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ATOMIC DATA AND NUCLEAR DATA TABLES 25,287-310 (1980)
SCATTERING OF PROTONS BY HYDROGEN ATOMS AT LOW ENERGIES
Phase Shifts and Differential Cross Sections
GEOFFREY HUNTER and MARY KURIYAN
Centre for Research in Experimental Space Science York University, Downsview, Ontario M3J lP3, Canada
Phase shifts and differential cross sections for spin exchange (charge transfer) and total elastic scattering of protons by hydrogen atoms are presented for 36 and 38 values, respectively, of the collisional kinetic energy in the range 0.0001 to 10 eV (center of mass). The phase shifts are tabulated with a precision of six decimal digits. Each cross section is presented as a graph covering the complete angular range from 0 to rr radians (in center-of-mass coordinates). The phase shifts were obtained via partial wave analysis within a modified Perturbed-Stationary-States theory by calculations based upon very accurate (nonrelativistic) internuclear potential energies for the lSuz and 2Pu, electronic states of HZ. The cross sections demonstrate a transition from purely quantum behavior at very low energies (~0.1 eV) to semiclassical behavior at higher energies (> 1 eV) in which protons scattered by spin exchange are angularly separated from those scattered without exchange. Thus the in-principle unobservable charge-transfer cross section becomes physi- cally measurable at energies greater than about 1 eV.
0092-640X/80/040287-24$02.00/0 Copyright 0 1980 by Academic Press, Inc. All rights of reproduction in any form reserved. 287 Atomic Data and Nuclear Data Tables. Vol. 25, NO. 4. July 1980
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
CONTENTS
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 288 Phase Shifts . . . . . . . ..I.................................. 288 Differential Cross Sections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289
EXPLANATION OF TABLE AND GRAPHS . . . . . . . . . . . . . . . . . 291
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 292
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms . . . . . . . . . . . . . . . . . . . . . . . . . . . 302
Both the Table and Graphs give values for the following 36 collisional energies in the center-of-mass system (eV):
0.0001 0.0036 0.0070 0.013 0.05 0.0005 0.0038 0.0080 0.014 0.10 0.0010 0.0040 0.0090 0.015 1.0 0.0015 0.0042 0.00% 0.016 2.7 0.0020 0.0046 0.0105 0.018 0.0024 0.0050 0.0110 0.020 0.0028 0.0055 0.0120 0.025 0.0032 0.0060 0.0125 0.030
In addition the Table gives phase shifts for 5.0 and 10.0 eV.
INTRODUCTION
The scattering of protons by hydrogen atoms is one of the few elementary collision processes for which the accuracy of theoretical calculations can surpass that of current experimental techniques. The results reported here were obtained by a computational theory whose feasibility and accuracy increase as the colli- sional kinetic energy decreases, whereas the feasibility of cross-section measurements decreases as the energy becomes very small. The lowest energy considered (0.0001 eV) corresponds to a translational temperature of 1.2”K; cross-section measurements at these very low energies are experimentally inaccessible, yet may be relevant to astrophysical observations. The highest energy (10 eV) is the approximate upper limit of feasi- bility for the computational theory. It is also just below the threshold (10.2 eV) for excitation of then = 2 states of atomic hydrogen. Thus only elastic scattering events are possible within our energy range. The results ef- fectively cover the range from essentially zero energy up to the threshold for the onset of inelastic collisions. The accuracy of the calculations is about six decimal digits as the tabulated phase shifts imply. The theory and computational method were described previously.’
Phase Shifts
The method by which the phase shifts were cal- culated was described previously1 and a few of the low- energy phase shifts were published (Table 2 of Ref. 1) together with the integrated cross sections. Phase shifts covering the whole energy range are presented in the Table given here. These are the basic scattering data produced by our Perturbed-Stationary-States calcula- tions. They may be used to verify our calculated inte- gral cross sections (Table 3 of Ref. 1) and also the differential cross sections in the Graphs. They are also the data required for the calculation of other cross sec- tions such as those for scattering of polarized protons by polarized hydrogen atoms.3
The tabulated phase shifts will be particularly useful when comparison with experiment is required, since experimental arrangements never achieve the ideal of measuring a totally integrated cross section at a precisely defined energy, nor a differential cross section resolved at a precisely defined angle. Experi- ments always correspond to a partially integrated cross section, the integration being over an angular range
288 Atomic Oata and Nuclear Oata Tables, Vol. 25. No. 4. July 1280
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.ooOl- 10 eV
and an energy range related to the resolution limits of the experiment.
The phase shifts are presented in the Table for 38 values of the collisional kinetic energy E covering the range E = 0.0001 eV to E = 10.0 eV. For each value of the energy there are two phase shifts for each value of the angular-momentum quantum number L. In principle L takes all integer values from zero to in- finity. However, the phase shifts tend to zero as L tends to infinity, and thus the calculated cross sections converge at a finite value of L . The maximum values of L in the Table were chosen to yield cross sections with errors no larger than 0.1%; in many cases the errors are much smaller (as small as 0.001%). A discussion of truncation error and the means of compensating for it was presented previously. l
Two electronic states of Hz+ are involved in proton-hydrogen scattering below 10.2 eV. The ISU, state has gerade symmetry and the 2Pu, state un- gerade symmetry; the gerade and ungerade phase shifts correspond to scattering in each of these elec- tronic states. The ISa, and 2Pa, potentials used in the calculation of the phase shifts were published previ- ously as Coo and C,,, respectively, in Table 1 of Ref. 1.
For each of the 38 energies the number of tabu- lated ungerade phase shifts is less than the number of tabulated gerade phase-shifts. This simplification of the Table was possible because the corresponding gerade and ungerade phase shifts (i.e. at the same energy and L) tend to become equal as L increases. Thus only the ungerade phase shifts that differ from the correspond- ing gerade phase shifts are tabulated. The equality of gerade and ungerade phase shifts for large L is illus- trated in the Table by printing both of them where this does not increase the size of the Table; e.g. for E = 0.0028 eV the L = 25-29 g and u phase shifts are both shown even though they are identical. The phase shifts were calculated by a method that produced them modulo 2~.
Differential Cross Sections
The formulas by which the differential cross sec- tions are calculated from the phase shifts are given in Ref. 2 (Eqs. (16), (17), (25), and (26)). They are reproduced here for the convenience of the reader.
Ten components us* of the differential cross sec- tion are defined by
(Ts9p = - j2 ,; [Z* (21 + W[’ + l)Pl(COS fwl~(COS 0)
x sin vf sin $, cos (71; - sf,) (1)
withp andq = even (e) or odd (0) , and s and t = gerade (g) or ungerade (u). P,(cos 6) is the Ith Legendre poly-
nomial.4 The collisional angular-momentum quantum number is 1 or 1’; in the Table it is denoted by L in order to avoid confusion with the numeral 1.
K is the momentum defined by
K = [W - Coo(w)]“2, (2)
where W is the total energy and C,,,,(w) is the asymp- totic limit of the lSu, and 2Po; potentials in atomic units. While K is, strictly speaking, momentum, for the atomic units implicit in Eqs. (1) and (2) its value is also, in effect, that of a reciprocal length. The phase shifts are denoted by 7B and rj’ in Eq. (1).
The ten components defined by Eq. (1) are com- bined to form three components (r++(6), a--(@, and o+-(0), the + denoting singlet and the - the triplet scattering amplitudes.2 These three components are de- fined in terms of the ten components of Eq. (1) by
a++(8) = 0% + a?” + tap”,
u--(e) = ug + CT?” + 2ugq;,
u’-(6) = ug + cr$ + (2;: + um SU’ (3)
Finally the total elastic cross section uel and the spin-exchange cross section a,, are obtained from the three singlet-triplet components by
u,,(e) = (1/4){u++(e) + 3u--(8)}, (4)
use(B) = (1/4)(u++(@ + u--(d) - 2u+-(e)). (5)
The total elastic cross section uel is the cross section for scattering of a beam of unpolarized protons by unpolarized hydrogen atoms with a nonpolarizing detector. The spin-exchange cross section a, is the cross section for a beam of spin-polarized protons scat- tered from unpolarized hydrogen atoms, with the detector registering only scattered protons having spin opposite from those in the incident beam.
The spin-exchange cross section uS, has often been referred to in the literature as the charge-transfer cross section. The reason is that a theoretical approach that assumes that the protons are distinguishable par- ticles (thus tacitly neglecting the Pauli principle) allows one to calculate separately the elastic cross sections for scattering with, and without, transfer of the elec- tron from the target hydrogen atom to the incident proton. For these two types of scattering one assumes spinless protons. The expression for scattering with exchange (i.e. with electron (=charge) transfer) ob- tained from this semiclassical theory turns out to be identical with the spin-exchange cross section given by Eq. (S).5
Since the Pauli principle does apply to protons, the charge-transfer cross section is, strictly speaking, unobservable. However, the semiclassical theory
289 Atomic Data and Nuclear Data Tables. Vol. 25. No. 4. July 1980
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GEOFFREY HUNTER and MARY KURIYAN
based upon distinguishable protons leads to the con- cept that protons scattered with electron transfer will appear roughly perpendicular to the incident proton beam (at approximately 8 = 7~ in center-of-mass co- ordinates), whereas protons scattered without electron transfer will appear close to the incident direction. The latter are virtually unobservable because it is difficult to resolve them from unscattered protons. Hence most ex- perimental and theoretical work has been concerned with the charge-transfer process.
The differential cross sections presented in the Graphs now reveal how an in-principle unobservable quantity becomes, nevertheless, observable even in an experiment that employs unpolarized protons. As the collisional energy increases a, tends to zero in the angular region 8 = 0-7r/2 (0-7r/4 in laboratory co- ordinates), being concentrated in the complementary region of space (7r/2-m, ?r/4-?r/2 in laboratory coordi- nates) with maximum value (per unit solid angle) close to 7~ (7r/2 in the laboratory). Furthermore the total elastic cross section uel (which includes scattering with and without spin exchange, i.e. with and without elec- tron transfer) tends to zero near ?r/2 (7r/4 in the labora- tory), being concentrated in two regions spatially cen- tered about 8 = 0 and 0 = rr (7r/2 in the laboratory), and as the energy increases the latter part of a,] (i.e. in the region about 8 = ?r) tends to become identical with a,. Thus protons scattered with spin exchange become spatially separated from those scattered with- out exchange. At sufficiently high energies an experi- ment with polarized protons and a polarizing detector will yield the same result (in the 8 = 7r/2-7r region) as a simpler experiment with unpolarized protons.
