential role is to allow
for effective spin-orbit variations with spectroscopic term and are parametrized2 4 6
by the quantities P ' ' . Ab initio calculations have been given by Newman and
Taylor (1972).
A summary of the parameters derived from LaCl, crystal studies is given
in Table 1, Crosswhite (1977). As a rule of thumb for estimating atomic param-Keters appropriate for the LaF, case, the LaCl3 F and c. values reported in
Table 1 should be increased slightly: 1.8% for F2, 1.1* for F4, 0.8% for F6
and 0.5% for t,. More extensive details are given elsewhere; Crosswhite et al.
(1976), Carnal! et al. (1976), Crosswhite et al. (1977), Crosswhite and
Crosswhite (1977). For the major parameters we have found on comparison with
ab initio calculations that the required corrections are remarkably uniform.
Computations with a Hartree-Fock program containing an approximate relativistic
correction, Cowan and Griffin (1976), are given in Table 2, and differences ofit
these and experimental F and t, values are shown in Figs. 1 and 2. The two-
body electrostatic correction parameters a, 3 and y show similar slow varia-i k
tions across the series; the T are essentially constant; and the P can be
taken proportional to ?. The M (spin-other-orbit) are shown in Fig. 2.
The crystalline environment can in principle make contributions to each
of these terms in addition to new ones specific to the particular point-group
symmetry. However, experimentally we find that there is a great similarly be-
tween the parameters for the LaCK-doped spectra and those of the few free ion
cases for which experimental data are complete enough to permit full param-
etrization (La II, Ce III and Pr IV 4f2 and Pr III 4f 3). Systematic values can mV ~ * '
• « r'
APPENDIX I - TABLE 1
3+Parameters f o r Ln :LaCl
ave
F2
F4
F6
Alpha
Beta
Gamma
T2
T3
T4
T6
T7
T8
Zeta
M O b
p 2 cB?BJB|
Pr9928
68368
50008
32743
22.9
-674
[1520]—
—
—
- -
—
—
744
1.76
275
107
-342
-677
466
Nd24186
71866
52132
35473
22.1
-650
1386
377
40
63
-292
358
354
880
1.97
255
163
-336
-713
462
Pm36805
75808
54348
38824
21.0
-645
1425
302
45
34
-315
554
[400]
1022
2.1
319
143
-395
-666
448
Stn47190
78125
56809
40091
21.6
-724
[1700]
291
13
34
-193
288
330
1168
2.4
341
186
-270
-623
470
Eu64542
84399
60343
41600
16.8
[-640]
[1750]
[370]
[40]
[40]
[-330]
[380]
[370]
1331
[2.38]
245
189
-287
-801
525
Gd87538
85200
60399
44847
[19][-643]
1644
[315]
[44]
[40]
[-300]
[325]
[360]
[1513]
[2.82]
495
216
-.72
-688
474
Tb68200
90012
64327
42951
17.5
[-630]
[1880]
[340]
[40]
[40]
[-330]
[330]
[380]
1707
[3.00]
590
185
-291
-457
302
Dy
55894
92750
65699
45549
17.2
-622
1881
311
116
12
-474
413
315
1920
2.8
591
193
-328
-470
287
Ho48193
95466
67238
46724
17.2
-621
2092
300
37
98
-316
440
372
2137
3.0
523
216
-284
-448
294
Er35490
98203
69647
49087
15.9
-632
[2017]
300
48
18
-342
214 f449
2370
4.5
667
216
-271
-411
272
o>
sra.<a>
(t>
-nCO
o
03
2u>n
2(t>
STto
tn
aValues in brackets were not f reely varied.b0nly M° was varied; the ratios M2/M° = 0.56, M4/M° = 0.38 were maintained.c0nly P2 was varied; the ratios P4/P2 = 0.75, P6/P2 = 0.50 were maintained.
•>a
-5-
APPENDIX I - TABLE 2
,NRelat iv is t ic Hartree-Fock Integrals for 4f IV.
4f2
4f3
4f4
4f5
4f6
4f7
4f8
4f9
4 f 1 0
4 f "
4 f 1 2
4 f 1 3
Ce
Pr
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
Yb
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
IV
F2
.
98723
102720
106520
110157
113663
117058
120366
123592
126751
129850
132897
-
F4
_
61937
64462
66856
69143
71373
73470
75541
77558
79530
81462
83361
-
F6
_
44564
46386
48111
49758
51342
52873
54361
55810
57227
58615
59978
-
696.
820.
950.
1091
1243
1407
1584
1774
1998
2197
2431
2680
2947
41
22
51
.46
.60
.71
.45
.46
.44
.06
.00
.97
.69
1.
2.
2.
2.
3.
3.
3.
3.
4.
4.
4.
M°
_
991
237
492
756
031
318
615
924
246
580
928
-
M2
-
1.110
1.248
1.391
1.540
1.694
1.855
2.022
2.195
2.376
2.563
2.758
-
M4
-
0.752
0.846
0.943
1.044
1.149
1.258
1.372
1.490
1.612
1.739
1 . i 72
-
Pr Nd Pm Sm Eu 6d Tb Dy Ho Er Tm
Fig. 1. Variation of the differences between the pseudo relativistic
Hartree-Fock (HFR) values of the Slater integrals i-"k and those determined
experimentally, Fk(HFR)-Fk(EXP) = AFk, with lanthanide atomic number.
C..
\J\J
80
60
4 0
20
o
C βi
—
—
i
Pri
c0
i
Ndi
Pm1
0
I
Smi
- 2 -
|
Eui
o
GdI
•' —
1
Tb1
o
i
Dy1
o
i
Hoi
\
o
1
Er1
1
TmI
X
l
Yb1
i 1
i
1
i
w —
—
i
1.0
0 . 8 -
0.6
/M° (SPIN OTHER ORBIT)EXP HrR
i
—
_
i
I
1
1
i
i i
o• " - " " - • ^ r
1 1
1
1
1
1
1
O
|
1 1
o
1 1
1
-
—
1
Pr Nd Pm Sm Eu Gd Tb Dy Ho Er Tm
Fig. 2. Variation of the differences between the pseudo relativist1c
Hartree-Fock (HFR) values of the spin-orbit Slater Integral c> and those
determined experimentally, 5(HFR)-c(EXP) = Ac; and the ratios of the
corresponding spin-other orbit values M|x p/Mf)
F R with lanthanide atomic
number.
A V', I
-6-
i k k
be found for the T and a. (or alternately M and P ) which satisfy all known
spectra, whether free ion or crystal, in terms of only a few constants. It
follows therefore that the same model can be used for preliminary estimates for
other spectra such as LaF3-doped crystals.
As to the parametrization of the crystal-field itself, the general spec-
ification that the number of possible two-particle operators is equal to the
number of available independent cells in the Hamiltonian requires 366 additional
ones besides the ten single-particle •mes (of which only four are formally used).
Fortunately, the single-particle modeu, Judd (1963), Wybourne (1965), Dieke
(T968), works very well, although we must recognize that these parameters repre-
sent much more complicated effects than the simple Coulomb model visualized by
the early theories. Newman and Taylofr (1971) give a discussion of the physical
significance of these parameters.
APPENDIX I I
A'A
V '"if
BLANK PAGEcuaa•a
7 ' . ' ' •• '
APPENDIX I I - TABLE 1
Atomic Parameters for Ln3+:LaF,
EAV
F2
F4
F6
a
0
y
C
T2
T3
T4
T6
T7
T8
M0(b)
M2(b)
M4(b)
P2(c)
p4(c)
p6(c)
Pr
10163.
69305.
50675.
32813
(21)
-842
1625
750.8
-
-
-
-
-
-
(1.99)
0.11)(0.75)
(200)
(150)
(100)
Nd
24490.
73036
52624
35793
21.28
-583.
1443
884.9
306
41
59
-283
326
298
(2.237)
(1.248)
(0.84)
213
160
106.5
Pm
(37272)
(77000)
(55000)
(37500)
(21.00)
(-560)
(1400.)
(1022.)
(330.)
(41.5)
(62.)
(-295.)
(360)
(310)
(2.49)
(1.39)
(0.94)
(440)
(330)
(220)
Sm
47760.
79915
57256
40424
20.07
-563
1436
1177.2
288
36
56
-283
333
342
(2.76)
(1.54)
(1.04)
344
258
172
Eu
(64263)
(84000)
(60000)
(42500)
(20.)
(-570)
(1450)
(1327)
(330)
(41.5)
(62)
(-295)
(360)
(310)
(3.03)
(1.69)
(1.15)
(300)
(200)
(150)
Gd
87847.
85587
61361
45055
(20.)
(-590)
(1450)
1503.5
(330)
(+41.5)
(+62)
-(295)
(+360)
(+310)
(3.32)
(1.85)
(1.26)
611
458
306
Tb
68608.
91220
65798
43661
19.81
(-600.)
(1400)
1702
(+330)
(+41.5)
(+62)
-(295)
(+360)
(+310)
(3.61)
(2.02)
(1.37)
583
437
291
Dγ
56492.
94877
67470
45745
17.64
-608
1498
1912
+423
+50
+117
-334-
+432
+353
(3.92)
(2.19)
(1.49)
771
578
386
Ho
48453.
97025
68885
47744
18.98
-579
1570
2144
(+330)
(+41.5)
(+62)
-(295)
(+360)
(+310)
(4.25)
(2.38)
(1.61)
843
632
421
Er
35915.
100274
70555
49900
17.88
-599
1719
2381
+441
+42
+64
-314
+387
+363
(4.58)
(2.56)
(1.74)
852
639
426
Tm
18000..
102459
72424
51380
(17.)
-737
(1700)
2640
(4.93)
(2.72)
(1.37)
729.6
547
364
No. ofLevels f i ta 41
11 139
16.6
180
16.7
649
(26 )d36
201
22
(27 )d
32
117
12.1
Values In parenthesis were not freely varied.
assumed.: 0.75, P6/P2 = 0 . 5 were maintained.
Relativistic Hartree-Fock values werec0nly P was varied, the ratios P4/P2 !
Free-ion Hamiltqnian only
(12) c
76
-2-
APPENDIX I I - TABLE 2
Crystal-field Parameters for Ln3+:LaF3
Nd
216
1225
1506
770
Sm
209
1042
1415
659
Gd
(210)
(1050)
(1250)
(600)
Dy
218
1099
1129
553
Er
229
965
909
484
0n
~ r
APPENDIX III
0n
e
;>:•
PAGE
APPENDIJ
PR+3:LAF3
OBSEBVED
200
4487
521565687031
1
: in
TABLE 1CENTERS OF
CALC
19123034495
519665957009
o-c9
• • •
-7
19-26
22
GRAVITY
STATE
3H43H53H6
3F23F33F4
10001 10012 -10 1G«
17047 17052 -4 1D2
20927 20935 -7 3P021514 21555 -40 3P1
2174322746 22690
46986 46986
11656 3P2
0 ISO
M
00000
11111111
?222222
222222
33333
4444
444
55
LEVEL 1
2093120931209312093120931
2155221552215522155221552215522155221552
5194519451945194519451945194
170541705417054170541705417054
65956595659565956595
189189189189
700870087008
23052305
J2
22446
12234456
2234456
234456
34456
4456
456
56
PAGE 2APPENDIX III
TABLEU(K)*2
LEVEL 2
519417054189
70084499
215525194
170546595189
700823054499
5194170546595189
700823054499
170546595189
700823054499
6595189
700823054499
189700823054499
700823054499
23054499
2FOR PR+3
(02)*2
00000
0000,00,0,0,
00.0,0,0.0.0,
0,0.0.0.0.0.
0.0.0.0.0.
0.0.0.0.
0.0.0.
0.0.
.2954
.0152
.0
.0
.0
.1607
.2685
.0799
.5714
.0
.0
.0
.0
.0618
.0140,0209.5090.0014.0.0
.3745
.0319,0027,6015,0,0
06250653,02526285,0
7782018910950000
014602965668
91921080
(U4)*2
0.0.0.0.0.
0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.
0.0.0.0.0.0.
0.0.0.0.0.
0.0.0.0.
0.0.0.
0.0.
.0,0,17291079,0
,00.019641702263628570
0065086605094030001229770164
329501770174000000190686
00303465073134673182
4645050320120333
242731166095
36682327
(U6)*2
0.0.0.0.0.
0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.
0.0.0.0.0.0.
0.0.0.0.0.
0.0.0.0.
0.0.0.
0.0.
,00,000726
00000008921246
0001173090565903038
000534020100040066
06256982005408459
2642488961151392
035844 0746 23
12146420
f
':J •
4499 4499 1.2383 0.7108 0.7878
APPENDIX IV
JBSERVB
045136296500
197820 3720 68209121872223
3918397840384076411842084278
58165874598661416167632364546556
1159211634
125961261412622126761269412754128 4312902
135141359013671136761371113715
PAGE 1
APPENDIX IV
ID CALC
338142294500
196320 H :2075209822032227
3901398340434102412642054275
58205838599761716187629364206545
1159611626
1258512589126301267812704127631285412873
135141358313673136931369513711
TABLI! 1ND+3:LAF3
O-C
-27-520
15-4-6-6-15-3
17-4-4
-25-733
-336
-10-29-19303H11
-38
1125-7-1-9-8
-1029
07
-1-16164
STATE J
4141414141
414141414141
41414141414141
4141414141414141
4F4F
2H24F4F4F4F2H22H22H2
4F4F4Fas4S4F
9/29/29/29/29/2
11/211/211/211/211/211/2
13/213/213/213/213/213/213/2
15/215/215/215/215/215/215/215/2
3/23/2
9/25/25/25/25/29/29/29/2
7/27/27/23/23/27/2
MJ
-9/25/23/21/2
-7/2
-11/25/23/21/2
-7/2-9/2
13/25/23/21/2
-7/2-9/2-11/2
15/2-7/2-9/25/21/23/2
-11/213/2
1/23/2
-7/23/21/25/21/23/2
-9/25/2
3/2-7/21/21/23/25/2
»BSEFVE
1463114861148921492614959
159971603316060160461610016165
17316173061736317510175201757117605
19147192351925219324
19567196 15196511970419686• • •197411979919835• • •
• • «
19960
2115521176211982123221252
2133821353
PAGE 2
APPENDIX IV
!D CALC
1484714861148861492414957
160281604616059160601609516140
17308173111736017491175051756417611
19139192451927119324
195671963219645196871969319737197381979019845199171992719971
2115021183211992123521267
2133921352
TABLf! 1ND+3:LAF3
O-C
-120622
-30-12
1-13
525
8-4319157-5
8-9
-180
0-16
617-6
• • •
39
-9• • •• m •
-10
5-60-2-14
01
STATE J
4F4F4F4F4F
2H22H22H22H22H22H2
4G4G4G462G14G4G
4G4G4G4G
2K4G2K4G4G2KUG2K4G2K2K2K
2G12G12G12G12G1
2D12D1
9/29/29/29/29/2
11/211/211/211/211/211/2
5/25/25/27/27/25/25/2
7/27/27/27/2
13/29/213/29/29/213/29/213/29/213/213/213/2
9/29/29/29/29/2
3/23/2
HJ
1/23/23/25/2
-7/2
5/2-11/2
3/2-7/21/2
-9/2
3/21/25/25/23/25/21/2
5/21/23/2
-7/2
13/25/21/2
-7/2-9/2
-11/23/23/21/25/2
-9/2-7/2
-7/23/2
-7/21/2
-9/2
3/21/2
77
!'J . \:
S.
)BSEPV
• * •
• • •
2163321718• • •• • *• • •• • *• • •
21816• • •• • •• • «
21992
23473
• • •2399124080
2637826426
2834128374
« • •28525• • •
28676289622946329489295682964429773
30275• • •• • •
• • «
• • •
• • •
30576• • •
30631306823071930807
PAGE 3
APPENDIX IV
!
ED CALC
2153521620216212173121774217792179021824218272185721901219312194621995
23455
239962399924057
2639426416
2836128369
28495285282863428686289382945929475295652965929767
302713034 63041130451305333053430602306153064 6307013071230792
TABLE 1»D+3:LAF3
O-C
• • •• • •12
-12• • «* « •• • #• « •• • •
-10• • •• • •* • •-2
18
• • •
-723
-1510
-195
• • •
-2• • •-9244143
-146
4• • •• • •• • •
• • •
• • •
-25• • •-14-18715
STATE J
4G2K4G464G2K4G2K2K2K2K2K2K4G
2P
2D12D12D1
2P2P
4D4D
4D4D214D4D2121212121
2L2L2L2L212L4D2L4D2L4D4D
11/215/211/211/211/215/211/215/215/215/215/215/215/211/2
1/2
5/25/25/2
3/23/2
3/23/2
5/25/211/25/21/211/211/211/211/211/2
15/215/215/215/215/215/27/215/27/215/27/27/2
MJ
-7/215/25/2
-9/2-11/213/2-9/21/25/23/2
-11/2-9/2-7/21/2
1/2
3/21/25/2
1/23/2
1/23/2
5/21/2
-11/23/21/2
-9/2-7/25/23/21/2
13/215/21/23/2
-11/25/25/2
-9/2-7/2-7/23/21/2
V;,; V*'t".v
experimentally, FR(HFR)-FR(EXP) = AFK, with lanthanide atomic number.
',-;>,
?.'•••'- '•".',"
)BSERVE
• • •3089330933309943103031068• • •
3178131859• • •• • •• • •• * •• « •• • •• • *
3303033107331813322833255
3361933649
34292343803441934521
• • •
• • •
3467834706
• • •
386903875538841
4010340155
a • •
40288
PAGE 4
APPENDIX IV
B CALC
30850308953095531002310413107031079
317673183631926319683199032013320483209332126
3303533137331683322633258
3361233631
342743437434445345193455134573346863470934818
387233877838815
40113401264018740254
TABLE 1ND+3:LAF3
O-C
• • •-1
-21-7
-10-1
• • •
1423• • •• • •• m •
• • •
• • •
• * «
• • •
-4-29132
-2
718
186
-252
• • *• • •-7-2• • •
-32-4226
-929
• • •34
STATE J
21212121212121
2L2L2L2L2L2L2L2L2L
2H12H12H12H12H1
2D22D2
2H12H12D22H12H12H12H12D22H1
2F22F22F2
2F22F22F22F2
13/213/213/213/213/213/213/2
17/217/217/217/217/217/217/217/217/2
9/29/29/29/29/2
3/23/2
11/211/25/211/211/211/211/25/211/2
5/25/25/2
7/27/27/27/2
HJ
-11/2-9/2-7/213/25/23/2V2
15/217/21/23/2
13/25/2
-11/2-9/2-7/2
-7/21/2
-9/25/23/2
3/21/2
-9/21/25/2
-7/21/23/2
-11/23/25/2
5/21/23/2
-7/23/21/25/2
BSEBVE
4789447937479994 80 43
48839489084897749088
• • •• • •• • •
• • •
• • •
• • «
• • •
PAGE 5
APPENDIX IV
ID CALC
4787147888479644800648055
48861488694897949065
6654 8667056679366859
678576785868075
TABLE 1ND+3:LAF3
O-C
• • •6
-26-6
-11
-2139-123
• • •• • •• • •• • •
* • •
• • •
• • *
STATE
2G22G22G22G22G2
2G22G22G22G2
2F12F12F12F1
2F12F12F1
J
9/29/29/29/29/2
7/27/27/27/2
7/27/27/27/2
5/25/25/2
MJ
5/2-9/2
3/2-7/2
1/2
-7/23/25/2V2
5/2-7/2
3/21/2
5/23/2V2
•- A
!#l
PAGE 6
APPENDIX IV
TABLE: 1AND+3:LAF3 CENTERS OF GRAVITY
CALC CENTER
235211440986148
11621126601276813619136911489916105
1742817469192931970919785214252171421780234582400426424
STATE
41 9/24111/24113/24115/2
4F 3/24F 5/22H 9/24F 7/24S 3/24F 9/22H11/2
4G 5/24G 7/24G 7/24G 9/22K13/22D 3/24G11/22K15/22P 1/22D 5/22P 3/2
01
1/21/21/21/21/21/21/21/21/21/21/21/21/21/21/21/2
3 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 2
3 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 23 / 2
XEVEL
23U58234582345823458234582345823458234582345823458234582345823458234582345823458
1162111621116211162111621116211162111621116211162111621116211162111621116211162111621116211162111621
136911369113691136911369113691136911369113691136911369113691
1 J2
3 / 23 / 23/23 ,25 / 25 /25 /27 / 27 / 27 / 29 /29 / 29 / 29 /2
11/213/2
3 / 23 / 23 / 25 / 25 / 25 /27 / 27 / 27 / 29 /29 / 29 / 29 / 2
11/211/211/213/213/215/215/2
3 / 23 / 25 /25 / 27 / 27 /29 / 29 / 29 / 29 /2
11/211/2
PAGEAPPEKDIX
TABLEi 2U(K)*2 FOR
LEVEL 2
11621136912142526424126601742824004136191746919293
2351276814899197091610519785
116212142526424126601742824004136191746919293
2351276814899197092114
1610521714
4098197856148
21780
214252642417428240041746919293
23512/681489919709
211416105
7IV
ND+3
(U2)*2
0000000000000000
0000000000000,0,0,00.0.0,0,
0.0.0,0 .0 .0 .0 .0.0 .0 .0 .0 .
.0131
.0175
.0291
.0056
.0101.0346.0260. 0. 0. 0. 0. 0. 0. 0. 0. 0
.0612
.0050
.0024
.0773
.4856
.0009
.0063
.0735
. 1062
. 0
. 0
. 0
. 0
.0
.0
.0
.0
.0
.0
.0
.0073
.0060
.0007
.0071,0006.0021.0.0,0,0,0,0
(04)*2
0600000000000000.
0,0,0.0.0.0,0.0.0.0.0.0.0.0 .0 .0 .0 .0 .0 .0 .
0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .
. 0
. 0
. 0
. 0
. 0
. 0
. 0
.0200
.0097
.0026
.0396
.0871
.0033
.0010
. 0
.0
. 0
.0
.0
.0533
.0433
.0007
.0800
.0400
.0629
.2283,0149,0046,05701423
,00010015
,0.000
001775000007312023002500440023192200000563
(06) *2
0 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00.16430.1746
0 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00.05540.02230.11150.14510.40830.00810.09920.20930.00760.02800.0099
0 . 00 . 00 . 00 . 00 . 00 . 00.23470.00010.00110.00090.20990.0016
J1
3/23/23/23/2
3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2
3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2
5/25/25/25/25/25/25/25/2
LEVEL
13691136911369113691
21425214252142521i»252142521425214252142521425214252142521425214252142521425214252142521425
2642426424264242642426424264242642426424264242642426424264242642426424264242642426424
1266012660126601266012660126601266012660
1 J2
11/213/215/215/2
3/23/25/25/25/27/27/27/29/29/29/29/211/211/211/213/215/215/2
3/25/25/25/27/27/29/29/29/29/211/211/211/213/213/215/215/2
5/25/25/27/27/27/29/29/2
PAGEAPPENDIX
TABLE: 2U(K) *2 FOR
LEVEL 2
2171440986148
21780
2142526424126601742824004136191746919293235
1276814899197092114161052171419785614821780
264241266017428240041361919293235
12768148991970921141610521714-' 4098197856148
21780
126601742824004136191746919293235
12768
8IV
ND+3
(U2)*2
0000
000000000000000000
000.0,0,00,0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0161
.0052
.0038
.0002
.1744
.0025
.0104
.0206
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0838
.0022
.0058
.0074
.0003
.0063
.0
.0
.0
.0
.0
.0,0,0,0,0,0
04622671,000506552504256900060062
(U4)*2
0000
000000000000000,0,0.0
0.0,0.0.0.0-0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
.3245
.0
.0
.0
.0
.0
.0000
.0039
.0011
.0001
.0839
.0418
.0202
.0259
.0003
.0023
.0016
.1078
.0300
.0
.0
.0
.0
.0033
.0000
.0001
.0007
.0052,0010,01000527,0601,0159,019400430000
02181301000605400075000923370308
(06) *2
0000
000000000000,0,0,000.0,
0,0.0.0,0.0.0.0,0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
.0004
.3295
.3306
.0030
.0
.0
.0
.0
.0
.0
.0
.0
.0001
.0872
.0139
.0325
.0326
. 1807
.0003
.0860
.0083
.3482
.0
.0,0.0,0,0,0005.0813,05780647,0005,013600000098231900290076
00008720750119539830052
t e « >- O U-< j - a
J1
5/25/25/25/25/25/25/25/25/2
5/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/2
5/25/25/25/25/25/25/25/25/25/25/25/25/25/2
7/27/27/27/27/27/27/27/2
LEVEL
126601266012660126601266012660126601266012660
17428174281742817428174281742817428174281742817428174281742817428174281742817428
2400424004240042400424004240042400424004240042400424004240042400424004
1361913619136191361913619136191361913619
1 J2
9/29/2
11/211/211/213/213/215/215/2
5/25/27/27/27/29/29/29/29/211/211/211/213/213/215/215/2
5/27/27/27/29/29/29/29/2
11/211/211/213/213/215/2
7/27/27/29/29/29/29/2
11/2
PAGEAPPENDIX
TABLE: 20(K)*2 FOR
LEVEL 2
1489919709211416105217144098197856148
21780
17428240041361917469192 93235
127681489919709211416105217144098197856148
21780
24004136191746919293235
1276814899197092114161052171440981978521780
136191746919293235
1276814899197092114
9IV
ND+3
(02)*2
000000000
000000000000000.0,
0.0,0.0.0.0.0.0.0.0.0.0.0.0.
0,0.0.0.G.0.0.0.
.0105
.1912
.0
.0
.0
.0
.0
.0
.0
.0024
.0014
.0382
.0002
.0000
.8975
.0012
.0026
.0000
.0
.0
.0
.0
.0
.0
.0
.2977
.0005
.0064
.0003
.0000
.0078
.0003
.0000,0,0.0.0,0,0
,15251267174700110056093455480009
(04)*2
000000000
00,000,00,0,0,00,0,0.0,0,0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
.0508
.0995
.1698
.0030
.0611
. 1817
.0026
.0
.0
.1883
.0008
.1047
.1321
.2391
.4126
.0134
.0070
.1035
.2867
.0002
.0094
.0342
.0018
.0,0
,0045,0171.0688,0481,00021994,01100077000125230314003700330
00820589073204060344091200012335
(U6)*2
0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
o.0.,0.0.0.0.0.0.
,1091,002203690239,19764010004823000051
00,16260845057103460018130324770961014509140485007700460051
00064175605580017079101320064002901840006016918284889
1033,0104002342720040078308~253076
J1
7/27/27/27/27/27/2
7/27/27/27/27/27/27/27/27/27/27/27/27/2
7/27/27/27/27/27/27/27/27/27/27/27/2
9/29/29/29/29/29/29/29/29/29/29/2
9/29/29/29/2
LEVEL
136191361913619136191361913619
17469174691746917469174691746917469174691746917469174691746917469
192931929319293192931929319293192931929319293192931929319293
235235235235235235235235235235235
12768127681276812768
1 32
11/211/213/213/215/215/2
7/27/29/29/29/29/211/211/211/213/213/215/215/2
7/29/29/29/29/211/211/211/213/213/215/215/2
9/29/29/29/211/211/211/213/213/215/215/2
9/29/29/211/2
PAGE 10APPENDIX
TABLII 2U (K)*2 FOR
LEVEL 2
16105217144098
197856148
21780
1746919293235
12768148991970921141610521714409819785614821780
19293235
127681489919709211416105217144098197856148
21780
235127681489919709211416105217144098197856148
21780
1276814899197092114
IV
SD+3
(02)*2
000000
0000000000000
0000,0.0,0.0,0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.
.0336
.1729-0.0.0.0
.0111
.0633
.0707
.0088
.0261
.0730
.3996
.0068
.0119
.0
.0
.0
.0
.0937
.0596
.0508
.0006
.0375
.6684
.0011
.0023
.0
.0
.0,0
1195,0095,0009,0044,0194,0000,00000000007100
1156048703900028
(U4)*2
000000
0,00,0,0,00,0,0,0,0,0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.
.0154
.1623
.3314
.0664
.1553
.0000
.0002
.0008
.1720
.0292
.0504
.1395
.1764
.0000
.1233
.0875
.7062
.0010
.0383
.0433, 1709,0543,0112,144910750197,03412407517902730186
17270082009205841072002700520135000200000052
0016002904780004
(U6)*2
000000
00000,0000,0,00,0,
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.1.0.0.0.0.0.0.
0.0.0.0.
. 1287
.1447
.0001
.0003
.6166
.0077
.0189
.0359
.0274
. 1989
.2665
.0034
.0522
.3593
.0015
.0345
.0012
.1064
.0122
.0772
.0566
.3685,0099.1417, 0099,1020,3811,0613,001400450018
68921195040603831639010400794549033004520149
2728001809820254
6
J1
9/29/29/29/29/29/2
9/29/29/29/29/29/29/29/29/2
9/29/29/29/29/29/29/2.9/2
11/211/211/211/211/211/211/2
11/211/211/211/211/211/2
11/211/211/211/211/2
13/215/213/2
LEVEL
127681276812768127681276812768
148991489914899148991489914899148991489914899
1970919709197091970919709197091970919709
2114211421142114211421142114
161051610516105161051610516105
2171421714217142171421714
409840984098
0
1 J2
11/211/213/213/215/215/2
9/29/211/211/211/213/213/215/215/2
9/211/211/211/213/213/215/215/2
11/211/211/213/213/215/215/2
11/211/213/213/215/215/2
11/213/213/215/215/2
13/213/215/2
PAGE 1APPENDIX
TABLI: 2(K)*2 FOR
LEVEL 2
16105217144098197856148
21780
1489919709211416105217144098197856148
21780
1970921141610521714409819785614821780
21141610521714409819785614821780
1610521714409819785614821780
217144098197856148
21780
4098197856148
1IV
ND+3
(02) *2
000000
000000000
00000000
0,00.0.0,0,0,
0.0.0.0.0.0.
0.0.0.1.0.
0.0.0.
.0687
.1796
.0389
.1211
.0
.0
.1407
. 1181
.0001
.0873
.9423
.0029
.0462
.0
.0
.0042
.1403
.0032
.0521
.9552
.0210
.0
.0
.1321
.0043
.0044
.0256
.0002
.0000
.0020
.0107
.0009
.0043,0014, 1293,1556
,00151283000153010099
169300320195
(U4)*2
000000
00,0,00,0,0,0,0,
0,0.0.0.0.0.0.0.
0.0.0.0.0.0.0.
0.0.0.0.0.0.
0.0.0.0.0.
0.0.0.
.0037
.0001
.0064
.0063
.2155
.4675
.0960
.1593
.0328
.0239
.2060
.2148
.0042
.5000
.0003
.0063
.3495
.0308
.5102,3843.0440, 1426, 1408
,1159,00940645,1352,000001090003
,000908090168004406870017
63443514007789150162
172900011187
(U6)*2
0.0.0,1.0.0.
0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
0.0.0.1.0.0.0.
0.0.0.0.0.1.
0.0.0.0.0.
0.0.1.
.2755,0037.1217, 1292,0775,4145
,000302073702017204115102293146282037
01220505231012060157113123980246
0673006205632376016841800039
028401090029479500005224
18581609023315900912
233100244522
'.1
7 '•'
• 'f,' c' -' '~\••* „ • i
8
1 08CD
CO
ro
gABSORBANCE UNITS
-4278
— 4208
— 4076
>=—4038
In
OJ00
4*.ro
o>
-3978
•o
c 3918
',. » '
' - <•':
.'.•;.-• £4
o
a>§o
o>-P>oo
I O
o>
8o
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APPENDIX; V
PAGE 1
APPENDIX V
TABLE 1PM+3:LAF3 CENTERS OF GRAVITY
OBSERVED CALC
1201612323919516714
126381308013933
. . . 144861488716223
1693918053180751825518565198622030720554219352247522807231402377224216247022484024907258112589525907
O-C STAT
. . . 514
. . . 515
. . . 516
. . . 517
. . . 518
. . . 5F1
. . . 5F2
. . . 5i>3
. . . 5S2
. . . 5F4
. . . 5F5
3K6. . . 562. . . 3H4. . . 3K7
5G 33K8
. . . 3H5
. . . 5G4
. . . 3G 3
. . . 5G5. . . 5G6. . . 3D2. . . 3L7. . . 3P1
3H63G4
. . . 3L 8
. . . 3P0
. . . 3D3
. . . 319
BLANK PAGE
/*<?
M
000000
11111111111111111111
111111111111111
222222
LEVEL 1
258102581025810258102581025810
1265812656126581265812658126581265812658126581265812658126581265812658126581265812658126581265812658
242212422124221242212422124221242212422124221242212422124221242212422124221
130941309413094130941309413094
J2
244666
12223334444555566777
222334455566677
222333
PAGE 3APPENDIX V
TABLEU(K)*2
LEVEL 2
231421488218083
32471695722787
12658130941807023142139391857721946
161148821808320565
1639162082030322476
324722787
49371825823796
13094180702314218577219461808320565
16392030322476
32471695722787
493718258
130941807023142139391857721946
2FOR PM+3
(02)*2
000000
00000000,00,0,0,00,0,0,0,0,0,0.
0.0.0.0.0 .0.0.0.0 .0 .0 .0 .0 .0 .0 .
0 .0 .0 .0.0.0.
.0054
.0
.0
.0
.0
.0
.0268
.0529
.2682
.0032
.0177
.1965
.0225
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0,0.0
.0013
.0077,0082.0100,0539,0,0,00000000
020228600001089914860339
(04) *2
0.0.0.0.0.0.
0.0 .0 .0.0.0 .0.0.0.0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .
0.0.0.0 .c.0.0 .0.0 .0 .0.0.0 .0 .0 .
0.0 .0 .0.0.0 .
,0,0019,0142,00
,0
,0.0,00
,0641046901051405032202770604153200160090006600000
000010105370137023600470402034000000
079407220011000303700127
(U6) *2
0.00.00.00.00370.08200.0168
0 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00 . 00.15440.13030.04620.08560.29860.03030.06800.00460.0016
0.00.00.00 . 00 . 00 . 00 . 00.01320.01210.00540.00490.00190.06540.00190.2964
0.00.00.00.00.00.0
•4 .,'
I - y--*'
J1
22222222222222
22222222222222
22222222222222222222
LEVEL 1
1309413094130941309413094130941309413094130941309413094130941309413094
1448614486144861446614486144861448614486144861448614486144861448614486
1807018070180701807018070180701807018070180701807018070i30701807018070180701807018070180701807018070
J2
44445555666788
23344455b56678
22333444455556677788
PAGE 4APPENDIX V
TABLE0(K)*2
LEVEL 2
1611488218083205651639
1620820303224763247
169572278749376674
19845
180701857721946
16118083205651639
1620820303224763247
2278749376674
1807023142139391857721946161
1488218083205651639
1620820303224763247
227874937
18258237966674
19845
2FOR PB+3
(U2)*2
00000000000000
000000,0,0,0,0,0,0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0»0.0.0.0.0.0.0.
.0016
.0385
.0916
.2071
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0030
.0033
.0000
.0000
.0003
.0007
.0
.0
.0
.0
.0
.0
.0,0
,0011,0035,0610.0013,0013729300240006002700000000000
(U4)*2
00000000000000
00,00,0,0,0,0.0.0.0,0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.2042
.0705
.0097
.0209
.0594
.0172
.0733
.0634
.2200
.0032
.0032
.0
.0
.0
.1411
.2032
.0308
.0011
.0794
.2059
.0000
.0035
.1422
.1509
.0023
.3099
.0,0
,03450013,11192434,0203241202121209140927020003036502350372000800000
<U6) *2
0000000000,0000
0,0,0,0.0,0,0,Is.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.1258
.0537
.0174
.0929
.2878
. 1467
.0135
.0125
.0825
.00 33
.1147
.3057
.0743
.0130
.0
.0
.0
.2296
.0003
.0022
.1908
.00 04
.0014
.0023
.23 94,00 37,36 833463
,00000004920000081113304070988080209230781020302030097015800130111
11°
PAGE 5APPENDIX V
TABLE 20{K)*2 FOB PM+3
J1 LEVEL 1 J2 LEVEL 2 (02)*2 (04) *2 (06)*2
I'0
222222222222222222
3333333333333333333
3333333333
231422314223142231422314223142231422314223142231422314223142231422314223142231422314223142
13939139391393913939139391393913939139391393913939139391393913939139391393913939139391393913939
18577185771857718577185771857718577185771857718577
233344445555666778
3334444555566677789
3344445555
23142139391857721946
161148821808320565
16391620820303224763247
1695722787182582379619845
139391857721946
161148821808320565
1639162082030322476
32471695722787
49371825823796
667425888
1857721946
161146821808320565
1639162082030322476
00000000000,00,0,0,00.0,
0.0.0.0,0.0.0.0.0.0.0 .0.0 .0.0 .0.0 .0 .0 .
0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .
.0521
.0104
.0161
.0002
.0044
.0010
.0878
.0067
.0
. 0
.0
.0
.0
.0
.0
.0
.0
.0
.0221
.3740
.0344
.0001
.1295
.0407
.2248
.0000,0285,18191560
,000
,0,0000
0000007015380623018400487098001100000020
0.08300.00000.00780.00660.00200.00450.07910.04120.00030.00030.02010.0S700.01970.00810.03310 . 00 . 00 . 0
0.05890.04150.00070.10790.03490.00070.03790.24290.06730.09280.05950.07770.00560.07270.24880.00460.00080 . 00 . 0
0.04710.00000.28550.07920.11970.09220.02760.00320.19070.0568
0 . 00 . 00 . 00 . 00.00250.00240.01270.00000.03420.00090.13290.09270.01840.07230.06470.01260.01370.4641
0.04090.12230.03440.42260.11350.00400.03160.02600.08100.02850.01100.20990.00120.17610.25510.00320.00080.33260.0094
0.08760.05790.05120.01560.00020.05700.01730.22120.09100.0397
K' i .-'-*• -A
' , ' , ' ' ' . ' •}•
J1
333333333
33i333333333333333
44444444444444444
444
f\
LEVEL 1
185771857718577185771857718577185771857718577
219462194621946219462194621946219462194621946219462194621946219462194621946219462194621946
161161161161161161161161161161161161161161161161161
148821488214882
J2
666777889
344445555666777889
44445555666777889
444
PAGE 6APPENDIX V
TABLEU(K) *2
LEVEL 2
324716957227874937
182582379666741984525888
21946161
1488218083205651639
162082030322476324716957227874937
182582379666741984525888
1611488218083205651639
1620620303224763247
1695722787493718258237966674
1984525888
148821808320565
2FOB PM+3
(02)*2
000000000
00000,0,0,0.0,0,0,0.0,0,0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.
.0
.0
.0
.0
.0
.0
.0
.0
.0
.1057
.0137
.0108
.0298
.0495
.1623
.0004
.0042
.0224
.0
.0
.0
.0
.0,0.0.0.0
,1156,0004.007900810247000000010002001700210000000000
018022262695
(U4)*2
000000000
00000000,00.00,00.0,0.0.0.
0,0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.
.3298
.0008
.0238
.0533
.0245
.0606
.0
.0
.0
.0228
.0428
.0269
.0264
. 1601
.0314
.0100
.0005
. 1341
.0422
.0189
.0022
.0048
.0806
.2660
.0
.0
.0
.1393
.0290
.0313
.0883
.1172,0020,00790082,030000230003002400180014000000020
000011790467
(06) *2
000000000
00,00,0,0,0,0.0.0.0,0.0.0.0,0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.
.0388
.0073
. 1178
.0611
.0070
.0088
.00 48
.0105
.0362
.0094
.0056
.0000
.1162
.0046
.0201
.0106
.0163
.0825
.0003
.04 98,00 97.0174,0310.1614,00 86.0026,0110
,34 952400,027807649702034101020330689101010016157301910095010100800017
069304 530319
//a-
11
44444444444444
4444444444444444
444444444444444
55
LEVEL 1
1488214882148821488214882148821468214882148821488214882148821488214882
180631808 31808318083160831808318083180831808318083180831808318083180831608318083
20565205652056520565205652056520565205652056520565205652056 5205652056520565
16391639
J2
5555666777889
10
445555666777889
10
45555666777889
10
55
PAGE 7APPENDIX V
TABLE 2U(K)*2
LEVEL 2
163916208203 122476
32471695722787
49371825823796
6674198452588830230
1808320565
1639162082030322«76
3 *4 71695722787
49371825823796
6674198452586830230
205651639
162082030322476
32471695722787
49371825823796
6674198452588830230
163916208
FOR PM+3
( 0 2 ) * 2
0.00250.13600.25520.33710.00560.00090.20400 .00 . 00 . 00 . 00 . 00 .00 . 0
0.07710.12870.05150.02450.00170.03020.21660.02650.01460 . 00 . 00 . 00 . 00 . 00 . 00 . 0
0.01290.17730.02630.00720.00110.76270.02560.00000 .00 . 00 . 00 . 00 .00 .00 .0
0.10780.0003
(04)*2
0.14680.14090.02130.00000.29310.00030.22080.15890.02540.00120.20250.01180 . 00 . 0
0.28550.09250.04490.00250.01220.07440.00010.04000.01330.19030.06170.07830.02490.06520 . 00 . 0
0.07440.27200.03560.26390.08040.05060.02570.12900.31060.02a70.01060.02520.00010 . 00 . 0
0.04980.0229
(0 6) *2
0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .
0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .
0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .
0 .0.
3679014313510587"S3001£8091502390257013772 3200 5001860041
039603 03097909460196066900003893160604 93775119010004402400950141
05200052167900650116015926 291574035334 7506620325109004 980097
05141551
\
1
J1
555555555555
5555555555555
555555555555
5555555555
LEVEL 1
163916391639163916391639163916391639163916391639
16208162081620816208162081620816208162081620816208162081620816206
203032030320303203032030 32030320303203032030 3203032030 320303
22476224762247622476224762247622476224762247622476
J2
5566677788910
55566677788910
55666777889
10
5666777089
PAGE 8APPENDIX V
TABLEU(K)*2
LEVEL 2
2030322476324716957227874937
18258237966674198452588830230
162082030322476324716957227874937
18258237966674198452588830230
20303224763247
1695722787493718258237966674
198452588830230
22476324 7
16957227874937
182582379666741984525688
2FOR PM+3
(U2)*2
000000000000
00,0,0,0,1,00,0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0120
.0072
.0352
.0000
.0001
.0023
.0003
.0014
.0
.0
.0
.0
.1448
.2912
.1431
.0027
.0000
.0815
.0100
.0003
.0000
.0
.0
.0
.0
,0199,13681014,0009,02765669,00920000,0000
0557137700240019735203880005000
(U4)*2
000000000000
0000,00,00,0,0.0.0,0,
0,0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0673
.0792
.1378
.0016
.0096
.0372
.0003
.0002
.0018
.0004
.0014
.0
.1799
. 1071
.0674
.1118
.0000
.2777
.3247
.0026
.0003
.5368
.0305
.0152
.0
.0479,2224.1560,0044.1058,0540,0097,0311,34150226,14050
0445255200783339153502160230186604180243
(U6) *2
00C000000000
00,00,00,00,0,0.0.0.0,
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0867
.0376
.7160
.0219
.0181
.7862
.0024
.0088
. 1248
.0034
.0093
.0010
.0011
.06 34
.0828
.3966
.0123
.0181
.6748
.0069
.0135,59 27,0032.0013.0516
.0891,06 46.1462,2903,2984,0185,0397304103 9456 2623780220
0226006034940775002907802824043149742139
?, : .If
PAGE
J 1
5
666666666
666666666
66666666
7777777
777777
7777
LEVEL 1
22476
324732473247324732473247324732473247
169571695716957169571695716957169571695716957
2278722787227872278722787227872278722787
4937493749374937493749374937
182581825818258182581825818258
23796237962379623796
J 2
10
66677788
10
66777889
10
6777889
10
777889
10
77889
10
7869
PAGE 9APPENDIX V
TABLEU(K)*2
LEVEL 2
30230
32471695722787
49371825823796
66741984530230
1695722787
49371825623796
6674198452588830230
227874937
1825823796
6674198452588830230
49371825823796
6674198452588830230
1825823796
6674198452588830230
237966674
1984525888
2FOR PM+3
(U2)*2
0 .