While vindicating the semiclassical theory of the charge-transfer cross section for energies greater than about 1 eV, the differential cross sections of the Graphs reveal the need for careful control of the acceptance angle of the detector. Even at 2.7 eV the detector should collect throughout the cone 8 = 7r/4 (in the laboratory coordinates) in order to measure the inte- grated cross section &.; it is not sufficient to collect within a small solid angle centered on 8 = 7r/2 except at very high energies.
Proton Scattering by H Atoms, O.OOOl- 10 eV
A considerable amount of computation is in- volved in the calculation of the differential cross sec- tions from the phase shifts of the Table. One reason is that each of the ten components defined by Eq. (1) involves a double summation over L; the integral cross sections involve only a single summati0n.l As the number of significant phase shifts increases (with in- creasing energy) the number of terms in the double summation becomes very large. Furthermore these ten double summations (for a single energy) must be re- peated for many values of the scattering angle in order to generate detailed plots of the cross sections. Since the number of maxima in the cross sections increases with increasing energy the number of plotted values of 8 increases correspondingly. The differential cross sec- tions were not plotted at the two highest energies be- cause of the anticipated high cost of the computations.
The computer time involved in the calculation of the differential cross sections of the Graphs was about five times larger than that needed to calculate the phase shifts of the Table. Thus quite apart from the convenience of having plotted cross sections to look at, the computing involved justifies the presenta- tion of the Graphs as well as of the Table, even though the former is derived from the latter by a straightfor- ward computational procedure.
References
1.
2.
3.
4.
5.
G. Hunter and Mary Kuriyan, Proc. Roy. Sot. London A 353, 575 (1977)
G. Hunter and Mary Kuriyan, Proc. Roy. Sot. London A 341, 491 (1975)
S. Geltmann, Topics in Atomic Collision Theory (Academic Press, New York, 1969)
H. Margenau and G. M. Murphy, The Mathematics ofPhysics and Chemistry (Van Nostrand, Prince- ton, N. J., 1956), 2nd ed., Chap. 3
F. Masnou-Seeuws and A. Salin, J. Phys. B Ser. 2 2, 1274 (1969)
290 Atomic Data and Nuclear Data Tables. Vol. 25. No. 4. July 1980
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
EXPLANATION OF TABLE AND GRAPHS
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms Energy Collisional kinetic energy in electron volts in center-of-
mass system K Momentum number occurring in the expressions for the
cross sections in atomic units (&,v’/*)-~. See Eqs. (1) and (2)
wade (g) Phase shifts for scattering by the 1 ,!$a, state of Hz in radians ungerade (u) Phase shifts for scattering by the 2Pu, state of Hz in radians L Collisional angular-momentum quantum number
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms E Collisional kinetic energy in electron volts (Je1 Total elastic differential cross section defined by Eq. (4).
This cross section has a very high maximum close to 8 = 0. This peak is shown as an inset with the remain- ing part of the cross section plotted on a larger scale.
@se Spin exchange (charge transfer) differential cross section defined by Eq. (5)
Note Each of the cross sections is multiplied by sin(e) to produce an ordinate proportional to the total intensity scattered around the circle 19 = constant (4 = 0-27r). Thus the area under the plotted curve is equal to the correspond- ing integrated cross section Q,,, or Qse, which are given by’**
Qd
Qse
= $fey (21 + l)[sin* qf + 3 sin* @] 1
odd
+ 2 (21 + l)[sin2 q,I” + 3 sin* qf]},
= $- t (21 + 1) sin* (@ - $). 1 Cl
291 Atomic Data and Nuclear Data Tables. Vol. 25, No. 4. Juty 1080
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.OOOl- 10 eV
TABLE. Phase Shifts for Scattering of PrQtons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Energy = 0.0001 eV K L: 0.082146 Number: gerade
LEO-9 g 4.247439 5.056802 4.671842 3.499711 0.142018 0.070979 u 2.275753 3.140749 3.298945 0.596268 0.139854 0.070977
L=lO-19 g 0.009636 0.007318 3.147282 3.146104 0.003637 0.002975 L=20-24 g 3.142876 3.142705 0.000970 3.142444 3.142343
Energy = 0.0005 eV K = 0.183684 Number: gerade
L:O-9 g 2.287448 3.369113 3.925411 3.894835 3.308923 0.442889 u 0.395738 1.550599 2.259844 2.407556 1.278369 0.429888
L-10-19 g 0.048627 0.036825 3.170169 3.164223 0.018232 0.014906 u 0.048627 0.036825 0.028577 0.022631 0.018232 0.014906
L.20-29 g 3.148014 3.147157 0.004853 3.145852 3.145350 0.003332
Energy = 0.0010 eV K I 0.259768 Number: gerade
L.O-9 g 1.134537 2.304650 3.060045 3.369195 3.150411 1.416588 u 5.557853 0.515917 1.410479 1.911494 1.861639 1.066588
L--10-19 g 0.098404 0.074241 3.199069 3.187039 0.036575 0.029882 L=20-29 g 3.154445 3.152728 0.009712 3.150114 3.149111 0.006666 L.30-31 g 3.145485 0.003533
Energy = 0.0015 eV K = 0.318150 Number: gerade
Lzo-g g 0.341983 1.554635 2.400355 2.856658 2.854744 2.035587 u 4.793209 6.077645 0.781964 1.445360 1.717157 1.447984
L=lO-19 g 0.149444 0.112281 3.228305 3.210048 0.055033 0.044928 u 0.149429 0.112279 0.086713 0.068455 0.055033 0.044928
Ln20-29 g 3.160886 3.158307 0.014576 3.154381 3.152874 0.010002 L-30-33 g 3.147433 0.005301 3.146418 3.145998
Energy D 0.0020 eV K = 0.367368 Number: gerade
L-0-g g 6.000642 0.956446 1.857998 2.403845 2.542455 u 4.194616 5.506759
2.095146 0.269545 1.031474 1.470808 1.504169
L.lO-19 g 0.201991 0.151006 3.257893 3.233252 0.073607 0.060046 u 0.201846 0.150986 0.116297 0.091659 0.073607 0.060046
L:20-29 g 3.167337 3.163892 0.019445 3.158651 3.156640 0.013341 L=30-32 g 3.149380 0.007068 3.144285
Energy = 0.0024 eV K :: 0.402431 Number: gerade
L=O-9 g 5.575605 0.546718 1.479682 2.077538 2.298334 2.021708 u 3.788621 5.117137 6.197308 0.732154 1.260627 1.444149
L=lO-19 g 0.245431 0.182571 3.281840 3.251963 0.088552 0.182482
0.072193 u 0.244885 0.140234 0.110369 0.088551 0.072193
L-20-29 g 3.172504 3.168366 0.023344 3.162070 3.159655 0.016013 u 0.030912 0.026773 0.023344 0'.020477 0.018062 0.016013
L.30-31 g 3.150939 0.008483
Energy = 0.0028 eV
L-0-g g 5.197608 0.180845 1.138782 u 3.427494 4.769252 5.877053
LslO-19 g 0.290457 0.214782 3.306076 u 0.288882 0.214492 0.164431
L-20-29 g 3.177678 3.172843 0.027245 u 0.036085 0.031251 0.027245
L=30-39 g 3.152498 o.oOg8g8 3.150603 L:40-49 g 0.004653 0.004324 0.004026 L:50-59 g 0.002399 0.002262 0.002135 L.60-69 g 0.001395 0.001328 0.001265 L=70-79 g 0.000876 0.000853 0.000812
Energy = 0.0032 eV
= 25 ungerade I 10
0.041822 3.168451 3.159902 3.154645 0.041822 0.026858 0.018309 0.013052 3.144057 3.143658 0.001747 0.001491
= 30 ungerade = 14
0.225943 3.281224 3.235210 3.207770 0.225801 0.139612 0.093617 0.066178 3.153937 3.151931 0.008745 0.007464 3.153937 3.151931 0.008745 0.007464 3.144561 3.144248 0.002385 3.143743
= 32 ungerade = 10
0.513586 3.440895 3.334671 3.276385 0.508224 0.295324 0.192993 0.134787 3.166326 3.162299 0.017511 0.014942 3.147531 3.146905 0.004772 3.145895
= 34 ungerade = 14
0.857392 0.312702 3.442325 3.347889 0.832932 0.470574 0.299333 0.206165 3.178760 3.172697 0.026296 0.022433 3.178760 3.172697 0.026296 0.022433
3.150503 3.149564 0.007160 3.148048
: 33 ungerade = 14
1.139556 0.523675 3.563675 3.423241 1.099999 0.657969 0.412909 0.280687 3.191240 3.183125 0.035102 0.029939 3.191240 3.183125 0.035102 0.029939
3.153476 3.152223 O.Oog548 3.150201
= 32 ungerade = 25
1.263218 0.607517 3.678495 3.487188 1.223627 0.801915 0.507335 0.342532
3.201258 3.191489 0.042162 0.035954 0.059665 0.049897 0.042162 0.035954
3.155856 3.154352 0.01146'0 3.151924 3.155856 3.154352 0.011460 3.151924
K L 0.434675 Number: gerade = 80 ungerade = 25
1.776895 2.062911 1.907492 1.307957 0.660036 3.823933 3.555149 0.455979 1.051971 1.342589 1.273815 0.925523 0.602021 0.405859 3.270817 0.103575 0.084387 3.211305 3.199873 0.049234 0.041977 0.129216 0.103573 0.084387 0.069712 0.058280 0.049234 0.041977 3.165491 3.162671 0.018687 3.158236 3.156481 0.013372 3.153648 0.023898 0.021078 0.018687 3.158236 3.156481 0.017372 3.151648 3.14<8;Y 0.007531 3.148504 ii.O063;8 6.005862 0.00;4;7 0.00;016 0.003754 0.003507 0.003281 0.003073 0.002883 0.002708 0.002547 0.002017 0.001908 0.001807 0.001717 0.001625 0.001547 0.001466 0.001206 0.OOli50 0.00108j 0.001649 O.OOlOOi O.OiOs68 o.oOOyii~ 0.000804 0.000801 0.000657 0.000803 0.000811 0.000824 0.000793
K = 0.464687 Number: gerade E 76 ungerade : 25
L:O-9 g 4.855447 6.132046 0.827404 1.498657 1.836756 1.774099 1.298595 0.684667 4.030130 3.627964 u 3.101131 4.453719 5.583783 0.198784 0.848808 1.220631 1.271059 1.018882 0.693409 0.469888
LnlO-19 g 0.337458 0.247772 3.330667 3.289837 0.118684 0.096631 3.221383 3.208276 0.056319 0.04800y u 0.333660 0.247020 0.188915 0.148214 0.118679 0.096630 0.079790 0.066684 0.056319 0.048010
L.20-29 g 3.182859 3.177326 0.031151 3.168914 3.165689 0.021362 3.160618 3.158612 0.015285 3.155372 u 0.041266 0.035733 0.031151 0.027322 0.024097 0.021362 3.160618 3.158612 0.015285 3.155372
L=30-39 g 3.154058 0.011313 3.151892 3.150995 0.008607 3.149492 0.007267 0.006701 0.006191 0.005732 L.40-49 g 0.005318 0.004942 0.004601 0.004291 0.004008 0.003749 0.003512 0.003295 0.003095 0.002Yll L+50-59 g 0.002742 0.002585 0.002440 0.002306 0.002181 0.002065 0.001957 0.001857 0.001764 0.001676 L=60-69 g 0.001594 0.001517 0.001446 0.001378 0.001314 0.001257 0.001201 0.001145 0.001094 0.001056 L=70-75 g 0.001006 0.000982 0.000956 0.000886 0.000885 0.000828
292 Atomic Data and Nuclear Data Table& Vol. 25. No. 4, July 1990
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.OOOl- 10 eV
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Energy = 0.0036 eV
4.541674 5.827077 0.540065 2.801150 4.163027 5.312283
0.387142 0.281634 3.355678 0.378905 0.279990 0.213694 3.188045 3.181813 0.035059 0.046452 0.040220 0.035059 3.155618 0.012729 3.153180 0.005983 0.005560 0.005177 0.003085 0.002908 0.002745 0.001793 0.001707 0.001627 0.001137 0.001085 0.001044
K = 0.492875 Number: gerade = 76 ungerade = 25
L=O-g
LzlO-19
L.30-39 Lr40-49 L.50-59 L=60-69 L-70-75
1.238738 1.619815 1.631279 1.254604 0.685341 6.240947 0.652372 1.088852 1.233207 1.078747
3.309056 0.133889 0.108926 3.231491 3.216699 0.167377 0.133873 0.108923 0.089898 0.075107 3.172340 3.168710 0.024038 3.163001 3.160742 0.030748 0.027117 0.024038 3.163001 3.160742
4.350405 0.777374 0.063418 0.063418
E;“3% . 0.054051 0.054051
0.017199 0.017199 0.006966 0.003482 0.001984 0.001235
3.152172 0.009684 3.150480 0.008176 0.007538 0.004828 0.004509 0.004218 0.003952 0.003707 0.002594 0.002454 0.002323 0.002202 0.002089 0.001551 0.001479 ;.;;;;;; 0.001349 0.001293 o.ooog95 0.000921 .
K = 0.506381 Number: gerade = 74 ungerade = 21
1.114850 1.514705 1.557945 1.223798 0.678046 4.568133 6.125627 0.556702 1.021087 1.205214 1.096753 0.815263 3.318755 0.141536 0.115096 3.236558 3.220919 0.177027 0.141508 0.115091 0.094965 0.079326
3.157097 3.157097 0.006449 0.003276 0.001884 0.001187
Energy = 0.0038 eV
L=O-g
L=lO-19
L=20-29
k::;-;;
+;
LZ7OI73
4.393988 5.683308 0.404132 2.658906 4.025653 5.183440
0.413489 0.298915 3.368362 0.401602 0.296601 0.226192
3.748961 0.565193 0.057076 0.057076
0.066973 0.066973 0.018155 0.018155
0.007353 0.003676 0.002og4 0.001303
3.190641 3.184058 0.037015 0.049048 3.184058 0.037015
3.156398 0.013437 3.153825 0.006315 0.005869 0.005464 0.003256 0.003070 0.002898 o.oo189j 0.001802 0.001717 0.001186 0.001155 0.001106
3.174054 3.170221 0.025376 3.164193 3.161808 3.174054 3.170221 0.025376 3.164193 3.161808
3.152759 0.010223 3.150974 0.008630 0.007957 0.005096 0.004759 0.004453 0.004171 0.003q13
3.157959 3.157959 0.006808 0.003457 0.001990 0.001245
0.002738 0.002596 0.00245j 0.002325 O.OO;riOg ;.W;; 0.001562 0.001491 0.001424 0.001364
Energy r 0.0040 eV
L-O-9 g 4.250792 5.544001 0.272553 " 2.522247 3.892318 5.058497
L=lO-19 g 0.441398 0.316438 3.381169 u 0.424294 0.313264 0.238749
L-20-29 g 3.193238 3.186304 0.038971 u 0.051645 0.044712 0.038971
Ls30-39 g 3.157178 0.014145 3.154469 L=40-49 g 0.006648 0.006178 0.005752 L=50-59 g 0.003427 0.003232 0.003050 L-60-69 g 0.001993 0.001897 0.001807 L=70-74 g 0.001274 0.001216 0.001152
K 5 0.519536 Number: gerade = 75 ungerade = 25
0.994898 1.411811 1.483890 1.188664 0.666390 6.013454 0.462711 0.952672 1.172763 1.107607
3.328518 0.149213 0.121280 3.241633 3.225143 0.186720 0.149167 0.121271 0.100039 0.083551
4.814909 0.849789 0.070531 0.070531
3.793167 0.596222 0.060102 0.060102
3.175769 3.171732 0.026715 3.165385 3.162874 0.034176 0.030139 0.026715 3.165385 3.162874
0.019113 0.019113 0.007740 0.003869 0.002204 0.001373
3.153348 0.010761 3.151468 0.009085 0.008377 0.005364 0.005010 0.004687 0.004391 0.004119 0.002882 0.002727 0.002582 0.002447 0.002321 0.001728 0.001648 0.001570 0.001501 0.001435 0.001112 0.00110g
Energy = 0.0042 eV K = 0.532366 Number: gerade I 78 ungerade = 21
Lzo-g g 4.112654 5.409458 0.145193 0.878340 1.311079 1.409401 1.150034 0.650895 u 2.390507 3.764119 4.937561 5.904199 0.370339 0.883887 1.136738 1.112039
Lzlo-19 g 0.471720 0.334216 3.394102 3.338350 0.156926 0.127482 3.246717 3.229373 u 0.446949 0.329960 0.251359 0.196457 0.156854 0.127467 0.105122 0.087780
~~20-29 g 3.195837 3.188552 0.040928 3.177484 3.173243 0.028055 3.166577 3.163940 u 0.054244 3.188552 0.040928 3.177484 3.173243 0.028055 3.166577 3.163940
L=30-39 g 3.157958 0.014853 3.155114 ~~40-49 g 0.006980 0.006487
3.153936 0.011299 3.151962 0.009539 0.008795 0.006039 0.005632 0.005261 0.004921 0.004611 0.004325
L=50-59 g 0.003599 0.003393 0.003203 L-60-69
0.003027 0.002863 0.002711 0.002569 0.002437 g 0.002092 0.001992 0.001898 0.001810 0.001727 0.001649 0.001576 0.001507
L:70-77 g 0.001325 0.001265 0.001217 0.001162 0.001179 0.001015 0.000974 0.000698
0.007166 0.003639 0.002095 0.001309
5.064040 o .8805g4 0.074092 0.074092
0.063131 0.063131
0.0200k9 0.020069
0.008127 0.007525 0.004063 0.003821 0.002315 0.001443
Energy = 0.0046 eV K = 0.557141 Number: gerade = 72 ungerade = 25
0.654665 1.115897 1.260034 1.064718 0.610318 5.693888 0.190254 0.745995 1.056605 1.104583 3.358234 0.172471 0.139946 3.256915 3.237849 0.216055 0.172315 0.139909 0.115315 0.096255 3.180916 3.176268 0.030734 3.168963 3.166073 0.039323 0.034675 0.030734 3.168963 3.166073 3.155113 0.012376 3.152951 0.010449 0.009634 0.006169 0.005762 0.005390 0.005049 0.004737 0.003315 0.003136 0.002969 0.002814 0.002669 0.001982 0.001891 0.001808 0.001726 0.001648
Leo-9 g 3.848958 5.152403 6.184687 u 2.139124 3.519217 4.706004
L-10-19 g 0.548218 0.370638 3.420377 u 0.492015 0.363379 0.276690
L=20-29 g 3.201039 3.193050 0.044845 u 0.059447 0.051457 0.044845
L=30-39 g 3.159519 0.016269 L=40-49
3.156403 u. 0.007646 0.007106 0.006615
?%782 . 33849;;; 0.081225 0.069196 0.081225 0.069196 0.021985 3.161410 0.021985 3.161410 0.008902 0.008242 0.004450 0.004186 L=50-59 i 0.003942 0.003716 0.003508 .._.__ __
L=60-69 g 0.002292 0.002182 0.002078 L=70-71 g 0.001461 0.0013g4
Energy = 0.0050 eV
0.002535 0 ;002409 0.001577 0.001512
K I 0.580859 Number: gerade : 69 ungerade = 20
L.O-9 g 3.599956 4.909386 5.954011 u 1.902173 3.288052 4.486713
0.442287 0.928736 1.111390 0.971516 0.559799 5.493243 0.016113 0.608560 0.968815 1.079809 3.378409 0.188195 0.152504 3.267159 3.246349 0.235777 0.187887 0.152422 0.125548 0.104753 3.184350 3.179295 0.033415 3.171349 3.168207 3.156290 0.013454 3.153939 0.011358 0.010472
5.702716 0.963449 0.088372 0.088371
4.047751 0.737331
L.lO-19 g 0.723241 0.408470 3.447688 " 0.536429 0.396734 0.302078
L.20-29 g 3.206248 3.197553 0.048765 L-30-39 g 3.161080 0.017686 3.157692 L-40-49 g 0.008311 0.007724 L=50-59
0.007191 g 0.004284
L:60-68 0.004039 0.003813
g 0.002491 0.002371 0.002259
0.075269 0.075297
0.001691
3.163136 0.008959 0.004549 0.002618
0.006706 0.006263 0.005859 0.005489 0.005149 0.003603 0.003408 0.003227 0.003058 0.002902 0.002155 0.002056 0.001951 0.001876 0.001794
Atomic Data and Nuclear Da ta Tables. Vol. 25, No.4.July 1980
![Page 8: Scattering of protons by hydrogen atoms at low energies: Phase shifts and differential cross sections](https://reader030.fdocuments.in/reader030/viewer/2022020312/575070b41a28ab0f07d62b0f/html5/thumbnails/8.jpg)
GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Energy = 0.0055 eV K = 0.609210 Number: gerade = 76 ungerade = 26
LnO-9 g 3.306685 4.622654 5.680744 u 1.624042 3.016236 4.227814
LnlO-19 g 3.442685 0.458573 0.338930 u 0.590295 0.438299 0.3337gl
L=20-29 g .3.212769 3.203188 0.053669 u 0.071176 0.061595 0.053669
L=30-39 g 3.163033 0.019457 3.159304 k&o-$9 g o.oog142 0.008497 o.oO791o L=50-59 g 0.004713 0.004444 0.004194 L.60-69 0.002740 0.002609 0.002485 L.70-75
g g 0.001733 0.001655 0.001593
Energy = 0.0060 eV
L:O-9 g 3.030877 4.352461 5.422368 u 1.362792 2.760589 3.983580
LzlO-19 g 3.662576 0.513091 0.374093 u 0.640772 0.479519 0.365405
L=20-29 g 3.219299 3.208830 0.058579 u 0.077707 0.067237 0.058579
L=30-39 g 3.164985 0.021228 3.160916 t&l-4g g 0.009974 0.009269 0.008629 L.50-59 g 0.005142 0.004848 0.004576 L=60-69 g 0.002gEg 0.002846 0.002711 ~170-75 g o.oo18g5 0.001808 0.00171g
Energy = 0.0070 eV
Leo-9 f ;:5ggj gg;g ;:;#j
Islo-lg g 3.799449 0.643681 0.448496 u 0.724762 0.558994 0.'428380