0 .0 .0 .0.0.0 .0 .0 .0 .
0 .0 .0 .0 .0 .0 .0 .0 .0 .
0 .0 .0 .0 .1 .0 .0 .0 .
0 .0 .0 .0 .0.0 .0 .
0 .0 .0 .0 .0.0 .
0 .0 .0.0 .
0
12160017
,0099036500010013001400000
013900000000040419360000000100
01441320000000003628000300
1535007200000266000400090
079308400000052100000
3401000000010010
(U4)*2
0 . 0
0.05420.00060.08510.15280.00430.00010.02430.00010.0033
0.00640.00000.00140.02270. 11510.00000.01820.00460.0000
0.24780.36480.00000.00060.76290.00000.04590.0617
0 .12250.00260.00050.13630.00850.00300.0005
0.00540.03510.00360.08060.03880.0168
0.73100.00000.04760.1302
(06) *2
0.0109
0.05620.00050.08461.02110.03420.00000.62240.01090.0024
0.00000.02990.00720.09531.15230.00460.14700.25820.0159
0. 19070.18180.10990.05510. 14950.12120.15450.1374
0.03310.00000.01161.55290.04880.03250.0044
0.35510.53250.01810.00001.29920.3257
0.00330.00870.06450.0867
J1
7
CO
CD
CO
00
00 C
D 0
0
99
LEVEL 1
23796
6674667466746674
198451984519845
2588825888
J 2
10
889
10
89
10
910
PAGE 10APPENDIX V
TABLE 20(K) *2 FOR PM+3
LEVEL 2
30230
6674198452588830230
198452588830230
2588830230
(U2)*2
0 . 0
0.20o50.01740.00«20.0000
0.14020. 19420.0000
1.32400.3074
(04)*2
0.0215
0.33660.00940.01560.0354
0.00560.58840.5142
0 . 1 5 5 71 .2875
(06) *2
0.0057
1.67410.02510.03210.0577
0.34640.67291.5495
0.48921.3587
10 30230 10 30230 3 .3000 0 . 0 0 0 4 1.5336
PAGE 10
r"
APPENDIX VI
PAGE 11
BLANK PAGE
ill
BSEKVE
04 8
1 1 5
1000104411851280
22102245234324092473
352035683651367637 2737 91
497249835007504650 5651235160
6309634264066450646165676567• • •• • •66916707
717671847223
PAGE 1
APPENDIX V]
D CALC
- 15 2
126
1000101712031258
21912236233524082461
352935313651365837313794
49714995500 65014503851165183
6299633564176464649 3656565806588666067106736
716871797228
TABLE 1SM+3:LAF3
O-C
2- 3
- 1 0
027
- 1 722
19971
12
- 837
018- 3- 2
1- 1 1
13218
7- 2 2
107
- 1 0- 1 3- 3 1
2- 1 2• • •• • •- 1 8- 2 8
85
- 4
C
STATE J
6H6H6H
6H6H6H6H
6H6H6H6H6H
6H6H6H6H6H6H
6H6H6H6H6H6H6H
6H6H6F6H6H6H6F6H6H6F6F
6F6F6F
5 / 25 / 2V 2
7 / 27 / 27 / 27 / 2
9 / 29 / 29 / 29 / 29 / 2
11/211/211/211/211/211/2
13/213/213/213/213/213/213/2
15/215/2
1 / 215/215/215/2
3 / 215/215/23 / 23 / 2
5 / 25 / 25 / 2
HJ
3 / 21 / 25 / 2
1 / 25 / 2
-7/23 / 2
1 / 2-7/2-9/2
3 / 25 / 2
1 / 2-9/2-7/2
3/2-11/2
5 / 2
-11/23 / 21 / 25 / 2
••9/2-7/213/2
-7/2-9/2
1 / 25 / 2
-11/23 / 21 / 2
15/2-11/2
3 / 21 / 2
1/25/.?3/2
. <•
)BSERVI
799280U180608092
91709178922892529268
10561105841059310603106 1310644
178581794918045
1892418942
200372009 32011220164
20416204732049920526
•
•
•
•
••
•
PAGE 2
APPENDIX V]
!D CALC
79958020804 8
' 8096
91709171920992409268
10560105771058110616106 1810640
178741796918077
1892118934
20050200942012020159
204132048 32051720528205412065320790207932087020874209092091620941209872110321124211482124921272
TABLE 1SM+3:LAF3
O-C
- 22112-3
07
1912
0
17
11- 1 2
- 44
- 1 5- 1 9- 3 1
3S
- 1 20
- 75
3- 9
- 1 7- 1
•
•
m
•
r
STATE J
6F6F6F6F
6F6F6F6F6F
6F6F6F6F6F6F
4 64G4S
6F6F
4G4G464G
4H4 1414 1414M4H4M4H4M4H4H4 14H41414 14 14 1
7 / 27 / 27 / 27 / 2
9 / 29 / 29 / 29 / 29 / 2
11/211/211/211/211/211/2
5 / 25 / 25 / 2
3 / 23 / 2
7/27 / 27 / 27 / 2
15/29 / 29 / 29 / 29 / 2
15/215/215/215/215/215/215/211/215/211/211/211/211/211/2
MJ
3 / 2-7/2
V 25 / 2
1/2-7/2-9/2
3 / 25 /2
-7/2-9/2
5 /2-11/2
3 / 21/2
1/25 / 23 / 2
3 / 21/2
1/2-7/2
3 / 25 / 2
-9/21/25 / 23/2
-7/2-11/2
-7/213/25 / 2
-9/21/23 / 25 / 2
15/2-11/2
3 / 2-7/2
1/2-9/2
PAGE
PAGE 3
APPENDIX VI
TABLE 1SH+3:LAF3
OBSEEVED CALC O-C STATE J MJ
21539 41 13/2 -7/2a a a
mm*
21663216742170621736
221642220722240
a • a
• * a
a a •
a a •
• « a
a • a
a a a
a a a
a a a
a a a
a a a
a a a
a a a
a a a
a a a
a a a
a • ')
a a a
• • •
a a a
• a a
a a a
a • a
a a a
a a a
J4084a a •
241 19a a a
• a a
* a a
24153* a a
• a a
a * a
216072162321638216592166621681
221712222322242
224862253922546225592257022631226782272722734
2279422816228542290222943229812301823025230352304 5230772311123146
23973240322407424079241002411524118241402414724160241652417224178
a a a
• mm
25154055
-6-15-1
a a •
a a a
a a a
a a a
• a a
• a a
a a a
a a a
a a a
m m »
a a a
a a a
a a a
a a •
• a «
a a a
a a •
a a a
a • •
a a a
a a a
a a •
m m m
a a a
a a •
5a a a
4a a a
a a a
a a a
-6a a a
a a a
a a a
414141414141
4F4G4F
4H4M4M4M4H4M4H4H4H
4G464G414G4141414141414141
4H4H4M4M4M4M6P6P4H4M6P4M4H
13/213/213/213/213/213/2
5/25/25/2
17/217/217/217/217/217/217/217/217/2
9/29/29/215/29/215/215/215/215/215/215/215/215/2
19/219/219/219/219/219/25/25/219/219/25/219/219/2
13/2-9/25/2
-11/21/23/2
3/25/21/2
13/215/2
-11/2-9/2-7/25/23/21/2
17/2
-9/25/23/2
-11/2-7/2
-11/2-7/2-9/213/25/23/21/2
15/2
15/213/217/2
-11/2-9/2-7/21/23/21/23/25/2
-19/25/2
PAGE 4
APPENDIX V]
OBSERVED CALC
24608246292463124644246782466224710
2491124993250072506425081
...2516625182•. .252042521625248• • •25282.........• • •
• • •
. . .
. . .
. . .
• * •
• « m
m • •
• • •
. . .
• • •
. . .
. . .
* • •
• • •
• * •
. . .
. . .
• • •
246202464 02464124659246852469324724
249132497424997250552506 225093
251532515925198252022520425238252552527525312253352540425420254442552225555255822560 32563625641256892569125692256982576425765257782581225812258492586625896
TABLE 1SM+3:LAF3
O-C
-11-10-9
-14-6-10-13
-11910919
• •.7
-15...0
-21-6• * •-29* * •• • *• • •• • •
• • •
• • •
. . .
. . .
• • •
• * •
. . .
. . .
. . .
• • •
. . .
. . .
. . .
. . .
. . .
. . .
. . .
. . .
STATE J
4L4L4L4L4L4L4L
4G4F4G6P6P4F
4H4K4K4K4K4K4H4K4H4H4H4M4N4H4H4H4L4L4L4H4L4L4L4L4G4L4G4G4G4G4G
13/213/213/213/213/213/213/2
7/27/27/23/23/27/2
21/211/211/211/211/211/221/211/221/221/221/221/221/221/221/221/215/215/215/221/215/215/215/215/211/215/211/211/211/211/211/2
HJ
1/23/213/2
-11/2-7/25/2
-9/2
5/23/2-7/21/23/21/2
17/21/23/25/2
-9/2-11/215/2-7/2-19/21/23/25/213/2-11/2-9/2-7/21/23/213/2
-21/2-11/2
5/215/2-9/25/2-7/23/2-7/2-11/21/2
-9/2
26492 4D 1/2 1/2
I*-
v . V JJ3 u. u
JDSEEVI
• • •* • •• • •a • a
• • •
• • •
• • •
• • •
• a •
• • •
• a •
• • *
a • •
• • •
• • •
• • •
• • •
• • •
• • •
• a •
2736327417274322744827508
2764627658
276912773127758
28248282622834328409
287152872628753
a • a
2877828790
• • a
28810
PAGE 5
APPENDIX VI
3D CALC
26691266932670726735267472677126792267992680726809268392684 526852
26926269532698326990270112707027110
2736127432274682748427533
2765527664
277192776527773
28250282532834928403
2873 828742287532875428781287942880628811
TABLE 1SH+3:LAF3
O-C
• • •• • •« • •• • a
a a a
a a •
a • •
• • m
mem
• a a
• a •
• a a
a a a
a a •
• a •
• mm
a a a
a a a
a a a
a a a
2-14-35-35-24
-6-5
-27-30-14
-19-56
-22-150
a • a
-2-3
• • a
0
STATE J
4K2K4L4K6P2K4L6P4K6P6P4LUK
4K4K4K4K4K4K4K
4F4F4F4F4F
4D4D
6P6P6P
6P4H4H6P
4K4K4K4K4K4K4K4K
17/217/217/217/27/217/217/27/217/27/27/217/217/2
13/213/213/213/213/213/213/2
9/29/29/29/29/2
3/23/2
5/25/25/2
7/27/27/27/2
15/215/215/215/215/215/215/215/2
MJ
1/23/25/213/2-7/215/217/25/2
-11/23/21/2
-7/2-9/2
1/2-9/23/2
-11/25/2
-7/213/2
-7/25/23/21/2
-9/2
. 1/23/2
1/25/23/2
1/25/2
-7/23/2
5/21/23/2
-11/213/215/2-9/2-7/2
II i
//<=
BSEBVE
28938• • •
28981290 37290552908629094
a • •
« • •
• * •
• • a
• • •
• • a
• • •
• • «
• • •
• • •
* • •
• > •
• • •
* • *
• • •
• • a
• « •
• • •
• • a
• • •
« * •
• • •
• a •
a • •
• • •
• • •
• • •
• • •
• • •
• • •
• • •
• • •
• • •
• • •
PAGE 6
APPENDIX VI
:D CALC
28935289562900 7290632907629103291032910729117291362913729143291382915129168291842920529223
2929829307293122933129347293562936129365294122944829456294762950329572295822958729590296322964029683297082971229761
TABLE! 1SM+3:LAF3
O-C
3• • a
-25-25-20-16-8
• • •
a • «
a « •
• • a
• « a
• • •
• • •
• • *
• • a
• a •
• • a
• a a
» * m
• • a
• • •
• • •
• * •
* m •
• a *
a • •
• a •
• a •
m • •
• • a
• a •
a • •
• • •
* * m
• • •
• • a
• a •
• • a
a a •
• • •
STATE J
4H4H4H6P4H6P6P4K4K4K4K4K6P4K4K4H4K4K
4H4M4L4H4L4H4H4H4H4M4L4M4H4H4H4L4H4H4H4H4H4H4H
9/29/29/27/29/27/27/217/217/217/217/217/27/217/217/29/217/217/2
19/219/219/211/219/211/211/211/211/219/219/219/211/219/213/219/219/213/213/213/213/213/213/2
MJ
-7/21/2
-9/25/23/23/21/25/2-7/2-9/2-11/217/2-7/213/23/25/21/2
15/2
1/23/25/2-9/217/2
-11/21/2
-7/23/2
15/2-19/213/25/2
-11/2-11/2-7/2-9/23/21/25/2
-9/213/2-7/2
u.vv^u U.UDOO
PAGE 7
APPEHDIX VI
OBSERVED CALC
300273012530141
• m m
• a •
30219302353028630329
* a •
• • •
. . .
a • •
• a •
• a •
314203144231473
• a a
a a a
a a a
« • *
a a a
31627a • a
• mm
. . .
3171631761
328003282232853
336083368133765
a a a
m m •
a • •
• mm
• a a
• mm
a • •
a • •
• a •
a • •
a a a
a • a
300253013930142301913020730217302623027530346304443048930539
31222
31341313583141231454314743148831515315183152531552316083161531628316763171031735
328083282932861
335833365833742337953382433891339033394233961339663399634033340483405634090
TABLESM+3:L
O-C
2-13
0......2
-2611
-16• m •
a a a
• • a
a a •
a • •
a • •
8-11
0• • a
• • •
a • •
• • *
. . .
19a * a
• * a
• a a
626
-7-6-7
252323
a • a
• • •
• • a
• • a
a • a
• • a
• • •
• a a
a • •
a * a
« a •
1AF3
STATE J
4G4G4G4G4G4G4G4G4G4G4G4G
4P
2K2K2L2L2L2K4G4G2L4P2K4G4G2L4G4G
4P4P4P
2F2F2K2K2F2K2K4F2K4F4F4F2K4F2K
7/27/27/29/29/25/29/29/27/25/25/25/2
1/2
15/215/215/215/215/215/211/211/215/23/215/211/211/215/211/211/2
5/25/25/2
5/25/213/213/25/2
13/213/29/213/29/29/29/213/29/213/2
HJ
5/2-7/21/23/2
-9/25/2
-7/21/23/21/25/23/2
1/2
13/2-11/2-9/25/23/21/2
-11/25/2
-7/23/21/2
-7/215/2-9/21/2
1/25/23/2
1/25/2
-11/2-9/23/21/2
-7/2-7/23/25/2
-9/21/25/23/2
13/2
II)
PAGE 8
APPENDIX VI
TABLE 1SH+3:LAF3
OBSEFVEP CALC O-C STATE J
a • •
• • •
• • *
• • •
• • •
• a a
• • *
• • •
• • •
• • •
• • •
• • •
• • •
• * •
* a a
• a •
• • •
• a a
a • a
• • •
a • •
• • •
• • •
• • •
• • *
• • •
• • •
• • a
• • •
358903590535954359963600736055
3433134347343973440234407344533445534474344873453434557345883459934630
355753565135666356783569935701357183572835737357593576235762357943586435874
359023592035955359833600936052
• • •• • •• • •* • •• • •• • •a * •
a • •
• • a
• a *
• • •
• • •
• a •
• • •
• a •
• a •
• • •
a a a
a • •
• • •
• • a
a • a
• • •
• • •
• * •
a a a
• • a
a a *
• • •
-11-14
013-13
2L2L2L2L2L2L2L2L412L41414141
2N4F2N4F2N2N2N2N2N2N2N2N4F2P4F
414141414141
17/217/217/217/217/217/217/217/29/217/29/29/29/29/2
19/27/219/27/219/219/219/219/219/219/219/219/27/21/27/2
11/211/211/211/211/211/2
13/215/2
-11/2-7/23/25/2
-11/2-9/25/217/25/23/2-9/21/2
-19/25/217/21/2
-9/2-11/2-7/217/213/25/23/21/2
-7/21/23/2
-7/2-9/25/2
-11/23/21/2
PAGE 9
APPENDIX VI
TABLE 1SM+3:LAF3
OBSEBVED CALC O-C STATE J HJ
• a •
• a •
• a a
• • a
a • a
• a *
a a a
• • a
36567a a •
• • •
a a •
• • a
• • a
• • a
• • •
a • •
366 51a a •
• a •
• • a
• a a
• • a
* a a
a a •
36755a • •
a • •
• a •
a * •
a • •
9 9a
• a a
• a a
9 a a
• • a
• a a
9 a a
a • •
• • a
376233763^376343765737679
3631036339364043646136496365203652636526365503657136572366023663236643366453664 83665136659366803670036702367093672636735367383675 23678136839368393684036845
369033692236960370373705137072371313721637268
375993761U376193763837661
• a a
9 9a
a • 9
9 9 a
a a a
a a 9
a • a
a a a
17a a a
• a •
• 9 •
a • a
• a a
9 • 9
a a a
a a *
-7a a a
* * m
9 9*
a a a
a a a
• a a
9 a •
39 9 9
9 a a
a a a
9 9*
9 9 •
9 9 9
9 a «
a a a
9 9 9
9 • m
9 9 9
* 9 a
• 9 9
9 9a
2420151918
41412K414F2K41414F2K41412N2N2N4F414F2N2N4141-41412N4F2N2N2N2N2N
2M2M2M2M2H2H2M2M2H
2H2H2H2H2H
15/215/215/215/25/215/215/215/25/215/213/213/221/221/221/23/213/25/221/221/213/213/213/217/221/23/221/221/221/221/221/2
17/217/217/217/217/217/217/217/217/2
9/29/29/29/29/2
13/2-11/2-9/2-7/21/2
. 3/21/25/25/215/2
-11/2-9/2
-19/2-21/217/23/2
-7/23/21/23/25/21/23/213/25/21/215/2-7/213/2-9/2-11/2
17/217/2-9/21/25/23/2
-11/215/213/2
-7/21/2
-9/23/25/2
PAGE 10
APPENDIX VI
TABLE 1SH+3:LAF3
OBSERVED CRLC O-C STATE HJ
381843825638280
38467 3846738492 38484
38499
389023897139000391173914239171392143924539316393613940039446394553946839475395063954139581
403164048640505405554069640698407194076240781408064084 9408834089540909409724098141061410874113941178412504125241359'41382
... 2F
... 2F
. .. 2F0 2P9 2P
... 2F
... 2K
... 2K26
. .. 2K2G2G
... 2K
... 2K
... 2G
... 2K2H2H
... 2H
... 2K
... 2H
... 2H2G
... 2K
... 2M2M
... 2H
... 2M
... 2H2.12M2D
... 2D
... 2D2D21
... 2M
... 21
. .. 2121
... 2H
... 212K21
... 2K
... 2K
... 2K
... 2K
7/27/27/23/23/27/2
15/215/27/215/27/27/215/215/27/215/211/211/211/215/211/211/27/215/2
19/219/219/219/219/219/219/25/25/25/25/211/219/211/211/211/219/211/213/211/213/213/23/2
Id/2
3/2-7/21/23/21/25/2
13/2-11/2
5/23/21/2
-7/21/25/23/2
-9/2-7/2-9/2
-11/215/25/21/23/2-7/2
-19/2-7/2-9/2
-11/21/25/23/21/21/25/23/2
-11/217/23/21/2
-9/215/2-7/2-11/2
5/2-9/21/25/23/2 r
PAGE 11
APPENDIX VI
TABLE 1SM+3:LAF3
OBSEPVED CALC O-C STATE J HJ
4139741534
42066
421354217642227
423784246242466
42616
4265842711
429594299043040
430 74
43258
43324
4173741756
4205442102421124215842199
423904246542481
42616426254264242700
427154287542923429384296342973429934302343025430454304543079430884311843144431464316743169431964321543226432284323743266432664327243276432944330243368
1611
-13-217
• • •
29
-7
22
2K 13/2 13/22K 13/2 -7/2
... 2D2D
12 2G22 2G23 2G1828
2G2G
-11 4G-2 4G5 4G
4G4G4G4G
202K2K4H4H4H4H4H204H2N2K202K2K2K4H2K20414H2020204H4H4H2K2020
3/23/2
9/29/29/29/29/2
5/25/25/2
7/27/27/27/2
21/215/215/29/29/29/29/29/221/29/221/215/221/215/215/215/211/215/221/211/211/221/221/221/211/211/211/215/221/221/2
1/23/2
-9/25/23/21/2
-7/2
1/25/23/2
-7/21/23/25/2
-21/213/2-11/23/25/2-9/21/2
-7/2-9/2-7/2-9/21/2
-11/25/215/2-7/21/2
-9/213/2-11/23/2
-19/23/21/2-7/2-9/25/2-7/217/215/2
r 1 •
*3Bt A*'
PAGE 10
APPENDIX VI
TABLE 1SH+3:LAF3
OBSERVED CALC O-C STATE J MJ
X"K' • % ' • • • •
fro ,•1':. °. . ,
*" - *4/t;'. /'<'^\
381843825638280
38467 3846738492 38484
38499
38902389713900039117
.. . . 391423917139214
.... 3924539316393613940039446394553946839475395063954139581
40316... 40486
405054055540696406984071940762407814080640849408834089540909
'.'... 40972... 40981... 41061
41087.. 41139.. 41178...J: ~41250. . % 41252
'••a. •".•, • »«rv 4:1382
... 2F
... '2F
. .. 2F0 2P9 2P
... 2F
2K... 2K
26. .. 2K
26262K2K
... 2G
... 2K
... 2H
... 2H
... 2H
... 2K
... 2H
... 2H
... 26
... 2K
... 2H
... 2M
... 2M
... 2H
... 2H2H2M2D
. .. 2D
... 2D2D21
... 2H
... 21
... 2121
... 2H
... 21
... 2K
... 21
... 2K
... 2K
... 2K
... 2K
7/27/27/23/23/27/2
15/215/27/215/27/27/215/215/27/215/211/211/21V215/211/211/27/215/2
19/219/219/219/219/219/219/25/25/25/25/211/219/211/211/211/219/211/213/211/213/213/213/213/2
3/2-7/21/23/21/25/2
13/2-11/2
5/23/21/2
-7/21/25/23/2
-9/2-7/2-9/2
-11/215/25/21/23/2-7/2
-19/2-7/2-9/2
-11/21/25/23/21/21/25/23/2
-11/217/23/21/2
-9/215/2-7/2-11/2
5/2-9/21/25/23/2
='f—.-
r
IBSEFVI
• • •• • •
• • •
• • •
4206642124421354217642227
423784246242466
42616• • •
4265842711
• • •• • •• • *• • *• • •
429594299043040• • •
43074• • •• • m
• • •
• • •
• • •
• • •
• • •
• • *
• • •
• • •
• • •
• • •
• • •
43258• • •• • a
• • •
43324• • *
PAGE 11
APPENDIX V3
iD CALC
4139741534
4173741756
4205442102421124215842199
423904246542481
4261642625426 24270u
427154287542923429384296342973429934302343025430454304543079430884311843144431464316743169431964321543226432284323743266432664327243276432944330243368
TABLE! 1SM+3:LAF3
O-C
• • •• • •
• • *
• * •
1222231828
-11-25
0• • •1611
• • •• • *« • •• « a
• • •
-13-217
• • •29• • •• • •a • «
• • •
• • •
• • *
• • a
• • •
• • •
• • •
a a a
a • a
• • •
• • a
-7• a a
• • •
• • a
22• a •
STATE J
2K2K
2D2D
2G2G2G2G2G
4G4G4G
4G4G4G4G
202K2K4H4H4H4H4H204H2N2K202K2K2K4H2K20414H2020204H4H4H2K2020
13/213/2
3/23/2
9/29/29/29/29/2
5/25/25/2
7/27/27/27/2
21/215/215/29/29/29/29/29/221/29/221/215/221/215/215/215/211/215/221/211/211/221/221/221/211/211/211/215/221/221/2
MJ
13/2-7/2
1/23/2
-9/25/23/21/2
-7/2
1/25/23/2
-7/21/23/25/2
-21/213/2
-11/23/25/2
-9/21/2
-7/2-9/2-7/2-9/21/2
-11/25/215/2-7/21/2
-9/213/2
-11/23/2
-19/23/21/2
-7/2-9/25/2
-7/217/215/2
PAGE 12
RPPENDIX VI
TABLE 1SH+3:LAF3
OBSERVED CALC 0-C STATE 3 MJ
43446 ...43542 ...43545 ...43545 ...43565 ...43576 ...43590 ...43703 ...