Lr20-29 g 3.232397 3.220137 0.068415 u 0.090802 3.220137 0.068415
Lz30-3g g 3.168892 0.024773 3.164142 L-40-49 g 0.011637 0.010815 0.010069 IdO-59 g 0.005999 0.005656 0.005339 L.60-69 g 0.003488 0.003320 0.003163 L=70-70 g 0.002217
Energy D 0.0080 eV
L-O-9 g 2.065913 3.403637 4.507294 u 0.444753 1.860108 3.118737
t=lo-lg g 3.885379 0.830830 0.530550 u 0.779301 0.628795 0.490236
L-20-29 g 3.245556 3.231479 0.078273 u 0.103953 0.089885 0.078273
L:30-39 g 3.172802 0.028320 3.167370 L=40-49 g 0.013301 0.012361 0.011508 L=50-59 g 0.006856 0.006464 0.006102 L=60-69 g 0.003986 0.003795 0.003615 L170-75 g 0.002525 o.002398 0.002314
Energy = 0.0090 eV
L=O-g g 1.646883 2.990950 4.107084 u 0.042747 1.464699 2.736934
Lnlo-lg g 3.948082 1.158710 0.621479 u 0.803886 0.682772 0.547543
Ls?odg g 3.258817 3.242872 0.0881.58 u 0.117181 0.101268 0.088156
Lz30-39 g 3.176714 0.031869 3.170599 Lr4o-49 g 0.014965 0.013908 0.012948 Lsjo-59 g 0.007714 0.007273 0.006865 L-60-69 g 0.004484 0.004269 0.004067 ~~70-75 g 0.002839 0.002736 0.002588
0.190103 0.705059 0.928153 0.847314 0.486591 5.849825 4.192544 5.254551 6.089513 0.438482 0.852090 1.030929 0.983688 0.793359
3.404017 3.349703 0.168357 3.280046 3.257015 0.097328 0.082876 0.260526 0.207493 0.168172 0.138404 0.115412 0.097326 0.082876 3.188647 3.183080 0.036768 3.174334 3.170875 0.026296 3.165295 0.047054 0.041488 0.036769 3.174334 3.170875 0.026296 3.165295 3.157761 0.014801 3.155175 0.012495 0.011520 0.010644 ct.009855 0.007377 0.006890 0.006445 0.006038 0.005664 0.005321 0.005005 0.003963 0.003749 0.003550 0.003365 0.003192 0.003031 0.002881 0.002369 0.002261 0.002161 0.002063 0.001972 0.001882 0.001809 0.001525 0.001533 0.001439
K D 0.636299 Number: gerade
6.233857 0.491613 0.749144 5.028035 5.888026 0.271118
3.430032 3.369896 0.184405 0.285258 0.227191 0.184034 3.192947 3.186868 0.040124 0.051354 0.045276 0.040124 3.159233 0.016147 3.156411 0.008047 0.007517 0.007031 0.004324 0.004090 0.003873 0.002585 0.002467 0.002356 0.001636 0.001643 0.001425
K = 0.687282 Number: gerade
5.786412 0.089918 0.405951 4.606044 5.507791 6.229951 3.483606 3.410963 0.217051 0.334456 0.266548 0.215962 3.201559 3.194454 0.046841 3.201559 3.194454 0.046841 3.162178 0.018842 3.158884 0.009389 0.008770 0.008204 0.005045 0.004772 0.004518 0.003016 0.002878 0.002749
K = 0.734735 Number: gerade
5.374416 5.998183 0.081330 4.218002 5.153936 5.920829 3.540840 3.453117 0.250221 0.383566 0.305592 0.247799 3.210187 3.202051 0.053566 0.068594 0.060458 0.053566
3.165123 0.021538 3.161357 0.010732 0.010024 0.009376 0.005766 0.005454 0.005164 0.003447 0.003289 0.003142 0.002200 0.002175 0.001958
K e 0.779304 Number: gerade
4.993301 5.645953 6.054872 3.857150 4.821904 5.626281 3.603704 3.497411 0.283988 0.432439 0.344595 0.279324 3.218832 3.209659 0.060301 0.077239 0.068067 0.060301 3.168070 0.024235 3.163832 0.012074 0.011277 0.010549 0.006487 0.006136 0.005810 0.003878 0.003701 0.003534 0.002502 0.002496 0.002196
= 76 ungerade = 25
0.717522 0.405483 0.730425 0.967665
3.293043 3.267738 0.151340 0.126117 3.177320 3.173545 3.177320 3.173545 0.013632 0.012568 0.006587 0.006179 0.003671 0.003483 0.002251 0.002151
= 71 ungerade = 21
0.4 0381 0.4 0058 ii
0.2265 8 0.8126 5 8
3.319443 3.289418 0.177451 0.147694
3.183297 3.178888 3.183297 3.178888 6.015906 6.014665 0.007686 0.007209 0.004283 0.004063 0.002625 0.002510
= 76 ungerade = 25
0.184032 0.031746 0.228539 0.634988 0.204738 3.311486 0.203731 0.169496 3.189281 3.184235 3.189281 3.184235
3.159774 0.016762 0.008784 0.008240 0.004895 0.004644 0.003001 0.002872
= 76 ungerade = 25
6.208055 6.111528 6.264354 0.446484 0.231899 3.333881 o.229870 0.191389 3.1g5271 3.189588 3.195271 3.189588 3.162049 0.018860 0.009882 0.00927 1 0.005507 0.005224 0.003376 0.003230
5.908051 4.340849 0.983716 0.836282 0.106313 0.090498 0.106307 0.090497 0.028692 3.167454 0.028692 3.167454 0.011613 0.010752 0.005805 0.005459 0.003307 0.003143 0.002063 0.001965
5.902259 4.607 88 0.938010 0.881 05 8 0.124403 0.105805 0.124366 0.105796 0.033488 3.171776 0.033488 3.171776 0.013549 0.012545 0.006773 0.006370 0.003858 0.003667 0.002408 0.002297
5.824513 4.781800 0.849552 0.880645 0.142728 0.121234 0.142589 0.121193 0.038287 3.176099 0.038287 3.176099
0.015487 0.014339 0.007741 0.007281 0.004409 0.004191 0.002744 0.002626
5.713824 4.854741 0.733292 0.842963 0.161350 0.136854 0.160975 0.136717 0.043090 3.180426 0.043090 3.180426 0.017425 0.016133 0.008709 0.008191 0.004961 0.004715 0.003091 0.002953
294 Atomic Data and Nuclear Data Tables, Vol. 25, No. 4. July 1980
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.OOOl- 10 eV
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Energy : 0.0096 eV
L:o-g g 1.410451 2.758146 3.881352 u 6.098851 1.241204 2.520544
L:lo-lg g 3.974727 1.481019 0.681839 u 0.805397 0.706588 0.578073
L=20-29 g 3.266844 3.249745 0.094108 u 0.125165 0.108127 0.094101
L.30-39 g 3.179062 0.033999 3.172537 L.J+o-49 g 0.015964 0.014836 0.013812 L:50-59 g 0.008228 0.007758 0.007322 L.60-69 g 0.004783 0.004554 0.004339 ~~70-75 g 0.003032 0.002893 0.002779
Energy = 0.0105 eV
L=O-9 g 1.073461 2.426260 3.559515 u 5.775849 0.922838 2.211'jgg
L-lo-19 g 3.996710 2.080932 0.785019 u o.790781 0.730166 0.617125
Lr20-29 g 3.279009 3.260131 0.103072 u 0.137213 0.118467 0.103050
L=30-39 g 3.182587 0.037195 3.175446 L=40-49 g 0.017462 0.016228 0.015107 L=50-59 g L.60-69
0.008999 0.008485 0.008009 g 0.005232 0.004981 0.004746
L-70-79 g 0.003304 0.003172 0.003039
Energy = 0.0110 eV
L:o-9 g 0.894188 2.249642 3.388239 u 5.604366 0.753719 2.047275
L=lO-19 g 3.999417 2.358856 0.850598 u 0.774771 0.736984 0.635114
L-20-29 g 3.285828 3.265949 0.108079 u 0.143934 0.124240 0.108041
L.30-39 g 3.184545 0.038972 3.177062 L:40-49 g 0.018295 0.017001 0.015827 L.50-59 g L.60-69
0.009428 0.008889 0.008391 g 0.005481 0.005218
L.70-75 0.004971
g 0.003475 0.003329 0.003186
Energy I 0.0120 eV
L.O-9 g 0.551126 1.911306 3.059652 u 5.276949 0.430604 1.732770
L=lO-19 g 3.987177 2.702254 0.999369 u 0.728549 0.737345 0.662828
L-20-29 g 3.299556 3.277697 0.118175 u 0.157391 0.135844 0.118074
K = 0.899863 Number: gerade = 76 ungerade = 26
3.993263 4.708135 2
.201847 2.899001 3.927467
5.471878 5.505744 5.285577 .815123 5.558121 6.151659 0.308079
3.889301 3.648086 0.395343 0.317507 3.402244 3.359617 0.558454 0.458400 0.374223 0.307528 0.255999 0.215801
3.244953 3.232586 0.080564 0.071691 3.205677 0.057524 0.103327 0.090984 0.080562 0.071691 3.205677 0.057524
4.755800 0.592584 0.184757 0.183625
L=30-39 g 3.188465 0.042526 3.180296 3.176919 0.032332 3.171259 3.168880 0.025157 L--40-49 g 0.019959 0.018549
0.021518 0.017268
0.023245 0.016102 0.015039 0.014068 0.013179
Lr50-59 0.01028'6 0.009698 0.012363 0.011613 0.010923
g 0.009154 0.008649 0.008182 0.007747 0.007343 L260-69
0.006966 g 0.005979 0.005693
0.006149 0.006287 0.005423 0.005172 0.004936 0.004713 0.004502 0.004309
L-70-75 0.004119 0.003946
g 0.003782 0.003697 0.003481 0.003347 0.003154 0.002997
Energy = 0.0125 eV K = 0.918419 Number: gerade : 80 ungerade = 31
L:O-9 g 0.386819 1.749060 2.901737 3.842199 4.566234 5.070679 u 5.120292 0.275852 1.581953
5.354591 5.407337 5.208484 2.754217 3.790884 4.689246
4.715205 5.445782 6.056020 0.232314 0.539370
L.lO-19 g 3.973904 2.799606 1.080136 3.995228 3.676578 0.415303 0.332949 3.414211 u 0.699525 0.731166 0.672363
3.369155 0.192753 0.574385 0.475263 0.389720 0.320636 0.266741 0.224772 0.191339
Lz20-29 g 3.306430 3.283617 0.123269 3.249359 3.236434 0.083955 0.074700 3.208364 0.059933 0.054003 u 0.164096 0.141662 0.123115 0.107712 0.094825 0.083951 0.074699 0.066771 0.059933 0.054002
Le30-39 g 3.190425 0.044304 3.181913 0.048832 0.044304 3.181913
3.178394 0.033682 3.172498 3.170019 0.026207 0.024212 u 3.178394 0.033682 3.172498
0.022415 3.170019 0.026207 0.024212 0.022415
L-40-49 g 0.020792 0.019322 0.017988 0.016774 0.015667 0.014655 L.50-59 0.013728 0.012878 0.012097 0.011378 g L:60-69
0.010715 0.010102 0.009535 0.009010 0.008523 0.008070 0.007649 0.007256 0.006890 0.006549 g 0.006229 0.005930 0.005649 0.005386 0.005140
L.70-79 o.oo4go8 0.004692 0.004485
0.003949 0.003773 0.003618 0.004292 0.004105
g 0.003444 0.003067 0.003377 0.003227 0.003085 0.003115 0.002618
K I 0.804862 Number: gerade = 76 ungerade = 25
4.777785 5.444794 5.875239 6.056317 5.988469 5.637045 3.651724 4.631666 5.455847 6.118730 0.331218 0.654804 3.644862 3.525451 0.304845 0.248315 3.347391 0.172642 0.460980 0.368099 0.298191 0.245407 0.204469 0.172044 3.224028 3.214231 0.064345 3.198868 3.192802 0.045974 0.082434 0.072638 0.064345 3.198868 3.192802 0.045974 3.169839 0.025854 3.165317 3.163415 0.020119 0.018588 0.012879 0.012029 0.011253 0.010542 0.009889 0.009289 0.006g19 0.006545 0.006197 0.005874 0.005572 0.005292 0.004137 0.003947 0.003768 0.003602 0.003443 0.003297 0.002651 0.002569 0.002379
K = 0.841745 Number: gerade I 80 ungerade = 24
4.470446 5.156548 5.614146 5.833170 5.805219 5.511324 3.357314 4.357517 5.208192 5.904394 0.157425 0.529311
3.714377 3.569529 0.337467 0.273378 3.367704 0.189654 0.501263 0.403162 0.326657 0.268593 0.223910 0.188597 3.231843 3.221098 0.070419 0.062676 3.197627 0.050303 0.090245 3.221098 0.070419 0.062676 3.197627 0.050303 3.172493 0.028282 3.167545 3.165464 0.022008 0.020333 0.014088 0.013158 0.012308 0.011530 0.010817 0.010161 0.007568 0.007159 0.006778 0.006425 0.006095 0.005788 0.004525 0.004317 0.004123 0.003939 0.003768 0.003602 0.002903 0.002755 0.002758 0.002635 0.002349 0.002296
K = 0.861554 Number: gerade = 76 ungerade = 28
4.307033 5.002949 5.473527 5.711271 5.704585 5.437599 3.200320 4.210619 5.074526 5.787449 0.060881 0.456849
3.760335 3.594930 0.356338 0.287703 3.379062 0.199105 0.52.l835 0.422204 0.342563 0.281498 0.234622 0.197725 3.236198 3.224920 0.073797 0.065679 3.200309 0.052709 0.094595 0.083325 0.073797 0.065679 0.058716 0.052709 3.173968 0.029632 3.168783 3.166603 0.023057 0.021303 0.014759 0.013785 0.012895 0.012080 0.011332 0.010645 0.007928 0.007499 0.007101 0.006731 0.006385 0.006063 0.004740 0.004523 0.004318 0.004128 0.003947 0.003777 0.003046 0.002880 0.002825
4.863251 0.806438 0.146337 0.146093
0.017209 0.008737 0.005029 0.003151
4.84 875 a 0.73 616
0.160699 0.160209
xt;:; 0:018825 0.009557 0.005501 0.003445 0.002277
4.821001 0.691753 0.168719 0.168046
295 Atomic Data and Nuclear Data Tables. Vol. 25. No. 4, July 1980
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Energy = 0.0130 eV K = 0.936607 Number: gerade = 76 ungerade = 31
L-O-9 g 0.226815 1.590976 4.967757
2.747703 3.694673 4.427556 0.125176
4.942433 5.239061 5.309486 5.131173 4.670281 u 1.435024 2.612990 3.657396 4.565803 5.335006 5.960882 0.155888 0.484256
L-10-19 g 3.956834 2.866569 1.162668 4.172784 3.707172 0.435587 0.348637 3.426484 3.378823 0.200745 u 0.667278 0.721079 0.678888 0.588661 0.491203 0.404821 0.333737 0.277557 0.233736 0.198999
L=20-29 g 3.313292 3.289553 0.128392 3.253789 3.240296 0.087353 0.077713 3.211052 0.062345 0.056173 u 0.170768 0.147479 0.128171 0.112111 0.098675 0.087345 0.077712 0.069459 0.062344 0.056173
L.30-39 g 3.192386 0.046083 3.183531 3.179870 0.035032 3.173737 3.171159 0.027257 0.025182 0.023313 u 0.050794 0.046083 3.183531 3.179870 0.035032 3.173737 3.171159 0.027257 0.025182 0.023313
Ln40-49 g 0.021625 0.02OOg6 0.018708 0.017445 0.016294 0.015241 0.014278 0.013394 0.012582 0.011833 L=50-59 g 0.011144 0.010506 0.009917 0.009371 0.008864 0.008393 0.007955 0.007547 0.007166 0.006811 L-60-69 g 0.006478 0.006167 0.005876 L.70-75
0.005603 0.005345 0.005106 0.004876 0.004662 0.004464 0.004278 g 0.004047 0.003924 0.003773 0.003597 0.003464 0.003267
Energy = 0.0140 eV K I 0.971963 Number: gerade = 80 ungerade = 29
L=O-9 g 6.202671 1.287041 2.450844 3.409394 4.158878 4.693969 5.013643 5.115491 4.976535 4.570381 u 4.674419 6.118400 1.151989 2.340432 3.399115 4.325920 5.118185 5.772482 0.001691 0.369409
LzlO-19 g 3.912995 2.941054 1.325451 5.329076 3.777717 0.478070 0.380331 3.451847 3.398765 0.216847 u 0.594838 0.690519 0.682761 0.611868 0.520217 0.433459 0.359539 0.299362 0.251756 0.214209
L;20-29 g 3.326949 3.301419 0.138703 0.121134 3.248073 0.094176 0.083753 3.216435 0.067168 0.060515 u 0.183973 0.159059 0.138301 0.120950 0.106409 0.094154 0.083747 0.074841 0.067167 0.060515
L=jo-39 g 3.196310 0.049641 3.186768 3.182824 0.037734 3.176216 3.173438 0.029357 0.027123 0.025110 ~~40-49 a 0.023291 0.021644 0.020149 0.018789 0.017548 0.016415 0.015377 0.014425 0.013550 ,0.012744 L.50-59 ;; 0.01~0~1 0.011315 0.01068t1 0.01009~ 0.009546 0.009039 0.008567 0.008127 0.007717 0.007334 L-60-69 g 0.006g77 0.006641 0.006327 0.006032 0.005755 0.005499 0.005254 0.005017 0.004811 0.004601 L=70-79 g 0.004415 0.004230 0.004069 0.003878 0.003740 0.003509 0.003509 0.003398 0.003309 0.002930
Energy = 0.0150 eV K = 1.006078 Number: gerade D 77 ungerade : 31
LsO-9 g 5.910722 0.998014 2.167910 3.136343 3.900556 4.454865 4.795852 4.924279 4.822006 4.461490 u 4.394858 5.842016 0.881872 2.079854 3.151440 4.094762 4.907574 5.587057 6.129840 0.249778