43728 ...43780 ...43789 ...43829 ...
... 43888 ...
43953 ...44003 . ..
... 44005 ...
... 44016 ...
... 44481 ...44559 ...
44597 44622 -2444692 ...44710 ...
45031 ...... 45065
45071 ...45122 45146 -23
45262 ...45320 ...45324 ...
45366 45379 -12... 45440 ...
4566845732 ...45770 ...
... • 45812 ...45817 ...4582845837 ...45845 ...45861 . .4586945891 ...45917 ...45930 ...
4H4H4H4H4H4H2H21
2121212121
4H4H4H4H
2G2G2G2G2G
4G4G4G4G
4G4G4G4G4G
2121214G214G464H4G4G214H4G
13/213/213/213/213/213/213/211/2
11/211/211/211/211/2
7/27/27/27/2
9/29/29/29/29/2
7/27/27/27/2
9/29/29/29/29/2
13/213/213/211/213/211/211/213/211/211/213/213/211/2
13/23/2-7/2-11/2
1/25/2
-9/25/2
-11/23/2-7/21/2
-9/2
-7/23/21/25/2
-7/21/2
-9/25/23/2
• 1/2-7/23/25/2
1/2-7/2-9/23/25/2
13/21/23/25/2
-11/23/21/25/2
-11/2-7/2-9/2-7/2-9/2
•tl
ill
IBSEBVE
• a •
• a •
a « m
a • m
• a •
46284• • •• * V
" • • * •
• • a
• • a
m * •
46402• • •• • •• a •
• • •
• • a
a • a
• a a
• • a
• • a
46603• m 9
a a a
a • •
a a •
• • •
4733647374• • •• • a
PAGE 13
APPENDIX VI
!D CALC
4620446222462674626 94629846300J»63304633446341463494639346412464224642246435464454644846473464924651246531465504658746592469624697247057472664732 7473974747147620
TABLE 1SM+3:LAF3
O-C
* • m
• • •
m • •
a a •
* m »
-15• • •4 a •
* a •
* • a
• • •
• • •
-19a • •
• • •
mm*
• • *
• • •
• • a
* • •
• a •
16• a •
• • a
• a •
a • •
a a a
9-22a a •
mm*
STATE J
2H2H4H2L2L2H2L2L2L2L2H4H4H4H2L2L2L4H4H4H4H4P4P2H2D2D2D2H2H2H2H2H
11/211/213/217/217/211/217/217/217/217/211/213/213/213/217/217/217/213/213/213/213/23/23/211/25/25/25/211/211/211/211/211/2
MJ
1/2-9/213/217/2-7/2-11/2
3/21/2
15/25/23/21/25/23/2
-11/2-9/213/2-7/2-7/2-11/2-9/23/21/2
-7/25/23/21/2
-11/25/23/2
-7/2-9/2
PAGE 12
APPENDIX VI
TABLE 1SH+3:LAF3
OBSEBVED CALC O-C STATE J MJ
43446 ...43542 ...43545 ...43545 ...
... 4356543576 ...43590 ...43703 ...
43728 ...43780 ...43789 ...43829 ...43888
43953 ...... 44003 ...
44005... 44016 ...
... 44481 ...44559 ...
44597 44622 -2444692 ...44710 ...
45031 ...4506545071 ...
45122 45146 -23
45262 ...45320 ...45324 ...
45366 45379 -1245440 ...
4566845732 ...45770 ...45812 ...45817 ...
... 45828 ...45837 ...45845 ...45861 ...
... 4586 9 ...45891 ...45917 ...45930 ...
4H4H4H4H4H4H2H21
2121212121
4H4H4H4H
262G2G2G2G
4G4G4G4G
4G4G4G4G4G
2121214G214G4G4H4G4G214H4G
13/213/213/213/213/213/213/211/2
11/211/211/211/211/2
7/27/27/27/2
9/29/29/29/29/2
7/27/27/27/2
9/29/29/29/29/2
13/213/213/211/213/211/211/213/211/211/213/213/211/2
13/23/2-7/2-11/2
1/25/2
-9/25/2
-11/23/2
-7/21/2
-9/2
-7/23/21/25/2
-7/21/2
-9/25/23/2
' 1/2-7/23/25/2
1/2-7/2-9/23/25/2
13/21/23/25/2
-11/23/21/25/2
-11/2-7/2-9/2-7/2-9/2
tl
12-°
IBSERVE
'• • •• • •• • m
• • a
m • *
46284• • •• • •• • •• • •• • m
• • •
4 6 4 0 2• • •• • •• • •« • •• « •a • •
• • a
• • •
a a •
46603• • •
• • •
• • »
• • •
• • •
4733647374• • *• • •
PAGE 13
APPENDIX VI
ID CALC
4620446222462674626946298463004633046334463414634946393464124642246422464354644546448464734649246512465314655046587465924696246972470574726647327473974747147620
TABLE: 1SM+3:LAF3
d-c
« • •• • •• * •• • •a • •
-15• • •a • •
• • •
* • *
• a a
• • •
-19a • •
• • •
* • •
a • a
* • •
• a a
• * *
• • •
16* • •• • •
• • •
• • •
• • •
9-22• • •a a a
STATE J
2H2H4H2L2L2H2L2L2L212H4H4H4H2L2h2L4H4H4H4H4P4P2H2D2D2D2H2H2H2H2H
11/211/213/217/217/211/217/217/217/217/211/213/213/213/217/217/217/213/213/213/213/23/23/211/25/25/25/211/211/211/211/211/2
HJ
1/2-9/213/217/2-7/2-11/2
3/21/2
15/25/23/21/25/23/2
-11/2-9/213/2-7/2-7/2-11/2-9/23/21/2
-7/25/23/21/2
-11/25/23/2
-7/2-9/2
7 /i
PAGE 14
APPENDIX VI
TABLEI 1 ASM+3:LAF3 CENTERS OF GRAVITY
CALC CENTER
10111352341366750726 3876520663771418009918910583
180311898220161206602082521147216442230122612228732304824132241382467624 9952506425201254342566725829264462676226786
STATE
6H 5/26H 7/26H 9/26H11/26H13/26F 1/261515/26F 3/26F 5/26F 7/26F 9/26F11/2
4G 5/24F 3/24G 7/241 9/24M15/24111/24113/24F 5/24M17/24G 9/24115/26P 5/24M19/24L13/24F 7/26P 3/24K11/24M21/24L15/24G11/24D 1/24L17/26P 7/2
J1
1/21/21/21/21/21/21/21/21/21/21/21/2V21/21/21/21/21/2
1/21/21/21/21/21/21/21/21/21/21/21/21/21/21/21/2
3/23/23/23/23/23/23/23/23/23/23/23/23/23/2
IEVEL
638763876387638763876387638763876387638763876387638763876387638763876387
26406264462644626446264462644626446264462644626446264462644626446264462644626446
66376637663766376637663766376637663766376637663766376637
1 J2
3/23/25/25/25/25/27/27/27/27/29/29/29/2
11/211/211/213/213/2
3/23/25/25/25/27/27/27/29/29/211/211/211/211/213/213/2
3/23/23/25/25/25/25/25/27/27/27/27/27/29/2
PAGE 15APPENDIX
TitBLI! 20(K) *2 FOR
LEVEL 2
663725064
1017141
223012413211358009
249952678623419189
20660366710583
' 258295072
24676
189822506418031223012413220161249952678620660228733667
2114725201258292164424676
66371898225064101
714118031223012413211358009
2016124995267862341
VI
SM+3
(02)*2
000000000000000000
00000000000000,0,0,
0.0.0,0.0.0.0.0.0.0.0.0.0.0.
.0174
.1920
.1938
.0140
.0011
.0106
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0079
.0061
.0180
.0532
.0106
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0029
.0011
.2922
.1444
.0222,0010,0036,0711243401830023,001000240
(04)*2
00000000000000000,0,
0.00,0.0.0,0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0
.0
.1386
.0306
.0030
.0966
. 1521
.0071
.0012
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0226
.0789
.0028,0805,0294,00,0,000
,00013650282000000030237117400800009006315921183
(06) *2
00000000000000000,0.
0.000,0,0,0,0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0
.0
.0,0.0.0.0.0.0.3365.0287.0015. 1026.0026
.0
.0
.0
.0
.0
.0
.0
.0,0,0.002909920527081602971446
00000000000003793
J1
3/23/23/23/23/23/23/23/23/23/23/23/2
3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2
3/23/23/23/23/23/23/23/23/23/23/23/23/23/2
LEVEL
663766376637663766 376637663766376637663766376637
18982189821898218982189821898218982189821898218982189821898218982189821898218982189821898218982189821898218982
2506 4250642506425064250642506425064250 64250642506425064250642506425064
1 J2
9/29/2
11/211/211/211/211/213/215/215/215/215/2
3/23/25/25/25/27/27/27/27/27/29/29/29/2
11/211/211/213/213/213/215/215/215/2
3/25/25/25/25/25/27/27/27/27/27/29/29/29/2
PAGE 16APPENDIX
TABLE 20(K)*2 FOB
LEVEL 2
91892287336671058321147252012582950726520208252304825667
189822506418031223012413211358009
2016124995267862341
206602287321147252 01258295072
2164424676208252304825667
250641C1
714118031223012413211358009
20161249952678623419189
20660
VI
SH + 3
(U2)*2
000000000000
000000,0,0,0,0,0,0,0,0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.c.0.0.0.0.0.
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0023
.0037
.0763
.0609
.0015
.0083
.0001
.0289
.0149
.0013
.0
.0
.0
.0
.0
.0
.0,0,0.0,0,0
,00960000263800080012122000001450001803264736000
(04)*2
0000000,0,0,0,0.0.
0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0301
.0000
.2119
.0041
.0062
.0013
.0000
.0
.0
.0
.0
.0
.0
.0,0440,0018.0771,000000131525,00010158002910750401299014830016000000
01630009400010310001315890469008700700000112514480101
(06) *2
0,0,0,0,0.0.0,0.0.0,0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0098
.0026
.0287
.0489
.0001
.0001
.0013
.4036,0615.0099,0028,0021
,0,0,000,00000004 90204372909850066239600140556075435771386001 c>
00000000000001100000023
34090 2K 13/2 13/2
J1
3/23/23/23/23/23/23/23/23/23/2
5/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/2
5/25/25/25/25/25/25/25/25/25/25/25/25/25/2
IEVEL
25064250642506425064250642506425064250642506425064
101101101101101101101101101101101101101101101101101101101101101101101101
71417141714171417141714171417141714171417141714171417141
1 J2
9/211/211/211/211/211/213/213/215/215/2
5/25/25/27/27/27/27/27/29/29/2V29/2
11/211/211/211/211/213/213/213/215/215/215/217/2
5/25/25/25/27/27/27/27/27/29/29/29/29/211/2
PAGE 17APPENDIX
TAB LI: 20(K)*2 FOR
LEVEL 2
228733667105832114725201258295072
216446520
25667
1017141
2413211358009
20161249952678623419189
20660228733667105832114725201258295072
21644246766520
208252566722612
714118031223012413211358009
20161249952678623419189
20660228733667
VI
SM + 3
(U2)*2
0000000000
000000000000000000000,0.0,0,
0,0.0.0.0.0.c.0.0.0.0.0.0.0.
-.0.0.0.0.0.0.0.0-0.0
.3881
.0331
.0000
.2062
.0020
.0003
.0002
.0000
.0257
.0000
.0022
.0000
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0007
.0062
.0072,1864.^118.0397.0004.0014024333740140000000230
(U4)*2
000000000,0,
00,0,0,0,0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0388
.0465
.3702
.0040
.0039
.0049
.0
.0
.0
.0
.0567
.2844
.0244
.1963
.1429
.0017
.0011
.0015
. 1397
.0205
.0005
.0009,0240,0006,00000004,0001,000600320080,0000
01170014004206740507003700080074180210130298001100042305
(06) *2
0000000000
000.0000,0,0.0,0,0,0,0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0016
.0118
.0000
.0470
.0000
.0118
.0570
.0574
. 1418
.0316
.0
.0
.0
.0952
.4301
.0023
.0005
.0663
.3262
.3416
.0014
.0027
.2649
.0516
.0111,0024.0010,0662,0237,00920043,031900560054
00004192004 500190003000004750356001900042087
J 1
5 / 25/25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 2
5 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 25 / 2
5 / 25 / 25 / 25/25 / 25 / 25 / 25 / 25/25 / 25 / 25 / 25 / 25 / 2
LEVE1
7141714171417141714171417141714171417141
180311803118031180311803118031180311803118031180311803118031180311803118031180311803118031180311803118031180311803118031
2230122301223012230122301223012230122301223012230122301223012230122301
1 J2
11/211/211/211/213/213/213/215/215/217/2
5 /25 / 25 /27 / 27 / 27/27 / 27 / 29 / 29 / 29 /29 /2
11/211/211/211/213/213/213/215/215/215/217/217/2
5 / 25 /27 /27/27 / 27 /27 / 29 / 29 /29 /29 /2
11/211/211/2
PAGE 18APPENDIX
TABLE: 2U (K) *2 FOB
LEVEL 2
10583211472520125829
50722164424676
65202082522612
180312230124132
11358009
201612499526786
23419189
2066022873
3667211472520125829
507221644246762082523048256672261226762
2230124132
11358009
201612499526786
23419189
2066022873
36671058321147
V I
SM + 3
( 0 2 ) * 2
0000000000
0000000000000000000000,0,0,
0.0 .0 .0.0.0.0 .0 .0 .0 .0 .0 .0 .0 .
. 0
. 0
. 0
.0. 0. 0.0. 0. 0. 0
. 3 4 2 4
. 0 0 9 8
. 0 1 0 6
. 0 0 0 0
. 0 0 0 0
. 0 0 0 0
. 0 0 2 2
. 0 0 1 8
. 0 0 9 6
. 0 0 1 6
. 0 3 6 9
. 0 0 3 2
. 0
. 0
.0
. 0
. 0
. 0
.0
.0
.0
.0
.0
.0
,0003,0444,0004,0123, 1850,0203.0125,0064009902290222000
(U4)*2
0000000000
00000000,00,0,0,0,0,0,0,0.0.0.0.0.0.0.0 .
0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .0 .
.0225
.0027
.0016
.0000
.2116
.0094
.0000
. 0
. 0
. 0
.2483
.0369
.0391
.0078
.0015
.0083
.0057
.0250
.0061
.0002
.1101
.0187
.0045
.0009
.0074
.0013
.0000
.3028
.1459,0,0.0,0,0
.03450016005900870808031901280008003700911156014100440054
(U6)*2
0.05110.00000.00040.00750.28670.00010.00180.34000.01790.0193
0 . 00 . 00 . 00.00750.00010.40940.02810.00080.00190.00020.01880.03090.00180.23500.02890.13140.00140.72180.07670.83540.04350.00570.02030.0092
0 . 00 . 00.00080.00000.03730.11240.00000.00000.00000.11220.07210.00800.00010.3369
J1
5/25/25/25/25/25/25/25/25/2
5/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/25/2
7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2
LEVEL
223012230122301223012230122301223012230122301
2413224132241322413224132241322413224132241322413224132241322413224132241322413224132241322413224132241322413224132
1135113511351135113511351135113511351135113511351135113511351135
U
1 J2
11/211/213/213/213/215/215/215/217/2
5/27/27/27/27/27/29/29/29/29/211/211/211/211/211/213/213/213/215/215/215/217/217/2
7/27/27/27/27/29/29/29/211/211/211/211/211/213/213/215/2
PAGE 19APPENDIX
TABLE! 2(K) *2 FOR
LEVEL 2
25201258295072
216442467620825230482566722612
241321135800920161249952678623419189
20660228733667105832114725201258295072
2164424676652020825230482261226762
11358009
20161249952678623419189
20660366710583211472520125S2S5072
246766520
VI
SM + 3
(U2)*2
000000000
00000000000000000000000
000,0.0,0,0,0,0.0,0,0.G.0.0.0.
.0
.0
.0
.0
.0
.0
.0
.0
.0
.2386
.0000
.3046
.0062
.0651
.2737
.0004
.3246
.0007
.0577
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.2831
.0420
.0000
.0000
.0000
.2938
.0017
.0002
.0382
.0000
.0002
.0016COOO000
(U4) *2
000000000
00000000000000000000000
0000000000,0,0.0.0.0.0.
.1495
.0056
.0035
. 1186
.1341
.0
.0
.0
.0
.0005
.0706
. 1199
.0319
.0110
.0077
.1302
.1715
.0185
.0195
.1527
.1616
.0205
.0265
.1119
.1224
.0002
.0047
.0
.0
.0
.0
.0
.0143
.2955
.0024
.0000
.0088
. 1652
.1328
.0007
. 1792
.0104
.0000
.0000
.0005
.0245,0000,0003
(06) *2
0.01160.20320.00700. 11110.06390.00820.01720.19340.6557
0.00.00500.00000.00170.00050.00010.01780.00000.13260.00520.04670.00000.00090.02170.06270.08240.04760.00150.07400.02490.20110.01860.1009
0.29510.00040.00480.00260.08620.00800.45550.00660.25420.22810.010aC.C06 10.00On0.28110.00950.0467
176
J1
7/27/27/27/27/2
7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2
7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2
LEVEL
11351135113511351135
800980098009800980098009800980098009800980098009800980098009800980098009800980098009
201612016120161201612016120161201612016120161201612016120161201612016120161201612016120161201612016120161
U
1 J2
15/215/217/217/219/2
7/27/27/27/29/29/29/29/2
11/211/211/211/211/213/213/215/215/215/215/217/219/2
7/27/27/29/29/29/29/211/211/211/211/211/213/213/213/215/215/215/217/217/219/2
PAGE 20APPENDIX
TABLE! 2(K) *2 FOR
LEVEL 2
2304825667226122676224138
800920161249952678623419189
20660228733667105832114725201258295072
2164465202082523048256672261224138
20161249952678623419189
20660228733667105832114725201258295072
2164424676208252304825667226122676224138
VI
SM + 3
(U2)*2
00000
000000000000000000,0,0,0,
0.0,0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0
.0034
.0070
.0035
.1128
.2493
.0550
.0000
.0000
.4881
.0065
.0000
.0000
.0012
.0
.0
.0
.0
.0
.0
.0
.0
.3327
.0066
.0003
.0000
.0004
.0099
.0006,0099,0010,0240,0000,00790,0,0000000
<U4)*2
00000
00000000000000,0,0.0,0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0019
.0076
.0
.0
.0
.0217
.0000
.0041
. 1713
.1320
.0051
.0023
.0007
.0308
.0497
.0006
.0018
.0000
.4372
.0049
. 1306
.0012
.0038
.0019
.0
.0
.1197
.0556
.0436
.0090,0000,0768,0005,0014,0000074100810022005901330685144112232806000
(06) *2
00000
0000,0,0,0,0,0,000,0,0.0,0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0104
.0071
.0220
.0033
.0043
.0290
.0004
.0000
.0000
.2625
.0586
.0009
.0031
.3276
.0357
.0013
.0013
.0017
.0002
.0017,7121,0043,0015,0031,02300215
,0001,02660062,0038,00061086190400000001166214390660000001693055000097511634502207690330
43368 20 21/2 15/2
J1
7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2
7/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/27/2
9/29/29/29/29/29/29/29/29/2
LEVEL
2499524995249952499524995249952499524995249952499524995249952499524995249952499524995249952499524995
26786267862678626786267862678626786267862678626786267862678626786267862678626786267862678626786
234123412341234123412341234123412341
1 J2
7/27/29/29/29/29/211/211/211/211/211/213/213/213/215/215/215/215/217/219/2
7/29/29/29/29/211/211/211/211/211/213/213/213/215/215/215/215/217/219/2
9/29/29/29/2
11/211/211/211/211/2
PAGE 21APPENDIX
TABLE: 2U(K)*2 FOR
LEVEL 2
249952678623419189
20660228733667
105832114725201258295072
216442467665202082523048256672676224138
2678623419189
20660228733667
105832114725201258295072
21644246766520
2082523048256672676224138
23419189
2066022873366710583211472520125829
VI
SM+3
(02)*2
00000000000000000000
000,0,0,00.0,0,0,0.0,0,0,0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0048
.0000
.0009
.0137
.0092
.2300
.0074
.0230
.0122
.0003
.0137
.0
.0
.0
.0
.0
.0
.0
.0
.0
.1550
.0000
.3402
.0002
.0000
.0004
.8957
.0002
.0000
.0765
.0
.0
.0
.0
.0,0,0,0,0
,3286,0336,0002000034320007,000000100001
(04)*2
00000
o,0.000,0,0.0.0.0,0,0.0,0.0.