LnlO-19 g 3.857490 2.966535 1.475261 0.136603 3.865522 0.526396 0.412278 3.477756 3.419659 0.233423 u 0.513894 0.648371 0.674873 0.627180 0.545149 0.459772 0.384300 0.321844 0.270053 0.229447
Lt20-29 g "
L.30-39 g
L.40-49 : L-50-59 g L.60-69 g ~~70-76 g
3.340608 0.197018
3.313205 0.149032 0.130155 3.255931 0.170505 0.148398 0.129822 0.114189 0.053201 3.190006 3.185778 0.040437 0.053201 3.190006 3.185778 0.040437 0.023192 0.021590 0.020132 0.018803 0.012124 0.011443 0.010813 0.010228 0.007116 0.006780 0.006464 0.006168 0.004543 0.004543 0.004322 0.004163
3.178695 3.178695
3.221831 0.080234
0.017588 0.009685 0 .oo%892 0.004027
0.031459 0.029064 0.026906 0.031459 0.029064 0.026906
0.016476 0.009179 0.005628 0.003702
ergy = 0.0160 eV K : 1.039073 Numb er: gerade : 76 unge rade : 26
0.722443 1.897787 2.874765 3.651722 4.223766 4.585235 4.736718 5.577636 0.623259 1.829971 2.913347 3.871676 4.703005 5.404999 2.963632 1.602842 0.406176 3.975509 0.587308 0.445484 3.503566 '0.596915 0.656471 0.634014 0.565430 0.483658 0.407568 0.342470
0.064862 0.064862
3.200237 0.058644 0.024957 0.012859 0.007475 0.004736
0.014518 0.013655 0.008269 0.007859 0.005149 0.004940
En
5.632429 4.127610
L.O-9 g "
L-10-19 g U
4.347577 0.126681
0.250764 0.244872
3.441195 0.288498
Lr20-29 g 3.354530 3.324923 0.159291 0.139205 3.263866 0.107997 0.095931 3.227249 0.076840 0.069213 u 0.210014 0.181792 0.158393 0.138682 0.122003 0.107878 0.095931 3.227249 0.076840 0.069213
L=30-39 g 3.204167 0.056763 3.193246 3.188734 0.043141 3.181175 3.177998 0.033561 0.031005 0.028703 L=40-49 g 0.026623 0.024740 0.023031 0.021476 0.020058 0.018762 0.017576 0.016487 0.015487 0.014566 L=50-59 g 0.013717 0.012932 0.012207 0.011534 o.ologtl 0.010331 0.009791 0.009289 0.008820 0.008383 L.60-69 g 0.007973 0.007591 0.007232 0.006895 0.006581 0.006283 0.006001 0.005740 0.005492 0.005244 L.70-75 g 0.005047 o.004829 0.004628 0.004421 0.004287 0.004030
Energy = 0.0180 eV K= 1.102103 Number: gerade = 76 ungerade = 26
LnO-9 g 5.110412 0.205604 1.391052 2.382903 3.180670 3.782446 4.182179 4.374776 4.359083 4.112201 u 3.624753 5.079870 0.135742 1.357977 2.462276 3.447132 4.310870 5.051735 5.667922 6.157535
L-10-19
L:20-29
k=EB Go,-;;
- - L.70-75
.633526 .236106 .384156 .236437 0.204229
0.063896 0.027838
EX 0:005420
.770436
.594002 0.608419 0.623132 0.157107 0.156139
xi% 0:012977 0.007757 0.005115
4.288260 0.589220
0.523798 0.449448
3.556137 0.382169
m;i
0:037765 0.018550 0.010451 0.006458
3.483914 0.324553 0.086581 0.086581
EW 0:009924 0.006178
0.022568 0.012275 0.007402
0.122074 0.121720 3.186138 0.021110 0.011623 0.007069
0.108324 0.108324 3.182561 0.019775 0.011016 0.006754
-179613 .I77992 .I99731 .025914
:X33: .005332
.212040
.029957
:X: .005673
o.oogE31 0.005907
0.004820 o.oos6oi
296 Atomic Data and Nuclear Data Tablea. Vol. 25, No. 4, July 1950
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.OOOl- 10 eV
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Energy I 0.0200 eV
L-o-g g 4.671668 6.054479 0.965501 u 3.202051 4.661109 6.008116
L=lO-19 g 3.474168 2.827926 1.830315 u 0.053045 0.341161 0.514530
L.20-29 g 3.412282 3.372294 0.198572 u 0.260738 0.224916 0.195595
L.30-39 g 3.219176 0.070346 0.063998 u 0.077574 0.070344 0.063997
L--40-4g g 0.032966 0.030634 0.028517 u a.032960 0.030634 0.028517
L+jo-=jg g 0.016981 0.016010 0.015111 L.60-69 g 0.009871 0.009397 0.008952 k-/o-79 g 0.006237 0.005979 0.005735
Energy = 0.0250 eV
L.&g g 3.542976 4.935227 6.148880 u 2.115509 3.583361 4.948076
L-10-19 g 2.978538 2.485798 1.750401 u 5.786464 6.189276 0.202744
L=20-29 g 0.349287 3.439655 0.258048 u 0.325731 0.283781 0.247742
Lt30-39 g 3.240196 0.089224 0.081033 u 0.098372 0.089224 0.081033
L-40-49 g 0.041636 0.038688 0.036013 Ln50-59 g 0.021441 0.020214 0.019079 L.60-69 g 0.012461 0.011863 0.011302 L-70-79 g o-007879 0.007551 0.007242
Energy = 0.0300 eV K = 1.422809 Number: gerade = 80 ungerade = 30
Lzo-g g 2.603879 4.003037 5.230376 u 1.207713 2.681929 4.059420
L-10-19 g 2.480816 2.099731 1.505702 u 5.257762 5.741176 6.124283
L=20-29 g 0.448201 3.511683 0.313265 u 0.378296 0.333959 0.294118
L.30-39 g 3.260377 0.107781 0.097939 L.40-49 g 0.0499Bg 0.046447 0.043233 Ln50-59 g 0.025734 0.024261 0.022899 L=60-69 g 0.014955 0.014237 0.013564 Lrj'o-j'g g 0.009469 0.009042 0.008686
K = 1.161719 Number: gerade = 80 ungerade = 41
1.969978 2.783767 3.406529 3.835520 4.062967 4.085525 3.894067 0.959251 2.079905 3.085568 3.974660 4.745533 5.396770 5.927266 0.703295 4.714593 3.747986 0.616286 3.611705 3.522417 0.319255 0.589207 0.590324 0.545856 0.481102 0.414453 0.354806 0.303817 0.173082 3.293905 0.134755 0.119652 3.248243 0.095488 0.085888 0.171527 0.151364 0.134129 0.119267 0.106448 0.095399 0.085856 3.199991 0.053438 3.190618 3.186680 0.041562 0.038395 0.035542 0.058398 0.053438 0.049026 0.045088 0.041562 0.038395 0.035542
a.026590 0.024834 0.023229 0.021760 0.020412 0.019173 0.018033 0.026590 0.024834 0.023229 0.021760 0.020412 0.019173 0.018033 0.014279 0.013507 0.012789 0.012121 0.008536
0.011499 0.008145
O.Ologlg 0.010377 0.007778 0.007431 0.007110 0.006800 0.006510
0.005500 0.005285 0.005078 0.004880 0.004690 0.004510 0.004350
K r ?.298841 Number: gerade = 80 ungerade = 31
0.900515 1.755583 2.428649 2.917793 3.223281 3.340117 3.258483 6.209278 1.083264 2.135600 3.082158 3.921756 4.653032 5.274747 0.785794 5.715711 4.210994 1.146512 0.520385 3.670343 0.421633 0.398207 0.503063 0.536595 0.522346 0.480846 0.427816 0.374214
0.223969 3.336428 0.170878 0.151492 3.276995 0.121532 0.109333 0.216825 0.190625 0.168710 0.150333 0.134634 0.120959 0.108939
3.215454 0.067546 3.203541 3.198555 0.052503 0.048498 0.044892 3.215454 0.067546 3.203541 3.198555 0.052503 0.048498 0,044892 0.033579 0.031359 0.029333 0.027476 0.025774 0.024209 0.018028
0.022769 0.017052 0.016146 0.015303 0.014517 0.013785 0.013101
0.010778 0.010282 O.oog818 o.oog3Bl 0.008971 0.008589 0.008225 0.006927 0.006676 0.006334 0.006176 0.005931 0.005916 0.006659
L=O-9
LrlO-19
L:20-29
L:50-59 L.60-69
:=780"-78; L:90:99
L.lOO-100
B U
B U
Energy = 0.05 eV K=
5.960681 1.093869 2.355866 4.649888 6.139648 1.265153
0.621167 0.488596 0.193866 3.316535 3.989427 4.580326 2.812580 0.953958 3.869013 0.369854 0.388708 0.384907 3.344576 3.326014 0.168101 0.195836 0.178186 0.162287 0.084236 0.078272 0.072741 0.083865 0.077941 0.072496 0.042926 0.040466 0.038192 0.024935 0.023737 0.022614 0.015751 0.015101 0.014486 0.010591 0.010157 0.009837 ym; 0.007197 0.007030
.
0.002 71 5.339 il 97
0.885077 1.595062 2.131264 2.490633 2.671226 2.670864 0.239792 1.324922 2.311499 3.198842' 3.986187 4.672725
0.697267 5.921102 4.545988 2.685193 0.966428 3.900585 0.562822 0.127616 0.323954 0.439415 0.488258 0.490188 0.464280 0.423903
0.271498 3.380172 0.210187 0.185054 3.305151 0.145843 0.131240 0.259399 0.229176 0.203072 0.180386 0.160997 0.144548 0.130472 3.230753 0.081390 3.216125 3.210057 0.063068 0.058241 0.053903 0.040309 0.037645 0.035209 0.032981 0.030937 0.029058 0.027329 0.021637 0.020466 0.019378 0.018366 0.017423 0.016544 0.015723 0.012932 0.012339 0.011783 0.011259 0.010767 0.010301 0.009853 0.008311 0.008048 0.007622 0.007554 0.007234 0.007065 0.006456
1.836838 Number: gerade = 101 ungerade :: 50
3.463617 4.417448 5.217736 5.864%79 0.073734 2.592673 3.838902 5.003658 6.086766 0.804870
EZ69 . 0.564441 0.367836 3.294477 0.148041 0.067666 0.067514 0.036085 0.021561 0.013908 0.009651 0.007145
5.379764 4.559241 3.545860 2.297974 5.519878 5.872573 6.151306 0.077351 0.459071 3.526905 0.331859 3.431693 0.344010 0.317252 0.289691 0.262750 0.138739 0.126040 3.256637 0.105706 0.135327 0.124013 0.114006 0.105181 0.063051 0.058873 0.055086 0.051638 0.062973 0.058840 0.055075 0.051636 0.034136 0.032315 o.O;i626 O.Oi90;3 0.020572 0.019644 0.018770 0.017947 0.013348 0.012831 0.012322 0.011857 O.Oogl61 0.008802 0.008393 0.008182 0.006515 0.006281 0.006041 0.005801
0.411624 1.724198
0.847720 0.224111
E%go: . 0.097716 0.097354 0.048485 0.048486 0.027585 0.017173 0.011410 0.008004 0.005560
0.090668 0.090305 0.045591 0.045592 0.026215 0.016441 0.010997 0.007693 0.005320
297 Atomic Data and Nuclear Data Tables, Vol. 25. No. 4. July 1980
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Energy = 0.1 eV K = 2.597682 Number: gerade I 147 ungerade = 73
6.169716 0.786002 1.553078 2.188734 5.656238 0.620891 1.804240 2.923188 3.019440 2.619948 2.087763 1.418635 2.684989 3.297152 3.848563 4.340205 4.776063 2.388038 5.356899 1.326143 6.282011 0.102835 0.177276 0.227357 3.457449 0.280776 3.393650 3.369691 0.244047 0.230459 0.216744 0.203043 0.128775 0.120975 0.113892 0.106925 0.125450 0.117585 0.110269 0.103389 0.068518 0.064999 0.061753 0.058704 0.068353 0.064825 0.061547 0.058464 0.041237 0.039344 0.037578 0.035921 0.041227 0.039344 0.037582 0.035924 0.026702 0.025654 0.024659 0.023716 0.026702 0.025654 0.024659 0.023716 0.018292 0.017659 0.017054 0.016482 0.013076 0.012679 0.012276 0.011924 0.009667 0.009419 0.009156 0.008903 0.007375 0.007185 0.007004 0.006825 0.005747 0.005614 0.005476 0.005353 0.004575 0.004476 0.004380 0.004279 0.003703 0.003592 0.003561
L=O-9
LzlO-19
L=20-29
L=30-39
L.40-49
L=50-59
L.60-69
L=70-79
L=80-89 L=90-99
yw;-;m;
LZl20-129 L.130-139 Ls140-146
1.234585 2.670207 3.970912 5.137192 0.019202 1.525372 2.966922 4.343868 3.317307 3.435921 3.426174 3.287318 5.895139 0.474987 1.274594 2.011081
2.694328 3.070521 3.977865 4.968444 0.608613 5.934937 4.773276 5.149637 0.890122 3.844310 0.258121 0.274018 0.207705 0.190315 0.189641 0.176740
0.099956 0.093232 0.096968 0.091090 0.055795 0.053003 0.055542 0.052772 0.034370 0.032906 0.034370 0.032906 0.022821 0.021969 0.022821 0.021969 0.015930 0.015393 0.011499 0.011199 0.008659 0.008424 0.006653 0.006485 0.005234 0.005114 0.004183 0.004103
B U
g U
4.821474 3.541610 2.074376 0.400325 5.471833 5.742663 5.965216 6.143411
g U
0.574716 3.623524 0.412469 0.358855 0.279115 0.276714 0.268846 0.257268 0.175269 0.161667 0.149138 0.138057 0.164588 0.153441 0.143302 0.134002
g U
g U
0.087050 0.081551 0.076701 0.072392 0.085754 0.080870 0.076357 0.072187
Number: gerade = 190 ungerade = 168
3.114529 4.226773 5.251148 6.189559 2.268483 3.662588 5.021640 0.062611
g U
0.050337 0.047818 0.045462 0.043271 0.050155 0.047695 0.045392 0.043239 0.031531 0.030231 0.028976 0.027808 0.031531 0.030231 0.028998 0.027808 0.021159 0.020389 0.019657 0.018958 0.014832 0.014406 O.Olj941 0.013480 0.010871 0.010550 0.010246 0.009951 o.oo8197 0.007980 0.007767 0.007557 0.0063% 0.006i82 O.OOab3i 0.005887 0.005001 0.004885 0.004778 0.004663 0.004028 0.003946 0.003862 0.003790
Energy = 1.0 eV K = 8.214591
0.760878 1.533639 1.352049 2.606973
5.186189 5.26449; 6.109538 0.752055 3.506928 3.060111 1.462491 2.099630 3.281089 2.38932; 0.440377 0.841076 5.207128 4.011134 3.599232 3.822654 3.227090 2.876071 5.261071 5.368054 1.154780 1.054416 6.005799 6.048698
L=O-9
L=lO-19
L.20-29
L=30-39
L.40-49
L=50-59
L-60-69
L-70-79
L=80-89
L=90-99
L=lOO-109
L.llO-119
L=120-129
4.040739 5.518352 0.619976 1.912733 2.622525 4.157877 5.657813 0.839198 2.226930 2.843118 3.384515 3.853352 3.827612 5.014216 6.167059 1.003247
5.284333 5.247184 5.154693 5.oo8095 1.646845 2.511138 3.345365 4.149975 2.566386 2.026513 1.440981 0.810470 2.710650 3.296067 3.856394 4.392235 1.455422 0.479894 5.746759 4.690788 1.221312 1.581721 1.922830 2.245256 2.842361 1.733344 0.718174 6.103807 4.031757 4.227172 4.409427 4.579184 2.572085 2.307428 2.075841 1.872336 5.466507 5.556952 5.639912 5.715821
B U
B U
g U
g U
g U
B U
B
U
8 U
8 U
g
U
B U
g U
g U
B U
g U
g U
g
U
0.964391 0.883560 0.810853 0.745268 6.087437 6.122389 6.153779 6.181924
0.431667 0.401784 0.374474 0.349592 0.026046 0.036681 0.045972 0.054054
L=130-139
L-140-149
0.225409 0.212991 0.201557 0.190941 0.084745 0.086495 0.087800 0.088734 0.135830 0.129969 0.124481 0.119419 0.087448 0.086549 0.085497 0.084370 0.091684 0.088564 0.085583 0.082816 0.075058 0.073625 0.072158 0.070681 0.066864 0.064966 0.063243 0.061599 0.061202 0.059900 0.058589 0;057321 0.051481 0.050391 0.049240 0.048007 0.049049 0.047944 0.046854 0.045818
L=150-159
L=l60-169
L=170-179 g 0.022235 0.021878 0.021528 0.021188 0.020851 0.020513 0.020179 0.019855 L=180-189 g 0.018927 0.018628 0.018327 0.018031 0.017743 0.017468 0.017201 0.016933
4.251944 2.089463 4.808849 4.925453
:-;::::tt . :‘::69% . 5.329861 4.737063 1.692-f91 5.785183 0.686136 6.207144
4.582497 3.142846
4.847017 4.163738 4.256774 0.107756 4.936521 5.858298 1.307312 3.106821 4.112590 5.019390 1.392693 5.906034
5.047630 5.152506
4.557988 5.672284
:*",;a;; . 2.467637 2.836684
:%::59: . 1.533830 5.848472
0.632692 6.229643
0.500688 0.46450; 6.283161 0.013854
0.253665 o.238950 0.079572 0.082428 0.148694 0.142029 0.088819 0.088184 0.098399 0.094936 0.077911 0.076489
4.130309 0.018569 0.122563 3.360802
;%:% . 1.266992 5.958335 0.540444 6.267436
0.326906 0.306109 0.287056 0.269640 0.060949 0.066837 o.071908 0.076135 0.181122 0.172116 0.163779 0.155958 0.089286 0.089540 0.089567 0.089321 0.114707 0.110248 0.106044 0.102097 0.083177 0.081903 0.080593 0.079271
0.080213 0.077664 0.075224 0.073010 0.069248 0.067862 0.066482 0.065100 0.059969 0.058376 0.056850 0.055374 0.056100 0.054881 0.053648 0.052433 0.046764 0.045591 0.044508 0.043492 0.044845 0.043913 0.042998 0.042097 0.037448 0.036651 0.035886 0.035186 0.036541 0.035771 0.035037 0.034339
0.040635 0.039791 0.039008 0.038239 0.039605 0.038842 0.038085 0.037311
0.070955 0.068904 0.063758 0.062473 0.053950 0.05264; 0.051269 0.050152 0.042510 0.041551 0.041226 0.040397 0.034540 0.03392; 0.033664 0.033015
0.028424 0.027782 0.027637 0.027127 0.022995 0.02260; 0.022995 0.022607 0.019540 0.019230 0.016674 0.01641~
0.033301 0.032668 0.030380 0.031429 0.032385 0.031758 0.031137 0.030520
0.030843 0.030271 0.029682 0.029067 o.o2gglO 0.029322 0.028748 0.028188 0.024818 0.024314 0.023843 0.023404 0.024722 0.024281 0.023842 0.023446
0.027147 0.026529 0.025931 0.025360 0.026635 0.026123 0.025645 0.025173
298 Atomic Data and Nuclear Data Tables. Vol. 25, No. 4,Juiy 1980
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001- 10 eV
TABLE. Phase Shifls for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Energy = 2.7 eV K = 13.497950 Number: gerade = 241 ungerade = 241
L-O-9 g 4.807064 0.012659 1.419841 2.746243 3.993058 5.161819 6.254343 0.989498 1.935887 2.812698 u 3.140238 4.680295 6.189641 1.385145 2.833262 4.250916 5.638243 0.712217 2.039397 3.336806