0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0668
.0030
.0011
.0010
.0009
.1546
.0002
.0010
.0098
.0576
.0245
.0121
.0230
.0061
.0185
.0001
.1892
.0196
.0
.0
.0042
.0361, 1343,0002,0714, 10800658,0072,00751692229501220082430900020000004900
021033400001002623170691000600000001
(U6)*2
00000000000,0,0.00.0,0,0,0,0.
0.0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0135
.0106
.0103
.0000
.2028
.004 9
.0121
.0001
.0373
.1335
.0991
.0016
. 1164
. 1391
.0007
.0074
.0009
.1390
. 1659
.7863
.0005
.0968
.0000
.1008
.0240,0933,0000,0975,06900281070607210481030500590594029503980394
263218090034002800005206001500430011
m
-'.™^^-iAJ..\_.^^_ -J^- , " ~ ~ ' '
• • >
J1
9/29/29/29/29/29/29/29/29/29/2
9/29/29/29/29/29/29/29/29/29/29/29/29/29/29/29/29/29/2
9/29/29/29/29/29/29/29/29/29/29/29/29/29/29/29/2
9/29/29/2
IEVEL
23m234123412341234123412341234123412341
918991899189918991899189918991899189918991899189918991899189918991899189
20660206602066020660206602066020660206 6 02066020660206602066020660206602066020660
228732287322873
1 32
13/213/213/215/215/215/217/217/219/221/2
9/29/29/2
11/211/211/211/211/213/213/213/215/215/215/217/217/219/221/2
9/29/2
11/211/211/211/213/213/213/215/215/215/215/217/217/219/2
9/211/211/2
PAGE 22APPENDIX
TABLI! 2U(K) *2 FOR
LEVEL 2
507221644246766520208252566722612267622413825434
918920660228733667105832114725201258295072
21644246766520208252304822612267622413825434
2066022873105832114725201258295072
216442467665202082523C4825667226122676224138
228733667
21147
VI
SM+3
(U2:*2
0000000000
000000000000000000,
0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.
.0337
.0000
.0002
.0
.0
.0
.0
.0
.0• 0
.0368
.0000
.0072
.2417
.0503
.0000
.0000
.0002
.7085
.0005
.0001
.0
.0
.0
.0
.0
.0
.0
.2267
.0029
.0000
.1471
.0316
.0007
.0000
.0306,0181,0.0,00000
314300000176
(04)*2
0000000000
0000,0.0,00,0,0,0.0,0.0,0,0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.
. 1744
.0001
.0014
.0117
.0008
.0000
.0002
.0066
.0
.0
.0094
.0009
.0001
.3531
.0652
.0035
.0010
.0008
.0332
.0013
.0018
.5743
.0010
.0037
.0002
.0023
.0,0
,1580,0356,0000,1009055401380000122519040000022202880630001100290
022400950879
(06) *2
0000000000
00000,0,00,0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.1.0.0.0.0.0.
0.0.0.
.3905
.0129
.0002
.2043
.0056
.0069
.0018
.0095
.0125
.0016
.0482
.0003
.0003
.0092
.0149
.0000
.0000
.0004
.4312,0020.0000.7457.0002.0090.0048.0061,0231,0160
,004 8140000090782225606870017271045060010005502652417463600270253
129100160067
••it
43368 20 21/2 15/2
J1
9/29/29/29/29/29/29/29/29/29/29/29/29/2
11/211/211/211/211/211/211/211/211/211/211/211/211/211/211/2
11/211/211/211/211/211/211/211/211/211/211/211/211/211/2
11/211/211/211/211/2
LEVEL
22873228732287322873228732287322873228732287322873228732287322873
366736673667366736673667366736673667366736673667366736 673667
1058310583105831058310583105831058310583105831058310583105831058310583
21147211U7211472114721147
1 J2
11/211/213/213/213/215/215/215/215/217/217/219/221/2
11/211/211/211/213/213/213/215/215/215/215/217/217/219/221/2
11/211/211/211/213/213/213/215/215/215/215/217/219/221/2
11/211/211/213/213/2
PAGE 23APPENDIX
TABLI! 2U(K)*2 FOR
LEVEL 2
25201258295072
21644246766520
20825230482566722612267622413825434
36671058321147258295072
2164424676652020825230482566722612267622413825434
105832114725201258295072
21644246766520208252304825667267622413825434
2114725201258292164424676
VI
SM + 3
(U2)*2
0000000000000
0000000000000,0.0,
0.0,0,0,0.0.0.1.0.0.0.0.0.0.
0.0.0.0.0.
.0015
.0100
.0044
.0120
.0002
.0
.0
.0
.0
.0
.0
.0
.0
.4871
.0158
.0017
.0002
.3428
.0000
.0005
.0171
.0000
.0000
.0002
.0
.0
.0
.0
.1382
.0000
.0000
.0066
.1668
.0002
.0000
.0103,0003,0018.0002.0,0,0
11810141009326400437
<U4)*2
0000000000000.
00,0,0.0,0.0,0,0,0,0,0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.
.0041
.0015
.0005
.0497
.0319
.0016
.0161
.0007
.0793
.2156
.4347
.0
.0
.0004
.2559
.0000
.0008
.3560
.0016
.0002
.1085
.0016
.0001
.0031
.0018
.0001
.0018,0
,0483.0008,0001,0001,5949,0038,00157789001200790034001200010
04950374073904811422
(U6)*2
0,20430.00050.00000.14060.02720.00020.07060.16300.28810.03571.10740.28490.0467
0.28370.76100.00500.00680. 10860.00110.01010.49780.00000.02090.00250.01370.00290.00320.0051
0.00260.00330.00120.00050.71120.00420.00350.34200.00040.00290.00470.00410.00270.0200
0.32970.33880.16360. 14490.1556
J1
11/211/211/211/211/211/211/211/2
11/211/211/211/211/211/211/211/211/211/211/211/211/2
11/211/211/211/211/211/211/211/211/211/211/211/2
13/213/213/213/213/213/213/213/213/213/213/2
IBVEL
2114721147211472114721147211472114721147
25201252012520125201252012520125201252012520125201252012520125201
258292582925829258292582925829258292582925829258292582925829
50725072507250725072507250725072507250725072
1 J2
15/215/215/215/217/217/219/221/2
11/211/213/213/213/215/215/215/215/217/217/219/221/2
11/213/213/213/215/215/215/215/217/217/219/221/2
13/213/213/215/215/215/215/217/217/219/221/2
PAGE 24APPENDIX
TABLI! 20(K) *2 FOR
LEVEL 2
652020825230482566722612267622413825434
252012582950 72
2164424676652020825230482566722612267622413825434
258295072
2164424676652 020825230482566722612267622413825434
50722164424676652020825230482566722612267622413825434
VI
SM + 3
(U2)*2
00000000
0000000000000
00000.0,0,0,0.0,0.0.
0,0.0.0.0.0.0.0.0.0.0.
.0000
.0278
.0129
.0316
.0
.0
.0
.0
.1673
.0005
.0000
.0251
.4310
.0000
.0052
.0048
.0001
.0
.0
.0
.0
.1454
.0017
.0409
.0120
.0000
.0004
.0010
.0298
.0
.0
.0
.0
.7978,0048,000725040001000000150000000000
(U4)*2
00000000
0000000,0,0,0,0,00.
0.0,0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
.0000
.5935
.0092
.0593
.0122
.0386
.0078
.0
.0033
.0051
.0000
.0020
.2064
.0000
.5504
.1994
.0549
.2208
.0801
.0063
.0
.0061
.0032
.1123
.0224
.0011
.0070,056900860415,003936230
074C0000000041480021001000090057003600240039
<U6)*2
000
.0028
.0427
.09500.31420000
0000000.0.00.0.0,0,
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
.8906
.1126
.4568
.0141
.0060
.0909
.0048
.2442
.0427
.0029
.1659
.3966
.1969
. 0289
.0920
.0648
.0038
.0652,0063.0487.0820.0012,0126.000109730828093507590548
10340022001469920039007401790038031003140028
tl
J1
13/213/213/213/213/213/213/213/213/213/2
13/213/213/213/213/213/213/213/213/2
15/215/215/215/215/215/215/215/2
15/215/215/215/215/215/215/2
15/215/215/215/215/215/2
15/215/215/215/215/2
LEVEL
2164U216442164421644216442164421644216442164421644
246762467624676246762467624676246762467624676
65206520652065206520652065206520
20825208252082520825208252082520825
230482304823048230482304823048
2566725667256672566725667
1 J2
13/213/215/215/215/215/217/217/219/221/2
13/215/215/215/215/217/217/219/221/2
15/215/215/215/217/217/219/221/2
15/215/215/217/217/219/221/2
15/215/217/217/219/221/2
15/217/217/219/221/2
PAGE 25APPENDIX
TABLI! 2U(K)*2 FOR
LEVEL 2
21644246766520
20825230482566722612267622413825434
246766520
20825230482566722612267622413825434
652020825230482566 722612267622413825434
20825230482566722612267622413825434
230482566722612267622413825434
2566722612267622413825434
VI
SM + 3
(U2)*2
0000000000
000000000
100,000.0,0.
0,
c,0.0,0.0.0.
Q.0.0.0.0.0.
0.0.0.0.0.
.0493
.0727
.0001
.3284
.0388
.0649
.0529
.0346
.0
.0
.0081
.0000
.5111
.2441
.0007
.0113
.0258
.0
.0
.3358
.0022
.0103
.0009
.0004
.0034
.0003
.0
.3461
.1093
.0334
.0501
.0071
.0154
.0
.0608,0336,1358.0855.0469,0
,00387604000102760
(U4)*2
00000,000,0,0,
0,0,0,0,0.0.0.0.0.
0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.
0.0.0.0.0.0.
0.0.0.0.0.
.0529
.1363
.0001
.1409
. 1682
.0926
.5293
.0208
.0228
.0055
.0818
.0000
. 1021
.0014
.0717
.0124,0452.0245.0000
,6497.0000.0001,0000,0019,0026.0095,0030
9739012207230137015616310009
4222160037010082444000C3
08582200143721821058
(06) *2
000000001
.0871
.0550
.0041
.0720
.2002
. 1637
.0138
.2962
.07420.3034
00.0,0,00,0.0,0,
0.0,0.0.0.0.0.0.
0.0.0.0.0.0.0.
0.0.0.0.0.1.
0.0.0.0.0.
.0001
.0034
.4209
.1029
.0032
.8855
.6603
.0316
.0681
.4629
.0001
.0038,0037,0015.0003.0056, 0C19
0240,204027133581259815813139
013909330002001301381875
07670417048499320364
45930 4G 11/2 -9/2
PAGE 26APPENDIX VI
TABLE 2U(K) *2 FOR SH+3
J1 IEVEL 1 J2 LEVEL 2 (U2)*2 (U4)*2 (U6)*2
17/217/217/217/2
17/217/217/2
19/219/2
22612226122261222612
267622676226762
2413824138
17/217/219/221/2
17/219/221/2
19/221/2
22612267622413825434
267622413825434
2413825434
0.60200.00070.04990.0056
0.00070.93570.0674
0.67710.0437
0.84420.06290.06760.0853
0.13500.55520.5015
0.90870.0943
0.00080.41900.49430.3317
0.04590.06700.7585
0.02750.8814
21/2 25434 21/2 25434 0.6674 1.2562 0.9348
/¥*"
APPENDIX VII
PAGE 1
APPENDIX VII
TABLE 1EU+3:LAF3 CENTERS OF GRAVITY
OBSERVED CALC
... 037210261666
... 282338494907
172931902721483243552532526357263922662226735267522676327244275862796028427
O-C STATE
... 7F0
... 7F1
... 7F2
... 7F3
... 7F4
... 7F5
... 7F6
... 5D0
... 5D1
... 5D2
... 5D35L 6
... 5L7
... 5G2
... 5G3
... 5G4
... 5G6
... 5G 5
... 5L85D4
... 5L9
... 5L10
It?
3 /2 6637 9 / 2 2341 0 . 0 U. l l B j U. 31-33
J1
000000
00000000
1111111111111
111111111111
2222222
LEVEL 1
000000
1729317293172931729317293172931729317293
372372372372372372372372372372372372372
190271902719027190271902719027190271902719027190271902719027
1026102610261026102610261026
J2
244666
2224U466
1123334556667
122333445667
2233445
PAGE 3APPENDIX VII
TABLEU(K)*2
LEVEL 2
10262823
275864907
2532526752
102621483263922823
26735275862532526752
3721902710261866
243552662228233849
267634907
253252675226357
1902721483263921866
24355266222823
275862676325325 "2675226357
1026214831866
243552823
267353849
2FOR EU+3
(U2)*2
000000
00000000
0,0,0.0,0,0,0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.
.1374
.0
.0
.0
.0
.0
.0032
.0142
.0146
.0
.0
.0
.0
.0
.1541
.0025
.0518
.2092
.0004
.0002
.0
.0
.0,0.0.0,0
,0133,0122,0209003801830164000000
1000001818630002222600000
(U4)*2
000000
00000,00,0,
0,0,0.0,0.0,0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.
.0
. 1402
.0011
.0
.0
.0
.0
.0
.0
.0023
.0359
.0134
.0
.0
.0
.0
.0
.1281
.0012
.0012, 1741.1192,0004.0,0,00
.00,0001900590594002800780484000
1219001521240020006200073153
(06)*2
000000
0000000,0,
0,00.0,0.0,0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.
.0
.0
.0
.1450
.0153
.0037
.0
.0
.0
.0
.0
.0
.2384
.2212
.0
.0
.0
.0
.0
.0
.0
.0544
.0097
.3774,0091,0049,0181
,0,0,00000023321479571720 20
0000032900782089
->/ *•
J1
22222
22222222222222
22222222222
333333333333
3333
LEVEL 1
10261026102610261026
2148321483214832148321483214832148321483214832148321483214832148321483
2639226392263922639226392263922639226392263922639226392
186618661866186618661866186618661866186618661866
24355243552435524355
J2
56678
22333444556678
23344456678
333445566689
3344
PAGE 4APPENDIX VII
TABLEU(K) *2
LEVEL 2
267634907
267522635727244
21483263921866
2435526622282326735275863849
2676325325267522635727244
263922435526622282326735275862676325325267522635727244
186624355266222823267353849
26763490725325267522724427960
24355266222823
26735
2FOR EU+3
<U2)*2
00000
00000000000000
0,0,0,0.0,0.0,0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.
.0
.0
.0
.0
.0
.0011
.0086
.0023
.0351
.0305
.0020
.0267
.0042
.0
.0
.0
.0
.0
.0
.0784
.0017
.1097
.0000
.0225
.0005
.0
.0
.0
.0
.0
02750010,00003880,00021754000000000
0149011500390215
((J4) *2
00000
00000000000000,
00,00,0,0.0,0.0,0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.
.0003
.0477
.0000
.0
.0
.0069
.0482
.0026
.0126
.0031
.0003
.0320
.0003
.0016
.0008
.0041
.0343
.0
.0
.0032
.0373
.0215
.0000
.0279,0040.0067,0480.0004.0.0
,0260,0005,00041352,00012527,001123100000000400
0023022900020005
(U6) *2
00000
0000000000,00.00.
0,0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.
.0046
.4696
.0019
.0110
.0193
.0
.0
.0
.0
.0
.0000
.2210
.0040
.0000
. 38 29
.1586
. 1586
.2479
.2481
.0
.0
.0
.0019
.0057,4282.1056,4599,01925130,0853
028100000048158800303836000541350013010200920168
003126 56000036 33
fl
5 / 2 71K1 Jbbt 0 . 0 0.2305 0.2087
J1
33333333
33333333333
444444444444
44444444444
4444
LEVEL 1
2435524355243552435524355243552435524355
2662226622266222662226622266222662226622266222662226622
282328232823282328232823282328232823282328232823
2673526735267352673526735267352673526735267352673 526735
27586275862758627586
J2
45566789
34455666789
4445566678910
445566678910
4556
PAGE 5APPENDIX VII
TABLEU(K)*2
LEVEL 2
275863849
267632532526752263572724427960
2662226735275863849
267634907
2532526752263572724427960
2823267352758o3849
267634907
25325 •2675226357272442796028427
2673527586384 9
267634907
253252675226357272442796028427
275863849
267634907
2FOR EO+3
(U2)*2
00000000
0,0,0.0,0,0,0.0,0.0,0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.
.0592
.0001
.0328
.0
.0
.0
.0
.0
.0227
.1414
.0021
.0000
.0292
.0
.0
.0
.0
.0
.0
.0117,0002,0005,5684,0001,085600000001,0000
04070156000909820000009402790000
0817003408250012
(U4)*2
00000000
00000,00,0000,
0.0.0,0,0,0.0,0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
V. .
0.0.0.
.0063
.0014
.0174
.0000
.0097
.0067
.0
.0
.0017
.0745
.0129
.0000
.0508
.0000
.0155
.0019
. 1106
.0
.0
.2841
.0009
.0006
.0128
.0000,5145.0002,0020.00000000,0,0
,00000381,00001241,0003029705380070189700
0022000403220000
(U6) *2
00000000
000,0000,0,0,00,
0,0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.
.0030
.0000
.2023
.0164
.0500
.1349
.3256
.34 77
.0644
.1508
.2131
.0010
.0086
.0020
.3677
.1249
. 1248
.5665
. 1166
.3528
.0005
.0002,4412.0059,2691,0046,0048,008000 4000520093
011611080036050500201569000126 62123282110161
0068000303840000
\f £. £. I I *f F
J1
444444
55555555
55555555
666666
666666
66666
7777
LEVEL 1
275862758627586275862758627586
38493849384938493849384938493849
267632676 3267632676326763267632676326763
490749074907490749074907
253252532525325253252532 525325
2675226752267522675226752
26357263572635726357
J2
66789
10
556678910
5666789
10
66789
10
6678910
678910
78910
PAGE 6APPENDIX VII
TABLEU(K)*2
LEVEL 2
253252675226357272442796028427
3849267634907
2675226357272442796028427
267634907
253252675226357272442796028427
490726752263572724 42796028427
253252675226357272442796028427
2675226357272442796028427
26357272442796028427
2FOB E0+3
(U2)*2
000000
000,00,0,0,0,
0.0,0.0.0.0.0.0.
1.0.0.0.0.0.
0.0.0.0.0.0.
0.0.0.0.0.
0.0.0.0.
.0005
.0363
.0
.0
.0
.0
.2762
.0020
.5410
.0001
.0000
.0
.0
.0
.0511
.0010
.0070
.0743
.0163
.00,0
,20290085,00000000.00
005000190147007600
10470004017700
0152024900830
(U4)*2
000000
00000000
0,00,0,0,0.0.0,
0,0.0.0.0.0.
0.0.0.0.0.0.
0.0.0.0.0.
0.0.0.0.
.0020
.0028
.0023
.0001
.0
.0
.2063
.0002
.6451
.0016
.0002
.0000
.0002
.0
.0008
.0011
.0403
.1716
.0692
.0134
.2596
.0
.3940,0022.0001,0003.0000,0020
,9355,03283310,072500000067
05780612048003842938
6740485608040000
(U6) *2
000000
00000,00,0
0,0,0,0,0,0.0.0.
0.0.0.0.0.0.
0.0.0.0.0.0.
0.0.0.0.1.
0.0.0.0.
.0166
.0000
.06 08
. 1575
.1547
.6379
.3225
.0047
. 1213
.0026
.0073
.0176
.0176
.0015
.0186
.0012
.0405
.0025
.1518
.3016
.4888
.6377
.02 94,0003.0013,0074.02420524
175800091468102000460563
00940509060130094460
0269167110320313
1%
7 / 2 1 1 3 5 1 5 / 2 6 5 2 0 0 . 0 0.0003 0.0467
PAGE 7APPENDIX VII
TABLE 20(K)*2 FOR EO+3
J1 LEVEL 1 J2 LEVEL 2 (U2)*2 (U4)*2 (06) *2
888
o> o>
272442724427244
2796027960
8910
910
272442796028427
2796028427
0.01760.03450.0055
0.01100.0379
0.71790.53120.0466
1.05740.4237
0.01750.19170.1105
0.05130.2855
10 28427 10 26427 0.0002 1.8415 0.4018
•I - , I - • •/
;• '-. 'if?
e l f
if? .;-/*
m
APPENDIX VIII
9/2 2341 11/2 25829 0.0001 0.0001 0.0011
OBSERVED
0.00.00.00.0
32177.1132185.6232199.6132228.57
32771.7532791.9632809.29
33352.0033370.00
35923.0035945.2435969.0335996.14
36275.2536286.0836306.2436314.2636333.45
36340.8136343.0336 347.1836351.6936354.8036364.5136371.713637 7.8636384.90
36551.433656 3.3336573.1836586.1436594.8636613.04
36661.8136670.9936679.9836690.1736700.50
PAGE 1APPENDIX VIII
TABLE 1GD+3
CALC
1111
32183321893220932232
327873278832799
3335133366
35929359393596235979
3626836276362973630536316
363423634436344363463034836350363553635836359
365563656736575365933659336611
3667436686366903670636707
I:LAF3
O-C
0000
-5-3-8-3
-14410
14
-56717
81091017
-1035715172026
-4-3-1-622
-11-14-9-14-5
STATE J
8S8S8S8S
6P6P6P6P
6P6P6P
6P6P
61616161
6161616161
616161616161616161
616161616161
6161616161
7/27/27/27/2
7/27/27/27/2
5/25/25/2
3/23/2
7/27/27/27/2
9/29/29/29/29/2
17/217/217/217/217/217/217/217/217/2
11/211/211/211/211/211/2
15/215/215/215/215/2
HJ
-7/25/23/21/2
-7/25/23/21/2
3/25/21/2
1/23/2
5/23/2
-7/21/2
5/2-7/23/2
-9/21/2
-9/2-11/2-7/213/215/25/23/2
17/21/2
-7/2-9/25/23/2
-11/21/2
-9/2-11/2-7/25/2
13/2
• • • " . • ! ' . ' • /
li .'V
- • %
OBSEBVED
36703367133671536720367243673436738367523676336772
3966739686397193974239758
• • •
40734407404074440751
• • •• • •
• • •
• • •
• • *
49170• « •
4922149240
• • •i « •
» • *
• •
• • •
• • •
• •
• •
• • •
• •
.65
.00
.52
.08
.82
.46
.99
.82
.02
.50
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
.00
PAGE 2APPENDIX VIII
TABLE 1GD + 3
CALC
36714367223672236725367323673736737367593676936770
3966039694397293974139763
40644
40732407374074340754
4089540909
410044104941061
49159492324923349248
49533495394960849633496434967049674496954973249735497414981549849
:LAF3
O-C
-10-8-6-3-6-22-5-52
7-7-91
-4
• • •
231
-2
• • •• a •
• • •
• • •
• • •
11• • •-11-7
• * •• • •
• • •
• • •
• * •
• • •
• • •
• • «
• • •
• • •
• as
• • •
• • •
STATE J
61616161616161616161
6D6D6D6D6D
6D
6D6D6D6D
6D6D
6D6D6D
6G6G6G6G
6G6G6G6G6G6G6G6G6G6G6G6G6G
15/213/215/215/215/213/213/213/213/213/2
9/29/29/29/29/2
1/2
7/27/27/27/2
3/23/2
5/25/25/2
7/27/27/27/2
11/29/29/29/25/29/29/29/211/211/211/211/211/2
MJ
15/2-7/23/215/21/2
-11/25/213/23/21/2
-9/21/23/2-7/25/2
1/2
5/23/21/2
-7/2
3/21/2
3/25/21/2
-7/23/25/21/2
-11/2-9/2-7/21/25/23/2-7/23/21/23/25/2
-7/2-9/2
11/2 21147 13/2 24676 0.0437 C.1422 0.1556
.'¥'
PAGE
APPENDIX
3
VIII
TABLE 1AGD+3:LAF3 CENTERS OF GRAVITY
CALC CENTER
2
322323282733398
359193629136345365823670436742
39723406544090141037
STATE
8S 7/2
6P 7/26P 5/26P 3/2
61 7/261 9/26117/26111/26115/26113/2
6D 7/26D 1/26F 3/26D 5/2
r
"NJi- ' - • }
' •*, **'*
BLANK PAGE
u
U. 1/JO4
J1
1/21/21/21/21/21/21/2
3/23/23/23/23/23/23/.?3/23/23/2
3/23/23/2-V2V23/23/23/23/2
5/25/25/25/25/25/25/25/25/25/2
5/25/25/25/25/25/25/25/25/25/2
LEVEL
40654406544065440654406544065440654
33398333983339833398333983339833398333983339833398
409014090140901409014090140901409014090140901
32827328273282732827328273282732827328273282732827
41037410374103741037410374103741037410374103741037
1 J2
3/23/25/25/29/29/211/2
3/23/25/25/27/29/29/211/213/215/2
3/25/25/27/27/29/211/213/215/2
5/25/27/27/29/29/2
11/213/215/217/2
5/27/27/27/29/29/211/213/215/217/2
PAGEAPPENDIX
TABLE
5VIII
2U(K) *2 FOR
LEVEL 2
33398409013282741037362913972336582
33398409013282741037322J23629139723365823674236704
409013282741037322323594936291365823674236704
32827410373223235949362913972336582367423670436345
410372
3223235949362913972336582367423670436345
GD + 3
<U2) *2
0000000
0000000000
00,0,0.0,0,0,0,0,
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0028
.0090
.0572
.0301
.0
.0
.0
.0109
.0222
.0430
.0725
.0090
.0
.0
.0
.0
.0
.0323
.0742
.0130
.0276
.0000
.0
.0
.0
.0
.0292
.0424
.0180
.0000,0001,20030,0,0,0
0005002608680002000100350000
(04)*2
0000000
00000.00.0,0.0,
0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0031
.0088
.0
.0
.0
.0002
.0013
.0004
.0002
.0022
.0016
.0
.0
.0
.0018,0061.0022,0045.0005,0116,00
0013,007300010023001500140000005200
0247000000050123008801200000024500
(U6)*2
0000000
000,00,00,0,0,0
0.0,0.0,0.0,0.0.0.
0.0.0.0.0.0.0.0.0.1.
0.0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0
.0
.003 3
. 0
.0
.0
.0
.0
.2310
.0000
.4382
.5719
.5483
.0
.0
.0
.0
.0
.0011,0362.0837.0355
.0,000017074410900021428002614351037
00000000004«V5094500020660001507151368
II
PAGE 6APPENDIX VIII
TABLE 20{K)*2 FOR GD+3
J1 LEVEL 1 J2 LEVEL 2 (U2)*2 (U<J)*2 (O6)*2
, <JU
7/27/27/27/27/27/27/27/21/27/27/27/27/27/27/27/27/2
7/27/27/27/27/2
9/29/29/29/29/2
9/29/29/29/29/2
11/211/211/211/2
13/213/213/2
15/215/2
222222220
3223232232322323223232232322323223232232
3594935949359493594935949
3629136 291362913629136291
3972339723397233972339723
36582365823658236582
367423674236742
3670436704
7/27/29/29/2
11/213/215/217/21/27/27/29/29/211/213/215/217/2
7/29/29/211/215/2
9/29/2
11/213/215/2
9/211/213/215/217/2
11/213/215/217/2
13/215/217/2
15/217/2
3223235949362913972336582367423670436345
03223235949362913972336582367423670436345
3594936291397233658236704
3629139723365823674236704
3972336582367423670436345
36582367423670436345
36742367043634 5
3670436345
00000000
0000000,0,
0,0.0.0.0.
0.0.0.0.0.
0.0.0.0.0.
0.0.0.0.
0.0.0.
0.0.
.0011
.0000
.0000
.0060
.0000
.0
.0
.0
.1202
.0000
.0003
.1879
.0000
.0
.0
.0
.0047
.0008
.0002
.0008,0
.0099
.00080021.00160
08540011000200
0129004500190
012200820013
00670115
00000000
00000000,
00.0.0,0,
0.0.0.0.0-
0.0.0.0.0.
0.0.0.0.
0.0.0.
0.0.
.0000
.0000
.0000
.0001
.0000
.0000
.0000
.0
.0017
.0018
.0048
.0210
.0051
.0019
.0037
.0
.0087
.0013
.0011
.0005
.0001
.0141
.0060
.00190013.0019
,0722,0191032603180140
0191000900330018
023500010055
01890088
00000000
00.0000,0,0,
0,0.0.0.0.
0.0.0.0.0.
0.0.0.0.0.
0.0.0.0.
0.0.0.
0.0.
.0000
.0044
.0110
.0000
.0188
.0257
.0287
.0228
.0001
. 1763
.3759
.0000
.5639
.7186
.8186
.7818
.0007
.0025,0046.0000,0009
0005,0099001800010002
00170075000200950409
0007001600000011
001500100012
00400008
ft?
APPENDIX IX
PAGE 1
APPENDIX IX
TABLE 1TB+3:LAF3 CENTERS OF GRAVITY
OBSERVED CALC O-C STATE
• • •
• • *
• • •
4423507455605814
205662631726529271112791928247• • •
28489290692934329595• • •
• • •
30750a a a
3149232998339423446635063• • •35344• • •• • •
3665737275• • •• • *• • •• a •
39287a • a
• • •
4091341447a • •
• • a
124217234394418510655615784
205682636026547270952789128231284112853229101293142958129655297343073431348
315033301533891344633505835060352553549836674367133726037606377223773238110
39297395154030940939414584147341817
• • •• • •• • •5
-310
30
-1-42-17162816
• • •-42-312914
• • a
• • •
16a • •
-10-165135
« • •89
a • •
a • a
-5515
• a •
a • •
• • a
• • •
-9a • •
• a a
-25-10• a •
• • •
7F67F57F47F37F27F17F0
5D45D35G65L105G55D25G45L95G35L85L75G25L65D15D0
5H75H65H55H45F55H35185F45F35175F25F1516514515
5K95D25G65K85K55G65K7
67
2 10262 1026
45
26735 0.0000 0.0007 0.00783849 0.0 0.3153 0.2089
J1
00000
111111111
222222222222
22222222222
333333333
LEVEL 1
57845784578 457845784
556155615561556155615561556155615561
510651065106510651065106510651065106510651065106
2823128231282312823128231282312823128231282312823128231
441944194419441944194419441944194419
J2
22446
123344567
223344455678
23344455678
334445568
PAGE 3APPENDIX IX
TABLEU(K)*2
LEVEL 2
5106282313439
20569125
556151064419
263603439
205692173125
29582
5106282314419
263603439
2056 9284122173
27892125
2958229315
282314419
263603439
20569284122173
27892265482958229315
4419263603439
20569284122173
27892125
29315
2FOR TB+3
(U2)*2
00000
0000,00,0,0,0,
0,0,0,0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.1391
.0010
.0
.0
.0
.1562
.0513
.2102
.0011
.0
.0
.0
.0
.0
.1002
.0010
.1829
.0014
.2224
.0011
.0016
.0
.0,0.0,0
,0168,0028,026900090362,060200000
027200073782002200251767001900
(U4)*2
0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0,0.1389,0017.0
,0,0,1273001317190025118800
121100102101002600600004000031350001048100
00800024005600050048000800270166025500
025300091343000500002504000123230
(06) *2
00000
00,00,00,0,0,0,
00.0,0.0,0,0,0.0,0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.1441
.0
.0
.0
.0
.0
.0
.0537
.3761
.00 93
.0
.0
.0
.0
.0324
.0001
.0005,2071.0014,4695,0157,0199
00,0,00000059021700061466351035792572
02780000157500 060026381600 2041290152
J 24355 4 26735 0.0215 0.0005 0.3633
11
3
33333333333
44444444444
4444444444
444444444
LEVEL 1
4419
2636026360263602636026360263602636026360263602636026360
34393439343934393439343934393439343934393439
2056920569205692056920569205692056920569205692056 9
284122841228412284122841228412284122841228412
J2
9
34445566789
444556678910
445566789
10
45566789
10
PAGE 4APPENDIX IX
TABLEU(K)*2
LEVEL 2
28532
263603439
20569284122173
27892125
26548295822931528532
343920569284122173
27892125
2654829582293152853227096
20569284122173
27892125
2654829582293152853227096
284122173
27892125
2654829582293152853227096
2FOR TB+3
(U2)*2
0
00000000000
0,0,0,00,0,0.0,0.0.0.
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0
.0000
.0065
.0535
.0058
.0005
.0837
.0
.0
.0
.0
.0
.0120
.0002
.0000
.5541
.0042
.0888
.0023
.0
.0
.0
.0
.0463,0004,0142,0046,0009113100,00
068200050285000101130000
(U4)*2
0
00000000000
0,0,0,00,00,0,0,0.0.
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0
.0021
.0001
.0291
.0228
.0028
.0303
.0002
.0341
.0035
.0
.0
.2792
.0022
.0006
.0120
.0009
.5159
.0000
.0029
.0014
.0,0
.0310,0051,0013,0631.00082067,03330104,00
01480000156 4000309032416001600
(U6) *2
0
00,0,0,0,0,0,0.0,0.0.
0.0,0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0255
.0027
.00 02
.0085
. 1398
.0016
.2981
.0014
.2412
.0221
.2546
.4161
,3500.0014,0068.43 74,0012.26 58,00 25,0069000401500322
00385115002239640013145703 36072327588669
00620021066500870677392000 3627360540
5 2173 5 21735 2173 5 278925 2173 6 125
0.2764 0.2071 0.317.90.0001 0.0002 0.00650.5377 0.6420 0.1178
Iff
44
2758627586
56
Jtujy26763
4907
U.0 .0 .
UU3408250012
0 .0 .0 .
000403220000
0 .0 .0 .
000303840000
11
55555
5555555
666666
66666
7777
LEVEL 1
21732173217321732173
27892278922789227892278922789227892
125125125125125125
2654826548265482654826548
29582295822958229582
J2
6789
10
566789
10
66789
10
6789
10
789
10
PAGE 5APPENDIX IX
TABLEU(K) * 2
LEVEL 2
2654829582293152853227096
27892125
2654829582293152853227096
1252654829582293152853227096
2654829582293152853227096
29582293152853227096
FOI2
I TB+3
( 0 2 ) * 2
0.0 .0 .0 .0 .
0 .0 .0 .0 .0 .0 .0 .
1 .0 .0.0 .0 .0 .
0 .0 .0 .0 .0 .
0 .0 .0 .0 .
00400002000
2578001202030115000
212500160006000000
58020464005900
0832082900030
(U4) *2
0.00280.00030.00190.00070 . 0
0.00010.00180.14660.10910.28770.00010 . 0
0.38810.00440.00010.00010.00190.0003
0.02880.00020.02560.25200.0068
0.44930.40470.03420.1037
(U6)*2
0 .0 .0 .0 .0 .
0 .0 .0 .0 .0 .0 .0 .
0 .0 .0 .0 .0 .0 .
0 .0 .0 .0 .0 .
0 .0 .0 .0 .
00 930066021001360015
05400131064830 75339605324457
02 7501160121022804550580
34 993264560771239143
2158087711390029
8 29315 8 293158 29315 9 285328 29315 10 27096
9 28532 9 285329 28532 10 27096
0.0509 0.6174 0.17990.0771 0.4809 0.12040.0000 0.0698 0.0803
0.0236 0.9206 0.17660.0727 0.4668 0.1548
10 27096 10 27096 0.0002 1.8580 0.3777
taX-stf
Iff
7 26357 10 28427 0.0 0.0000 0.0313
BLANK PAGE
•f: • • . •
APPENDIX X
•T/
' •''-<;.• 'A-.
(BSEEVE
0176912a184208307
• • •
3502• • •35763618363036453695
588259085924594459756020
76337665772877587801781478387842793379988077899290879074914491819235928293439435
102221028510345
:D CALC
222679106195216323335
3493357936163636363736713679
5873591059135931596 86021
761376547719mi78097839784 0785279388009809489749069907291399176924092779330944 7
102111026510336
PAGE 1
APPENDIX X
TABLI5 1DY+3:LAF3
O-C
-21-8-918
-10-7-15• • •
9• • •-39-17-6
-2516
9-1111370
20119
-18-7
-24-1-9-4
-10-161818255
-4513
-11
11209
STATE J
6H6H6H6H6H6H6H6H
6H6H6H6H6H6H6H
6H6H6H6H6H6H
6H6H6H6F6H6F6F6F6H6F6F6F6H6F6F6F6F6H6H6H
6H6H6H
15/215/215/215/215/215/215/215/2
13/213/213/213/213/213/213/2
11/211/211/211/211/211/2
9/29/29/211/29/211/211/211/29/211/211/^9/27/29/29/29/29/27/27/27/2
5/25/25/2
MJ
1/215/213/23/25/2
-11/2-9/2-7/2
13/2-7/23/25/21/2
-9/2-11/2
-7/2-11/2-9/25/23/21/2
5/2-9/23/21/2
-7/21/25/23/21/2
-7/2-9/25/23/2
-7/23/21/2
-9/2-7/21/25/2
5/21/23/2
36690.17 36706 -14 61 15/2 5/236700.50 36707 -5 61 15/2 13/2
BLANK PAGE
J
i _»
49849 6G 11/2 -9/2
)BSERVI
11037111091114011153
124561250412520
1327113285
• • •
2105721142211592120521395
2202222132221752218922213222922234222379
2346823497235132353723551* « •
• • •• • •
249902500825073• • •
250 98• • •
25195• • •
25303
!D CALC
11028111011114111143
124551249312512
1327713286
13827
2107121137211632120521393
2195622111221552218422209222722233222357
234572351223531235542357023616
2486524955249692498625097250972510225145252272522925272
PAGE 2
APPENDIX 3
TABLE 1DY+3:LAF3
O-C
98010
1118
-50
• • •
-135-302
66212054201022
11-14-17-16-18• • •
« • •• • •2122
-239 • •
-3• • • '-31• • «31
C
STATE J
6F6F6F6F
6F6F6F
6F6F
6F
4F4F4F414F
414141414F414141
4G4G4G4F4G4G
4H4H4M4M4H4H4M4H4N4H4M
7/27/27/27/2
5/25/25/2
3/23/2
1/2
9/29/29/29/29/2
15/215/215/215/215/215/215/215/2
11/211/211/211/211/211/2
21/^!21/221/221/221/221/221/221/221/221/221/2
HJ
5/21/2
-7/23/2
3/25/21/2
3/21/2
1/2
-9/25/23/2V2
-7/2
15/25/213/21/2
-7/2-9/2-11/213/2
-9/2-7/2
-11/25/23/21/2
-21/2-7/23/21/2
-9/2-11/2
5/213/215/2
-19/217/2
• 71
" 7 : - * > " ' V £ r "'••"•'?'
IBSEBVE
a • *
256612569125740257 4825778• • •
25824• • •
258492586'• • •• • •• • r
2590325918• • *
259402595325990
• • •
• • •
• • •
26260263582642926448265092657126583
2748227536
2758127624276 65
• • •279 19• * •
279882803628074
!D CALC
2558825647257132571625748258112581425819258312585925899259002590725910259202592925958259682597425986
26178261882619426228263482639626421264812651726527
2750827556
275862762627659
278412794427959280012800628035
PAGE 3
APPENDIX J
TABLH! 1DY+3:LAF3
O-C
• a •
14-21240
-32• • •5
• • •-9-31• • •• • *• • •-16-10• • •
-27-20
4
• • •• • •• • *32103327285456
-25-19
-4-16
• • •-24• • •-123039
STATE J
414141414F4K41414K414K414F4F4K4K4F4K4141
4M4M4H4H4M4H4H4M4M4H
4P6P
6P6P6P
414141414141
13/213/213/213/27/217/213/213/217/213/217/213/27/27/217/217/27/217/217/217/2
19/219/219/219/219/219/219/219/219/219/2
3/23/2
5/25/25/2
11/211/211/211/211/211/2
MJ
13/25/23/2
-7/21/2
17/2-9/2
-11/2-7/21/25/2
-9/2-7/23/21/23/25/2
15/2-11/213/2
-19/2-9/2-7/2
-11/213/25/23/21/2
17/215/2
1/23/2
5/23/21/2
-11/25/23/21/2
-7/2-9/2 •?"<•„ ' • " ' *
il
IBSERVE
2834728381
• • •
2853628577286132863628658286742871528734
• • «
• • •29535296382966729684297522978729855
29890• • *• * •• • •
• # •
29982• • •• • •
3007530141
• • •30243
* • •30302
3088730924
;D CALC
284092844828515285742860028632286532866228667287072876928797
2946729574296202962229688297322982529855
2991729945299492998429986299883003730047300663013130193302203026930293
3086830897
PAGE 4
APPENDIX X
TABLE: 1DY+3:LAF3
O-C
- 6 1-66• • •- 3 7- 2 2- 1 8-16
- 378
- 3 4• • •
• • •- 3 8
1845- 320
-370
-26• • •• • •• • •• • *
-5• • •• • •
910
• • •
23• • *
9
1927
STATE J
4K4K4H4H4H6P6P6P6P6P4H4M
4F41414F4F414141
464H4M4H4H4K4114K4K4M4G4G4G4G
6P6P
15/215/215/215/215/27 / 27 / 27 / 27 / 27 / 2
15/215/2
5 /29 / 29 /25 / 25 /29 / 29 / 29 / 2
9 / 217/217/217/217/217/217/217/217/217/2
9 /29 / 29 / 29 /2
3 /23 /2
HJ
15/25/23 /21/2
-7/23 /21/23 / 25 /2
-7/2-11/2
13/2
3 / 21 / 2
-9/25/21/2
-7/23 / 25/2
-7/25 /23 /2
17/2-9/2
1/215/2
-11/213/2-7/2
1/23 / 25/23 /2
1/23 /2
• s •••
5/2 41037 17/2 363450.00.0
0.00.0
tl
0.07150.1368
)BSEBVI
31055• • •
3113431169311943121131225• • •
312593128231294* • •
31328• • •• • •
3137931452• • •
3158031660• • •
31716
• • •• • •
• • •
• • •
33146• • •
33202• • •
332183323633256
• • •
3352733527335 27335273362333558
3366633652
!D CRLC
310613110131137311*23117131219312323123431250312823131531319313293134431348313823143131434
31570316553171231717
32060320893216932182
33149331793318633196332073321233225
33492335153351933520335233357833579
3364533646
PAGE 5
APPENDIX X
TABLE! 1DY+3:LAF3
O-C
-5• • •-21723-7-6• • •90
-20• • •
0• • •• • •-221
• • •
105
• « •0
• • •
• • •
• • •
• • •
-2• • •16
• • •
112431
• • •12674
45-20
216
STATE J
4K4K4K4L4K4K4L4H4M2L4L4H4H4K4L2L2L4K
4G4G4G4G
4D4D4D4D
4K4K4K4K4K4K4K
4H4H4H4H4H4K4H
4F4F
15/215/215/219/215/215/219/219/219/219/219/219/219/215/219/219/219/215/2
7/27/27/27/2
5/25/21/25/2
13/213/213/213/213/213/213/2
13/213/213/213/213/213/21V2
3/23/2
HJ
1/213/23/215/2
-11/25/2
-9/217/217/21/2
-9/25/2
-19/2-7/215/213/2
-11/2-9/2
5/23/21/2
-7/2
1/25/21/23/2
-11/2-7/213/23/21/2
-9/25/2
-9/213/25/23/213/2-7/21/2
1/23/2
)BSERVE
34029340403405234080
• • •
• # •
• • •
3424734250• • •• • m
m m •
3429834313
• • •
• • •
• • •
• * •
• • •
3436634393344 18344263447734466• • •
34525
348543487334904349143492534973
• • •• • •• * •
35940359663599436006360553605536080
iD CALC
34021340223403634058
3423634237342673427234284342843429334317343223432734328343453435434361343673438434418344373443934470344703448234502
348513487434902349063492934998
3578035781359103595 2359633598836008360543609536162
PAGE 6
APPENDIX X
TABLII 1DY+3:LAF3
O-C
8181622
• • •• • •• • a
-24-33• • #• • •• • m
-23-13• • •
• • •
a • •
• * *
• • •
-17-24-18-12
7-3
• • m
23
30286
-24
• • •• • *• m m
-1136-11
-39-81
STATE J
4D4D4D4D
4H4H4H4L4L4H4F4H4L4L4L4L4L4H4L4L4H4H4H4H4H4F4H
4G4H4H4G4G4G
4K4K4K4K4K4G4G4G4K4G
7/27/27/27/2
11/211/211/217/217/211/25/211/217/217/217/217/217/211/217/217/29/29/29/211/29/25/29/2
11/211/211/211/211/211/2
11/211/211/211/211/27/27/27/211/27/2
HJ
1/23/2-7/25/2
-9/2-7/2-11/2
3/21/2
-7/23/21/25/215/213/23/2
-11/2-7/2-9/217/2-9/21/2
-7/25/23/21/25/2
-9/2-7/25/21/23/2
-11/2
-9/21/2
-11/2-7/23/23/2
-7/21/2
-7/25/2
OBSERVED CALC
• • •• • •• • •
364943651236536
•#
#366 34• • •
366663665336686
3675236780* • •• • •• * •
• • •• • •• • •• • •• • •
37944• • •
37978
389 373899639090
3915239176
364673646936469365023652636543365443656436564365653658236586366043661036622366393664036677
367503678 5368123664036854
3763837672376813777737794
37948379773801138021381123821438223382963841638476
389083899439080
3916939192
PAGE 7
APPENDIX X
TABLE 1DY+3:LAF3
O-C STATE J
•••
-
•
m
•
•
•
•
•
•
• 4
m «
- ,
.. 4L
.. 4G
.. 4L-7 4L13 4L-6 4L.. 4L.. 4L.. 41.. 4L.. 4L.. 41.. 4G24 4G.. 4L29 4L13 4L9 4L
2 4G-4 4G.. 4G
4G4G
.. 4G
.. 4P4L
.. 4L. 4G
•3 2L. 4F32 2L.. 4F. 2L. 2L. 2L. 2L. 2L. 2L
29 4P
1
-1-1
2 4P0 4P
16 4P15 4P
13/25/215/215/213/215/213/215/215/213/213/213/25/25/213/215/215/213/2
9/29/29/29/29/2
7/21/27/27/27/2
15/23/215/23/215/215/215/215/215/215/2
5/25/25/2
3/23/2
HJ
5/21/23/21/2
-7/213/2-9/215/25/21/2
13/23/25/23/2
-11/2-7/2-9/21/2
-7/23/2
-9/2-7/21/2
3/21/25/2
-7/21/2
15/21/2
-7/23/2
-9/25/21/2
-9/2-11/213/2
3/25/21/2
3/21/2
PAGE 8
APPENDIX X
TABLE 1ADY+3:LAF3 CENTERS OF GRAVITY
CALC CENTER STATE
1753626595278067853916692231027311070124711326713814
212282222223563251092579425 85625890263342754327624
6H15/26H13/26H11/26H 9/26F11/26F 9/26H 7/26H 5/26F 7/26F 5/26F 3/26F 1/2
4F 9/24H15/24G11/24B21/24113/24F 7/24K17/24H19/26P 3/26P 5/2
333
441944194419
568
27892125
29315
0.0.0.
001900
0.0.0.
000123230
0.0.0.
002041290152
• ' • • * ( •
J1
1/21/21/21/21/21/2V21/21/21/21/21/21/21/21/2
3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2
3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2
LEVEL
138141381413814138141381413814138141381413814138141381413814138141381413814
132671326713267132671326713267132671326713267132671326713267132671326713267
2754327543275432754327543275432754327543275432754327543275432754327543275432754327543
1 32
3/23/25/25/25/27/27/27/29/29/211/211/211/213/213/2
3/25/25/25/2V27/27/29/29/2
11/211/213/213/215/215/2
3/25/25/25/27/27/27/29/29/29/211/211/211/213/213/215/215/2
PAGEAPPENDIX
TABLE 2U(K)*2 FOE
LEVEL 2
132672754310273124712762492231107025856780691665952785323563362625794
275431027312471276249223
11070258567806916659527853362625794
17522222
2754310273124712762492231107025856780691662122859527853 .
235633626
25794175
22222
9X
DY+3
(U2)*2
000000000000000
0000,00,00.0,0,0,0,0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0175
.0665
.1918
.0100
.0147
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.1391
.1396
.0222
.0964
.2421
.0134
.0000
.0
.0
.0
.0
.0
.0
.0
.0
,0572,0007,1151,0185,0004,042019070,0,00000000
(U4)*2
0000000000,00,0,0,0,
0,0.0,0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0
.1394
.0294
.0156
. 1512
.0060
.0
.0
.0
.0
.0
.0
. 1346
.0260,0227.1179,0104.0212, 1224,03111935,0166, C,000
00743002300000494017904790393075710310072173104170000
(U6)*2
000000000000,0,0.0,
0,0.0.0.0,0.0.0.0.0.0.0.0.0.0.
c.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.3478
.0050
.0020
. 1001
.0013
.0,0.0,0.0,0.0, 3636,01120390,03533950.007606110014
00000000089000901140070000002960016153105080051
5 2173 5 27892 0.0001 0.0002 0.00655 2173 6 125 0.5377 0.6420 0.1178
J1
5/25/25/25/25/25/25/25/25/25/25/25/25/25/25/2
5/25/25/25/25/25/25/25/25/25/25/25/25/2
5/25/25/25/25/25/25/25/25/25/25/25/25/25/2
7/27/27/27/27/2
LEVEL
102731027310273102731027310273102731027310273102731027310273102731027310273
12471124711247112471124711247112471124711247112471124711247112471
276242762427624276 2427624276 242762427624276242762427624276242762427624
92239223922392239223
U
1 J2
5/25/25/27/27/27/29/29/29/211/211/211/213/215/217/2
5/25/27/27/27/29/29/29/2
11/211/213/213/215/2
5/27/27/27/29/29/29/211/211/211/213/213/215/217/2
7/27/27/29/29/2
PAGE 10APPENDIX
TABLE 2(K) *2 FOB
LEVEL 2
1027312471276249223110702585678069166
2122859527853235633626175
2S890
12471276249223110702585678069166
2122859527853362625794
175
276249223110702585678069166
2122859527853
235633626
25794175
25890
9223110702585678069166
X
DY+3
(U2)*2
000000000000000
000,0,0,0.0.0,0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.
.3736
.0379
.0000
.2143
.0044
.0007
.0237
.0000
.0000
.0
.0
.0
.0
.0
.0
.0007
.2868
.1943
.0439
.0059
.3358
.0095
.0062
.0
.0
.0
.0,0
,2570,00004684,09100011,498100870000000
26180511003130350039
(U4)*2
00000000000,00,00.
0,0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.
.0659
.2727
.0302
.1919
.1315
.0059
. 1300
.0182
.0035
.0236
.0031
.0007
.0012
.0
.0
.0171
.0890
.0583
.0033
.0188
.1045,0333.0008,1971,0503,2103,0008,0
00040997186601461621255100463230163801991722009800
00872930004515341255
(U6)*2
000000000000000
000.0,0.0,0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.
.0
.0
.0
.0758
.4393
.0113
.3127
.3551
.0011
.2993
.0177
.0014
.0590
.0026
.0024
.0
.0
.4192
.0087
.0005
.0390
.0301
.0004, 1557.0898,2852,0007,3446
0,01440000,00050279,000001100564002902830820001007210633
28590000023101324498
J1
7/27/27/27/27/27/27/27/27/27/2
7/27/27/27/27/27/27/27/27/27/27/27/27/2
7/27/27/27/27/27/27/27/27/27/27/27/27/2
9/29/29/29/29/29/29/29/29/29/29/2
LEVEL
9223922392239223922392239223922392239223
11070110701107011070110701107011070110701107011070110701107011070
25856258562585625856258562585625856258562585625856258562585625856
78067806780678067806780678067806780678067806
1 J2
9/211/211/211/213/213/215/215/?17/219/2
7/27/29/29/29/211/211/211/213/213/215/217/219/2
7/29/29/29/2
11/211/211/213/213/215/215/217/219/2
9/29/29/211/211/211/213/213/215/215/217/2
PAGE 1APPENDIX
TABLE: 2U(K) *2 FOR
LEVEL 2
2122859527853
235633626
25794175
222222589026334
110702585678069166
2122859527853
235633626
25794175
2589026334
2585678069166
2122859527853
235633626
25794175
222222589026334
78069166
212285952785323563362<>
25794175
2222225890
1X
DY+3
(U2) *2
0000000000
0000000,0,0.0,0,0,0,
0,0,0.0,0,0.0.0.0.0.0-0.0.
0.0.0.0.0.0.0.0.0.0.0.
.0008
.0348
.0004
.0001
.0
.0
.0
.0
.0
.0
.0016
.0102
.2267
.0630
.0002
.4449
.0344
.0107
.0
.0
.0
.0
.0
.0512
.0027
.0544
.0465
.0405
. 1014
.0872
.0,0.0,0.0,0
,3081,0424,0021,34460037,000203380057000
(U4)*2
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
,0079, 1465.03060044,03090034,00060016,00
027402431387,00520043,05030344000042170015135200
0275007402660838031801981410011137560695038900
0160J327002416621159007417120000016600770202
(U6)*2
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.
0067342614380013276300010393000300210082
0267000425080435002925210843000000000076713800730156
0123011200083307002000012588032100070260004503932900
26841716003201374969000039210040201700000000
J1
9/2
9/29/29/29/29/29/29/29/29/29/29/29/2
9/29/29/29/29/2V29/29/29/29/29/2
11/211/211/211/211/211/211/211/211/211/2
11/211/211/211/211/211/211/211/211/2
11/211/2
LEVEL
7806
916691669166916691669166916691669166916691669166
2122821228212282122821228212282122821228212282122821228
5952595259525952595259525952595259525952
785378537853785378537853785378537853
2356323563
1 J2
21/2
9/29/211/211/211/213/213/215/215/217/219/221/2
9/211/211/211/213/213/215/215/217/219/221/2
11/211/211/213/213/215/215/217/219/221/2
11/211/213/213/215/215/217/219/221/2
11/213/2
PAGE 1APPENDIX
TABLI! 2U(K)*2 FOE
LEVEL 2
25109
91662122859527853235633626
25791*175
22222258902633425109
2122859527853
235633626
25794175
22222258902633425109
59527853
235633626
25794175
22222258902633425109
7853235633626
25794175
22222258902633425109
235633626
2X
DY+3
(U2)*2
0
000000000000
000000000.0.0,
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
0.0.
.0
.0313
.0007
.2561
.0239
.0061
.6670
.0012
.0
.0
.0
.0
.0
.0226
.0093
.0032
.4708
.0490
.0068
.0
.0
.0
.0
.0
.4989
.0021
.0001
.2547,0032.0912,0049,00,0
1428015b2518000493940020000
35770012
(U4)*2
0
000000000000
000,0000.0,0.0,0.
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
0.0.
.0
.0106
.0055
.3942
.0190
.0001
.0236
.0167
.5746
.0126
.0321
.0
.0
.2572
.0018
.0032
. 1686
.0164
.0418
.0046
.5584
.4557
.0
.0
.0328,19190001,49330031,03690026004202130
138500014^48006882990270003700010
05550299
(06) *2
0
000000000000
00000,00,0,0.0.0.
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
0.0.
.0226
.0428
.0004
.0114
.0154
.0085
.3778
.0082
.7186
.0063
.0132
.0425
.0919
.3827
.0033
.0024
. 1511
.0545
.3971
.0292
.0182
.0315
. 1410,9115
,0498.8336001903000221,63920006C11303300376
062400837751003820610022003602080318
01270065
J1
11/211/211/211/211/211/2
13/213/213/213/213/213/213/2
13/213/213/213/213/213/2
15/215/215/215/215/2
15/215/215/215/2
17/217/217/2
19/219/2
21/2
IEVEL
235632356323563235632356323563
3626362636263626362636 263626
257942579425794257942579425794
175175175175175
22222222222222222222
258902589025890
2633426334
25109
1 J2
13/215/215/217/219/221/2
13/213/215/215/217/219/221/2
13/215/215/217/219/221/2
15/215/217/219/221/2
15/217/219/221/2
17/219/221/2
19/221/2
21/2
PAGE 1APPENDIX
TABLf: 2U(K)*2 FOE
LEVEL 2
25794175
22222258902633425109
362625794
17522222258902633425109
25794175
22222258902633425109
17522222258902633425109
22222258902633425109
258902633425109
2633425109
25109
3X
DY+3
(U2)*2
000000
0000000
000,0,0,0,
1.0,0,0.0.
0.0.0.0.
0.0.0.
0.
c.0.
.0000
.0004
.1356
.0
.0
.0
.7945
.0014
.2454
.0049
.0022
.0
.0
.5060
.0039
.0220
.0009
.0
.0
.3310
.0071
.0101
.0002
.0
.4738,2741,0014,0
12638045,0018
04287683
6719
(04)*2
0000.00,
0,0.0.00,0,0.
0.0,0.0.0.0.
0.0.0.0.0.
0.0.p.0.
0.0.1.
0.0.
1.
.0053
.0141
.0812
.0981
.4117
.0
.0738
.0003
.4136
.0041
.0044
.0049
.0034
.2108
.0012
.0103
.1791,2761,0878
,64520003,00420139,0101
4363054 849092399
073303612616
06123865
2335
(U6)*2
0.0.0.0.0.0.
0.0.0.0.0.0.0.
0.0.0.0.0.0.
0.0.0.0.0.
0.1.1.0.
0.0.0.
1.0.
0.
5958000 39026769453936624
1064000468340107000100260037
1877024 90886008100294522
42660659090509680808
5634288902518452
134602650075
68291317
8622
APPENDIX XI
PAGE 1
APPENDIX XI
TABLE 1HO+3:LAF3 CENTERS OF GRAVITY
iSERVED
05146856811123• • •
15420183971852H20596210562127922187• • •
2394225872260872767227672• • •
28878288782994329943307S5• • •• • *
34100341003481135206
• • •
• • •
• • •
« • •
36724• • •• • •
38378• • •
' CALC
950648578
1114513212
15456183811853820594210392126722179222552398725859260582765227678282342887528895299412994730799330633324734072341563481235203360083600936294363143672037794379003833938515
0-C
82-9
-21• • •
-3516
-13217128
• • •-44132920-5
• • •
3-16
2-3-3• • •• • •28
-5503
• # •• m •
• • •
« * •
4• • •* • •39
a • •
STATE
518517516515514
5F55S25F45F35F23K85G65F15G55G43K75G53H65F25G33L93K6.3F45G23D 33P13M103L85G43G33P05D43F21L83H53P23L73173F4,
25303 25272 31 4M 21/2 17/2
{•, . " .
M
000000
111111111111111
2222222222222222
2222222222
LEVEL 1
360083600836008360083600836008
222552225522255222552225522255222552225522255222552225522255222552225522255
18381183811838118381183811838118381183811838118381183811838118381183811838118381
21040210402104021040210402104021040210402104021040
32
244666
122344455556677
2234445555666778
2344455556
PAGE 3APPENDIX XI
TABLEU(K) *2
LEVEL 2
2104013212185388579
2218027679
2225518381210402059513212185382585911146154572398827653857 9
221805065
26059
183812104020595132121853825859111461545723988276538579
22180276795065
260599
2104020595132121853825859111461545723988276538579
2FOR HO+3
(U2)*2
000000
000000000000,00,0,
0,0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0027
.0
.0
.0
.0
.0
.0302
.0109
.0539
.0084
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0
.0000
.0016
.0065
.0014,0000.0328.0.0,0,0,000000
0077052100050085260800000
(U4) *2
000000
000000000000,0,0,0,
0.0.0,0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0
.0089
.0013
.0
.0
.0
.0
.0
.0
.0586
. 1442
.0468
.0564
. 1396
.0000
.0070
.0074
.0
.0
.0
.0
.0016
.0035
.0000
.0302
.0159
.2811,0052.0123,1062,0570,024031280437000
0271000020110805001204730052142312331365
(06) *2
000000
000000000000,0,0,0.
0,0,0.0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0175
.0351
.0805
.0
.0
.0
.0
.0
.0
.0
. 1704
.1.147
.0537
.0548
.2383
.0528
.0568
.0020
.0
.0
.0
.2839,0033,0216.0968,005000040006145800470065419505532145
0002 930317120430241466011500121604
BLANK PAGE
• • > > " ;
J1
222222
3333333333333333
444444444444444
4444444444
LEVEL 1
210402104021040210402104021040
20595205952059520595205952059520595205952059520595205952059520595205952059520595
132121321213212132121321213212132121321213212132121321213212132121321213212
18538185381853818538185381853818538185381853818538
J2
667788
3444555566677889
44455556667788
10
4455556667
PAGE 4APPENDIX XI
TABLEU(K)*2
LEVEL 2
22180276795065
260599
21268
20595132121853825859111461545723988276538579
22180276795065
260599
2126828896
132121853825859111461545723988276538579
22180276795065
260599
2126834072
1853825859111461545723988276538579
22180276795065
2FOR HO+3
(U2)*2
000000
0000000000000000
0,0,0.0,0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0
.0
.0358
.0002
.0973
.2147
.0000
.0396
.1800
.1544
.0
.0
.0
.0
.0
.0
.0
.0
.1222
.0002
.0152
.0310
.0001
.0000
.0036
.0023,00050000,00,0.0,0
0770396200161980275129740011252601030
(U4)*2
000000
0000000000000,00,0,
0,0.0,0,0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
.0225
.0068
.0
.0
.0
.0
.0637
.0982
.0298
.0176
.2173
.0816
.1005
.0474
.0897
.0655
.0112
.2463
.0068
.0
.0
.0
.1308
.0241
. 1072,1237.0061.0091.0097,0282,0013,000000340006,000000460
0085105213340920023800252574238002101965
(U6) *2
000000
000000000,00,00,00,0,
0.0.0.0.0,0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
. 1010
.00 99
.0789
.0550
.2041
.0036
.0275
.3949
.0966
.0509
.0175
.0851
.0325
.0059
.2172
.1526
.0509
.2279
.0049
.3464
.0067
.0012
.3456
.2576
.0555,9103.0036,0418,00086639,000002001568006800 7600120019
0886021746660071139505171704128902590320
33666 3364533652 33646
21 4F6 4F
6//.3/2 3/2
J1
44444
44444444444444
5555555555555
555555555555
55
LEVEL 1
1853818538185381853818538
2585925859258592585925859258592585925859256592585925859258592585925859
11146111461114611146111461114611146111461114611146111461114611146
154571545715457154571545715457154571545715457154571545715457
2398823988
J2
788910
4555566677889
10
555566677889
10
55566677889
10
55
PAGE 5APPENDIX XI
TABLEU(K) *2
LEVEL 2
260599
212682889634072
25859111461545723988276538579
22180276795065
260599
212682889634072
111461545723988276538579
22180276795065
260599
212682889634072
1545723988276538579
22180276795065
260599
212682889634072
2398827653
2FOR HO+3
(U2)*2
00000
0000000000.0,0,0,0,
0.0,0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.1.0.0.0.0.0,0.0,
0.0.
.0
.0
.0
.0
.0
.0098
.2254
.0345
.0128
.0415
.6896
.0036
.0030
.0
.0
.0
.0
.0
.0
.1023
.0071
.0031
.0040
.0435
.0171,0004.0028.0072.0,0,0,0
072934250907011313051113019400150000
07060263
(04)*2
00000
00000000,0,00.0,0,0,
0,0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.
.0156
.2385
.0085
.0
.0
.0138
.2700
.0138
. 1484
. 1417
.0226
.2047
.0067
.2857
.0152
.0351
.0919
.0
.0
.0364
.0281
.0642
.0487
.1703,0312,0011,0226,00420102000402530
181503531752124236160000330901124201025806080
04730132
(U6) *2
00000
00000000000.00,0
0,0,0,0,0,0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.
0.0.
.0091
.7090
.0007
.0093
.0417
. 1812
.0329
.2147
.02 68
.0182
.0003
.2909
.00 93
.06 42
.0044
.0332
.0013
.0492
.2687
.0176
. 1630
.0568
.0418
.5720,0124.0153, 88 96.03120930,004102420368
005011450483497203210002429801425701019007411693
01392050
J1
555555555
55555c.5555
666666666
66666666
6666666
77
LEVEL 1
239882398823988239882398823988239882398823988
27653276532765327653276532765327653276532765327653
857985798579857985798579857985798579
2218022180221802218022180221802218022180
27679276792767927679276792767927679
50655065
J2
66677889
10
566677889
10
6' 6677889
10
667788910
677889
10
77
PAGE 6APPENDIX XI
TABLEU(K) *2
LEVEI 2
857922180276795065
260599
212682889634072
276538579
22180276795065
260599
212682889634072
857922180276795065
260599
212682889634072
22180276795065
260599
212682889634072
276795065
260599
212682889634072
506526059
2FOB HO+3
(U2)*2
000000000
00
.1286
.0565
.1987
.5696
.0164
.0
.0
.0
.0
.0360
.09490.00050000000,
0,0,0,0,0.0.0.0.0.
0.0.0.0.1.0.0.0.
0.0.0.0.0.0.0.
0.0.
.1501
.7003
.0036
.0
.0
.0
.0
.1273
.0091
.0001
.0314
.0011,0087,0059,0.0
,0025,0509,148400004830,0000,0,0
14990314004G2540107700
15020055
(U4)*2
000000000
00000,0,0,0,0.0,
0.0,0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.
0.0.
.1695
.2568
.0657
.0240
.0059
.5239
.0083
.3321
.0
.0058
.2452
.0711
.5825
.1913
.0104
.0938
.0051
.1803
.0
.0681
.0819
.0051
.1324,0057.0389,0041,0071,0177
,3968,2992428400038201004804020455
1032058605021399110911813381
11930059
(U6) *2
000000000
0.00,00,0,0.0,0.0.
0.0,0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
0.0.0.0.1.0.0.
0.0.
.0789
.24 56
.0168
.1171
.2487
.00 00
.0007
. 1702
.3522
.0012
.0460
. 1580
.00 00
.0584
. 4bO6
. 1596
.0214
. 1726
.2616
.0402
.1094
.0024
.9295,07 22,69200142,0357,0211
120900692633123914 00307628101696
0418008768540013598582 882755
02970047
39152 39169 -16 UP 3/2 3/239176 39192 -15 4P 3/2 1/2
PAGE 7APPENDIX XI
TABLE 2U(K)*2 FOR HO+3
J1 LEVEL 1 J2 LEVEL 2 (02) *2 (U4) *2 (06) *2
7777
77777
00 00 C
O 00
00 0
0 00
99
10
5065506 550655065
2605926059260592605926059
9999
212682126821268
2889628896
34072
88910
788910
88910
8910
910
10
9212682889634072
260599
212682889634072
9212682889634072
212682889634072
2889634072
34072
0.02490.00180.00090.0
0.00160.00560.08650.07880.0
0.19510.02050.01790.0003
0.02600.31630.0134
0.68580.7340
3.3219
0.13440.00440.00410.0003
0.02230.00440.00020.19630.3112
0.31170.03170.00510.0681
0.04650.05681.0322
1.35471.4855
0.0011
1.52310.04020.01030.0059
0.01750.03350.12230.13910.3289
1.54600.15350.14990.0789
0.20192.04950.8500
0.02910.5524
1.4872
APPENDIX XII
3/2 27543 15/2 175 0.0 0.0 0.05083/2 27543 15/2 22222 0.0 0.0 0.0051
I
)BSEBVI
051
121200219314400443
6604663066706700672367546823
103011031110330103441035810395
1241912518126151270112730
1539115432154431547415527
1855718588
192661930719314193591935919418
20656207032073420786
PAGE 1
APPENDIX XII
!D CALC
-950121188198310397442
6607663966776696673067656835
102991030910336103481035910408
1240112535126051270512725
1539 31543915447154761552 9
1855 918588
192711929619318193441935019403
20655206982073620788
TABU! 1ER+3:LAF3
O-C
10101222431
-2-8-64-6
-10-11
22-5-30
-12
18-1610-35
-1-6-3-1-1
-10
-411-315915
15
-1-1
STATE J
4141414141414141
41414141414141
414141414141
4141414141
4F4F4F4F4F
4S4S
2H22H22H22H22H22H2
4F4F4F4F
15/215/215/215/215/215/215/215/2
13/213/213/213/213/213/213/2
11/211/211/211/211/211/2
9/29/29/29/29/2
9/29/29/29/29/2
3/23/2
11/211/211/211/211/211/2
7/27/27/27/2
HJ
13/2-11/2
3/25/21/2
-9/2-7/215/2
-11/2-9/2-7/21/23/25/213/2
-9/2-7/21/23/25/2
-11/2
7/21/23/25/2
-9/2
5/23/2
-7/23/21/2
3/21/2
1/2-9/2-11/2-7/23/25/2
-7/21/25/23/2
7/27/2
9223 9/29223 9/2
7806 0.3035 0.1534 0.01329166 0.0039 0.1255 0.4498
)BSEEVI
223702237422407
22684227 51
2460224680247E42484024862
265302655826583266472664726709
276C627620276312764627671
278 1327820278302790427935• • •• • «
28127
• • •282432825728265
3168831746
• • •3310633119331673320133201• * •
PAGE 2
APPENDIX XII
SD CALC
223642236922399
2268922741
24580247102474824«4024858
265362656726587266502665026713
2761027617276242763927665
2781627823278512789127939279592798828135
28221282402824928252
3171131765
3309433105331423315333203332063331733405
TABLE 1£R+3:LAF3
o-c
659
-410
22-29604
-8-3-2-2-3
-33776
-2-2
-2013-3
• • •• • •
-7
• • •3813
-22-18
• # •3
-2214-1-4* • •• • •
STATE J
4F4F4F
4F4F
4F4F4F4F4F
4G4G4G4G4G4G
4G4G4G4GHG
2K2K2K2K2K2K2K2K
4G4G4G4G
2P2P
2K2K2K2K2K2K2P2K
5/25/25/2
3/23/2
9/29/29/29/29/2
11/211/211/211/211/211/2
9/29/29/29/29/2
15/215/215/215/215/215/215/215/2
7/27/27/27/2
3/23/2
13/213/213/213/213/213/2,1/213/2
MJ
5/21/23/2
3/21/2
-7/21/23/25/23/2
1/2-11/2
3/25/2
-9/2-7/2
-9/2
V23/25/2
-7/2
-9/2-7/2-11/2
5/23/213/21/215/2
5/2-7/23/21/2
3/21/2
-9/2-7/2
-11/25/21/23/21/2
13/2 ol
!••*?. ' "
9/29/2
78067806
15/217/2
2222225890
00
.0
.0
.0
000
. U Ibb
.0077
.0202
u.0.0.
00000000
PAGE 3
APPENDIX XII
TABLE 1EB+3:LAF3
OBSERVED CALC O-C STATE J MJ
261.Ol
ft • ft
• • •
• • •
34157341963422134260
350263505235085
3652236555366243672136805
388043884138834
394 54395393960639634
412384129741315
a • «
4138241497
• • •• • •• • •• • •• • •• • •• • •• m •
• • •
4249542526
4308843126
334823349433613
34167341973422834284
3504 23505335092
3652936537366363672136792
387943884 338844
39487395283960639638
412354130241330 ••413*714139141492
41809418334187441875419004192641980 .42071 .42087
4247142500
4309643121
• • •• • •• • •
-90-6-3
-150
-6
-618
-11013
10-1-9
-32110
-3
3-4-14• • •-95
> • •• • •» • •• •
» • •• •• •• •a •
2426
-75
4G464G
4G4G4G4G
2D12D12D1
2H22H22H22H22H2
4D4D4D
4D4D4D4D
212121212121
2L21212L2L2L2L2L2L
4D4D
4D4D
5/25/25/2
7/27/27/27/2
5/25/25/2
9/29/29/29/29/2
5/25/25/2
7/27/27/27/2
11/211/211/211/211/211/2
17/217/217/217/217/217/217/217/217/2
3/23/2
3/23/2
1/25/23/2
-7/23/2
V25/2
3/25/21/2
-9/25/23/21/2
-7/2
3/25/21/2
1/23/2
-7/25/2
5/23/2
-11/2-7/21/2
-9/2
-7/2-9/21/25/23/2
-11/213/217/215/2
3/21/2
1/23/2
" • > - . • • " ,
11/2 23563 11/2 2356311/2 23563 13/2 3626
0.3577 0.0555 0.01270.0012 0.0299 0.0065
PAGE 4
APPENDIX XII
TABLE 1EH+3:LAF3
OBSERVED CALC O-C STATE J MJ
436874374643746437604383443915
• • •
• • •
• • •
• • •
• • •
• • •
• a •
• • •
• • •
• • •
a • •
• • «
• • •
• a •
492234927249357
• • •• • •
* • «
• • •
* • a
• • •
43709437224372843749438214390943968
47313
4794147989479994801548035480974819348194
4837148374484274848348513
492104928749349
512955135551370514415151051512
-21241811136
• • •
• * •
# • •• • •• • •
• • •
• • •
• • •
• • •
• • •
• * a
* • •
* • •
• • •
• • •
13-14
8
• • •• • •• • a
a • •
• a •
• a a
21212121212121
4D
212L2L2L2L2L2L21
2H12H12H12H12H1
2D22D22D2
2H12H12H12H12H12m
13/213/213/213/213/213/213/2
1/2
15/215/215/215/215/215/215/215/2
9/29/29/29/29/2
5/25/25/2
11/211/211/211/211/211/2
5/21/23/213/2-7/2-9/2-11/2
1/2
-9/2-7/23/21/25/2
-11/215/213/2
5/23/21/2
-9/2-7/2
3/21/25/2
1/23/2
-11/25/2
-9/2-7/2
PAGE 5
APPENDIX XII
TABLE 1AER+3:LAF3 CENTERS OF GRAVITY
CALC CENTER
217671285831034612597
154551933720 715223762271224756
2663127637279222822433319
STATE
4115/24113/24S 3/24111/241 9/2
4F 9/22H11/24F 7/24F 5/24F 3/24F 9/2
4G11/24G 9/22K15/24G 7/22P 1/2
,5 , • 'J' " > -
J1
1/21/2V21/21/21/21/21/21/21/21/2
3/23/23/23/23/23/23/23/23/23/23/23/23/23/23/2
3/23/23/23/23/23/23/23/23/23/23/23/23/2
5/25/25/25/25/25/25/25/2
LEVEL
3331933319333193331933319333193331933319333193331933319
185831858318583185831858318583185831858318583185831858318583185831858318583
22712227122271222712227122271222712227122271222712227122271222712
2237622376223762237622376223762237622376
1 J2
3/23/25/27/27/29/29/29/2
11/211/211/2
3/23/25/27/27/29/29/29/29/211/211/211/213/215/215/2
3/25/27/27/29/29/29/29/2
11/211/211/213/215/2
5/27/27/29/29/29/29/211/2
PAGEAPPENDIX
TABLI! 2U(K)*2 FOB
LEVEL 2
1858322712223762071528224125971545527637103461933726631
1858322712223762071528224125971545524756276371034619337266316712217
27922
22712223762071528224125971545524756276 371034619337266316712217
2237620715282241259715455247562763710346
7XII
ER+3
(U2)*2
00000000000
00000.0,00,0,0,0,0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
.0057
.0353
.0073
.0
.0
.0
.0
.0
.C
.0
.0
.0371
.0266
.0077
.0000
.0475
.0
.0
.0
.0
.0
.0
.0
.0,0.0
,0709,0b05.0027,0961,0,0,0000000
01520765 '383101010005009216500
(04)*2
00000000000.
000,0.0,0.0,0.0,0,0.0.0,0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
.0
.0
.0
.0204
.0263
.0272
.0460
.0083
.0
.0
.0
.0
.0
.0036
.0055
.1631
.0765
.0001
.0036
.1659
.0046
.2002, 1282.0,0.0
,0,0351,0577034223380022,0188171109130004023200
00500498001706292345021908460984
(U6)*2
00000000000
0000.00,0,0.00,0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0
.0
.0
.0
.0316
. 1686
.0264
.0
.0
.0
.0
.0
.2569
.0228
.0014
.0103
.0773
.0097
.0040
.3419,2225,0035
,0,0,00054506160057112448310025090703471255
00998038011293491005600240028
22
2104021040
5 276536 8579
0.00.0
0.12330.1365
0.00120. 1604
i .•Kγmm
J1
5/25/25/25/25/2
7/27/27/27/27/27/27/27/27/27/27/2
7/27/27/27/27/27/27/27/27/27/27/2
9/29/29/29/29/29/29/29/29/29/2
9/29/29/29/29/29/29/29/29/2
LEVEL
2237622376223762237622376
2071520715207152071520715207152071520715207152071520715
2822428224282242822428224282242822428224282242822428224
12597125971259712597125971259712597125971259712597
154551545515455154551545515455154551545515455
0
1 J2
11/211/213/215/215/2
7/27/29/29/29/29/2
11/211/211/213/215/2
7/29/29/29/29/2
11/211/211/213/215/215/2
9/29/29/29/211/211/211/213/215/215/2
9/29/29/211/211/211/213/215/215/2
PAGEAPPENDIX
TABLEi 2(K) *2 FOR
LEVEL 2
19337266316712217
27922
20715282241259715455247562763710346
19337266316712217
28224125971545524756276371034619337266316712217
27922
125971545524756276371034619337266316712217
27922
1545524756276371034619337266316712217
27922
8XII
ER + 3
(02)*2
00000
00000000000
000,0,0,0,0,0,0.0.0.
0.0.0.0.
c.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0
.0
.0
.0
.0
.1542
.1221
.0155
.0119
.0894
.6234
.0032
.1258
.0867
.0
.0
.0033
.1649
.0000
.0152
.0034
.5073
.0006
.0140
.0
.0
.0
.0040
. 1220,0138.00410021.1953,0631,0003,00
136900752170071537904283010900
(04)*2
00000
00000,00,00,00,
0,00.0.0.0,0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.0.0.
.0581
.0373
.1794
.0
.0
.0103
.0409
.0935
.0372
.0483
.0067
.2653
.0164
. 1264
.3393
. 1465
.0048
.3703
.0123
.0052
. 1887
.2776
.0393
.0544
.0997
.0200, 1206
.0782
.00610066,00600690,06480122008715872101
075102613167010102360372153355i"'0867
(06) *2
00000
00000,0000,00
0,00.0.0.0,0.0.0.0.0.
0.0.0.0.0.0.0.0.0.0.
0.0.0.1.0.0.0.0.0.
. 1847
.0806
.3419
.2221
.0472
. 1001
.0070
.4337
.0109
.0273
. 1194
. 1545
.3984
.0168
.0001
.6272
.0005
.2168
.0163
.0244
.1494
.1616
.2710
.0177,0310
.1171,0048
,7932,0203,0032,0049152028370228710000720969
050704693650267100080112082846210142
I * ' " " .
PAGE '9APPENDIX XII
TABLE 20(K) *2 FOR ER + 3
J1 LEVEI 1 J2 LEVEL 2 (U2) *2 (U4) *2 (U6) *2
9/29/29/29/29/29/29/29/2
9/29/29/29/29/29/29/2
11/211/211/211/211/211/2
11/211/211/211/211/2
11/211/211/211/2
13/213/213/2
15/215/2
15/2
2475624756247562475624756247562475624756
27637276372763727637276372763727637
103461034610346103461034610346
1933719337193371933719337
26631266312663126631
671267126712
217217
279 22
9/29/211/211/211/213/215/215/2
9/211/211/211/213/215/215/2
11/211/211/213/215/215/2
11/211/213/215/215/2
11/213/215/215/2
13/215/215/2
15/215/2
15/2
24756276371034619337266316712217
27922
276371034619337266316712217
27922
1034619337266316712217
27922
19337266316712217
27922
266316712217
27922
6712217
27922
21727922
27922
0.0.0,0.0.0.0.0.
0.0.0.0.1.0.0.
0.0.0.0.0.0.
0.0.0.0.0.
0.0.0.0.
0.0.0.
0.0.
1.
.0165,0251.0381,0285,2951,0590,0,0
0018,0937023700001078,00
078403520002033202760463
00210004023571581010
0049100591560998
172301950001
24630213
8431
0.0.0.0.0.0.0.0.
0.0.0.0.0.0.0.
0.0.0.0.0.0.
0.0.0.0.0.
0.0.0.0.
0.0.0.
0.0.
1.
,05460004,07531635.1068,1059,02437139
0153,160134632117367223370056
036413850486170600020017
07261513062141380000
2513264852630579
173111720015
38030039
0174
0.53960.03280. 10470.06100.14140.35310.21470.0822
0.00780.01680. 15700.15160.01060. 13680.0558
0.02770.03720.01331.09150.39420.2426
0. 10680.04980.05020.09271.1445
0.06690.25700. 11670.6787
0.22981.43250.0257
1.86110.0735
0.0676
* . 'i
i - •••:-•<&'
A P P E N D I X X i l l
PAGE 1
APPENDIX XIII
TABLE 1TM+3:LAF3 CEHTERS OF GRAVITY
OBSERVED CALC O-C STATE
20058588336127111455915173
21352
28061
34886
356043655938344
• • •
17558188391
127211459715181
21314
28001
34975
355793661538268
75300
2540
-54-9
-37-7
38
60
-88
25-5576
• • •
3H63F43H53H43F33F2
164
1D2
116
3P03P13P2
1S0
PAGE 3APPENDIX XIII
TABLE 20(K) *2 FOR TM + 3
J1 LEVEL 1 J2 LEVEL 2 (U2) *2 (U4) *2 (06) *2
0000
11
2222222
222222
33333
4444
3562135621356213562135621
3660336603366033660336603
1 366033660336603
15180151801518015180151801518015180
280282802828028280282602828028
1459814598145981459814598
5828582858285828
4 127354 127354 12735
5 83965 8396
2244
12234456
2234456
234456
34456
1518028028582812735
366031518028028145985828127358396153
1518028028145985828127350396153
28028145985828127358396153
145985828127358396153
4 58284 127355 83966 153
4 127355 83966 153
0.36180.02970.00.0
153 0.0
56
8396153
0.16070.13740.45210.57140.00.00.00.0
0.14250.06420.00360.30260.29690.00.0
0.19310.16380.56890.12570.00.0
0.06250.00250.08170.62850.0
0.01040.12750.09090.5395
0.26720.0-.310.2357
0.91920.1074
0.00.00.27960.02350.0
0.00.00.00.19640.10990.40290.28570.0
0.04430.30730.07450.05620.17110.29070.0000
0.00510.06980.09610.01240.00120.3131
0.00300.00050.35220.34670.3164
0.40590. 13110.12990.7261
0.16500.47620.1081
0.36680.2314
0.00.00.00.00.0756
0.00.00.00.00.00.00.08920.1239
0.00.00.00.04400.07630.58440.2550
0.00.00.02150.23000.01820.0958
0.06250.16880.28440.00.8413
0.26510.21130.92640.24 21
0.57040.00950.5916
0. 12140.6385
153 153 1.2517 0.6916 0.7759
APPENDIX XIV
-1-
APPENDIX XIV - TABLE 1
Calculated Values of fix for Ln :LaF3
Pr3+
Nd
Pm
Sm
Eu
Gd
Tb
Dy
Ho
Er
Tm
JJ2xl0"20cm2
0.12
0.35
0.5
1.0
1.19
1.1
1.1
1.1
1.16
1.07
0.52
fl4xl0"20cm2
1.77
2.57
1.9
0.5
1.16
1.2
1.4
1.4
1.38
0.28
0.59
fi6xl0"20cm2
4.78
2.50
2.2
1.5
0.39
0.5
0.9
0.9
0.88
0.63
0.22
Reference
a
a
b
b
c
b
b
b,d
e
f
b.g.h
aKrupke (1966)
bApproximate values from present work
cWeber (1967a)
dKrupke (1974)
eWeber et al. (1972)
fWeber (1967b)
9Weber (1967c)
hPappalardo (1976)
-2-
APPEMDIX XIV - TABLE 23+Observed and calculated radiative life-times for Ln :LaF,
Pr
Nd
Pm
Sm
Eu
Tb
Dy
Ho
Er
Tm
ExcitedState
\
\
F3/25F14 rG5/2
\
\
\5°3\F9/2
%5FP3/2
4S*3/2
\
\
ysec
902
73
635
566
2160
9200
7700
6900
809
1450
896
826
779
430
1020
137
1560
TObserved(usec)
520
47
670
-
-
5400
4700
6700
-
-
-
-
290
1000
54
960
Reference
a
b
c
c
d
c
c
e
f
a,g
a,g
aWeber (1967c), (1968)bRiseberg and Weber (1976), Weber (1967c)
cPresent WorkdWeber (1967a), measured at 77CKeWeber et al. (1972)fWeber (1967b)
^Compare recent calculations by Pappalardo (1976)
-3-
A PENDIX XIV - TABLE 3
Partial lifetimes a Branching Ratios in the3+
Relaxation of Excited States in Tb :
Transition Partial Electric- Partial Magnetic- &RPi pole Lifetime (msec) Pi pole Lifetime (msec)
5D3-*-5D. 125.4 3.413 0.24
fn m 0
0.009
5.606 0.16
109.3 0.015
1.590 0.54
0.027
7F27F3
\
\
\
V'.7F,7F2
%
\
\
\
91.01
51.93
108.4
28.61
30.32
87.15
( DQ) TD - 0«809 msec.
425.6
275.9
466.4
208.3
144.1
27.52
114.0
(5D4) T R = 1.45 msec.
0.003
0.005
0.003
15.28 0.10
505.1 0.013
1.800 0.86
0.013
aThe intensity parameters used in the calculations are given in Appendix XIV -Table 1. The matrix elements of IT ' appear in Appendix IX.