L.lO-19 g 3.622402 4.367518 5.050552 5.673986 6.240294 0.468690 0.927830 1.336777 1.697689 2.012574 u 4.604675 5.843257 0.769641 1.950488 3.102925 4.227280 5.323896 0.109942 1.152156 2.167725
L.20-29 g 2.283420 2.512083 2.700313 2.849839 2.962217 3.039016 3.081663 3.091556 3.070025 3.018321 u 3.157036 4.120487 5.058486 5.971448 0.576598 1.440718 2.281042 3.098004 3.892038 4.663565
L-30-39 g 2.937682 2.829248 2.694174 2.533514 2.348352 2.139682 1.908528 1.655847 7.382615 1.089770 u 5.413000 6.140770 0.564131 1.249880 1.915237 2.560615 3.186450 3.793163 4.381142 4.950788
L:40-49 g 0.778255 0.449014 0.102962 6.024251 5.647423 5.256656 4.852892 4.437148 4.010420 3.573757 u 5.502529 6.036765 0.270677 0.771035 1.255066 1.723131 2.175590 2.612846 3.035268 3.443187
L.50-59 g 3.128231 2.674935 2.215021 1.749632 1.280001 0.807344 0.332951 6.141294 5.667328 5.195575 u 3.836982 4.217024 4.583632 4.937156 5.277961 5.606357 5.922672 6.227259 0.237230 0.519271
L.60-69 g 4.727358 4.264025 3.806848 3.357128 2.916032 2.484720 2.064198 1.655417 1.259176 0.876157 u 0.790530 1.051293 1.301866 1.542562 1.773652 1.995437 2.208205 2.412215 2.607763 2.795110
L=70-79 g 0.506908 0.151818 6.094360 5.768276 5.456794 5.159789 4.877096 4.608414 4.353415 4.111683 u 2.974506 3.146239 3.310541 3.467656 3.617864 3.761363 3.898400 4.029240 4.154048 4.273079
L-80-89 g 3.882772 3.666212 3.461482 3.268095 3.085498 2.913206 2.750677 2.597428 2.452962 2.316804 u 4.386565 4.494656 4.597613 4.695627 4.788843 4.877519 4.961803 5.041850 5.117896 5.190058
Ls90-99 g 2.188504 2.067619 1.953732 1.846451 1.745383 1.650182 1.560503 1.476010 1.396428 1.321435 u 5.258503 5.323434 5.384949 5.443225 5.498419 5.550631 5.600033 5.646740 5.690865 5.732560
LzlOO-109 g 1.250782 1.184214 1.121464 1.062427 1.006694 0.954150 0.904629 0.857922 0.813882 0.772353 u 5.771907 5.809034 5.844065 5.877061 5.908161 5.937457 5.965001 5.990930 6.015315 6.038197
L-110-119 g 0.733169 0.696212 0.661339 0.628432 0.597375 0.568057 0.540384 0.514245 0.489565 0.466260 u 6.059711 6.079906 6.098825 6.116583 6.133220 6.148781 6.163358 6.176985 6.189713 6.201610
Lsl2O-129 g 0.444228 0.423420 0.403761 0.385164 0.367590 0.350978 0.335256 0.320386 0.306316 0.293007 u 6.212701 6.223047 6.232696 6.241659 6.250008 6.257777 6.264967 6.271646 6.277849 0.000382
Lz130-139 g 0.280399 0.268456 0.257168 0.246464 0.236296 0.226693 0.217599 0.208920 0.200725 0.192977 u d.005673 0.010573 0.015072 0.019219 0.023041 0.026529 0.029733 0.032675 0.035337 0.037755
Ls140-149 g 0.185572 0.178527 0.171917 0.165609 0.159614 0.153903 0.148495 0.143316 _. .__
0.042080 0.043859 0.045484 0.046930 0.048197 0.138383 0.133707
u 0.039973 0.049335 0.050337 0.051191 0.051938 Ls150-159 g 0.129262 0.125008 0.120946 0.117091 0.113420 0.109904 0.106576 0.103379 0.100328 0.097398
u 0.052588 0.053109 0.053535 0.053902 0.054169 0.054345 0.054468 0.054533 0.054527 0.054467 L1160-169 g 0.094597 0.091930 0.089366 0.086906 0.084574 0.082330 0.080148 0.078072 0.076117 0.074223
IJ 0.054402 0.054242 0.054036 0.053815 0.053558 0.053236 0.052892 0.052550 0.052176 0.051768 Lz170-179 g 0.072354 0.070583 0.068935 0.067311 0.065733 0.064222 0.062801 0.061404 0.060057 0.058756
u 0.051345 0.050908 0.050478 0.050002 0.049541 0.049069 0.048563 0.048034 0.047517 0.046910 L-180-189 g 0.057492 0.056268 0.055108 0.053989 0.052881 0.050839 0.049855 0.048861
u 0.046477 0.045961 0.0.51849 0.047914
0.045455 0.044971 0.044423 0.043912 0.043380 0.042843 0.042297 0.041765 L=190-199 g 0.047039 0.046197 0.045342 0.044476 0.043692 0.042911 0.042174 0.041471 0.040792 0.040107
u 0.041258 0.040836 0.040314 0.039797 0.039264 0.038794 0.038314 0.037816 0.037332 0.036871 L:200-209 g 0.039421 0.038770 0.038124 0.037574 0.036922 0.036335 0.035799 0.035239 0.034691 0.034154
u 0;036417 0.035941 0.035462 0.035038 0.034583 0.034126 0.033662 0.033208 0.032767 0.032336 L-210-219 g 0.033627 0.033122 0.032643 0.032169 0.031692 0.031216 0.030757 0.030321 0.029901 0.029505
u 0.031897 0.031450 0.031013 0.030601 0.030210 0.029815 0.029406 0.028993 0.028638 0.028266 L.220-229 g 0.029107 0.028722 0.028355 0.027927 0.027526 0.027091 0.026678 0.026275 0.025884 0.025518
u 0.027904 0.027542 0.027174 0.026853 0.026511 0.026192 0.025878 0.025556 0.025229 0.024911 L=230-239 g 0.025196 0.024924 0.024584 0.024350 0.024041 0.023752 0.023455 0.023177 0.022927 0.022569
u 0.024610 0.024324 0.024054 0.023777 0.023490 0.023202 0.022890 0.022601 0.022363 0.022127 L.240-240 g 0.022327
u 0.021874
299 Atomic Data and Nuclear Data Tables, Vol. 25. No. 4, July 1980
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Energy = 5.0 eV K = la.368383 Number: gerade = 301 ungerade = 288
L=O-9 g 4.013988 5.507237 0.640203 1.980137 3.245137 U 2.630800 4.171661 5.682622 0.880562
4.436839 5.557183 0.325171 1.309544 2.229621 2.331951 3.753734 5.146073 0.225974 1.560027 2.465294
L-to-19 g 3.087979 3.887234 4.630000 5.318855 5.956315 0.261636 0.803547 i.301118 I.756499 2.171748 U 4.142046 5.390580 0.328026 1.521094 2.686951 3.825971 4.938541 6.025061 0.802756 1.838417
L=20-29 g 2.548812 2.889535 3.195674 3.468882 3.710727 3.922700 4.106198 4.262561 4.393046 4.498855 U 2.849281 3.835781 4.798345 5.737442 0.370305 1.263754 2.135044 2.984614 3.812907 4.620364
L=30-39 g. 4.581128 4.640944 4.679344 4.697302 4.695773 4.675643 4.637790 4.583030 4.512173 4.425975 U 5.407414 6.174480 0.638801 1.367175 2.076829 2.768161 3.441573 4.097468 4.736235 5.358246
L.40-49 g 4.325188 4.210518 4.082671 3.942305 3.790088 3.626641 3.452599 3.268548 3.075097 2.872804 U 5.963875 0.270316 0.844299 1.402982 I.946717 2.475858 2.990725 3.491640 3.978942 4.452939
L=50-59 g 2.662253 2.443979 2.218546 1.986467 1.748288 1.504506 1.255646 1.002192 0.744648 0.483490 U 4.913926 5.362218 5.798117 6.221894 0.350654 0.751060 1.140179 1.518279 1.885641 2.242502
L.60-69 g 0.219198 6.235424 5.966257 5.695339 5.423102 5.149991 4.876413 4.602802 4.329537 4.057035 U 2.589109 2.925730 3.252586 3.569911 3.877956 4.176928 4.467049 4.748554 5.021636 5.286508
L.70-79 g 3.785647 3.515765 3.247711 2.981853 2.718481 2.457930 2.200460 1.946370 1.695887 1.449274 U 5.543388 5.792457 6.033920 6.267977 0.211614 0.431399 0.644329 0.850566 1.050302 1.243697
LrBO-a9 g 1.206720 0.968450 0.734616 0.505403 0.280927 0.061333 6.129888 5.920329 5.715889 5.516637 U 1.430918 1.612136 1.787499 1.957174 2.121311 2.280056 2.433568 2.581977 2.725433 2.864077
L-90-99 g 5.322593 5.133786 4.950214 4.771867 4.598731 4.430757 4.267919 4.110138 3.957374 3.809530 U 2.998029 3.127442 3.252432 3.373124 3.489659 3.602135 3.710685 3.815430 3.916461 4.013914
L=lOO-109 g 3.666545 3.528321 3.394768 3.265797 3.141287 3.021163 2.905285 2.793573 2.685897 2.582151 U 4.107886 4.198472 4.285800 4.369948 4.451021 4.529128 4.604339 4.676764 4.746489 4.813588
LrllO-119 g 2.482233 2.386006 2.293392 2.204249 2.118486 2.035992 I.956644 1.880366 1.807022 1.736534 U 4.878167 4.940289 5.000042 5.057512 5.112757 5.165869 5.216911 5.265949 5.313068 5.358313
L=120-129 g 1.668796 1.603699 1.541173 1.481098 1.423403 1.367999 1.314785 1.263704 1.215096 1.168001 U 5.401762 5.443481 5.483510 5.521936 5.558799 5.594148 5.628064 5.660570 5.691729 5.721603
L=l30-139 g 1.122805 1.079409 1.037769 0.997798 0.959441 0.922630 0.887310 0.853417 0.820891 0.789688 U 5.750212 5.777626 5.803884 5.829014 5.853084 5.876116 5.898149 5.919238 5.939398 5.958677
Lrl40-149 g 0.759741 0.731016 0.703454 0.677002 0.651633 0.627284 0.603928 0.581528 0.560014 0.539388 u 5.977114 5.994723 6.011557 6.027638 6.042987 6.057655 6.071649 6.084998 6.097748 6.109898
L.l50-159 g 0.519589 0.500598 0.482374 0.464885 0.448110 0.432008 0.416550 0.401722 0.387497 0.373831 u 6.121481 6.132535 6.143058 6.153085 6.162644 6.171734 6.180392 6.188631 6.196463 6.203921
L.l60-169 g 0.360728 0.348144 0.336062 0.324490 0.313349 0.302647 0.292407 0.282538 0.273085 0.264101 u 6.211007 6.217730 6.224131 6.230200 6.235958 6.241444 6.246666 6.251509 6.256248 6.260625
L.170-179 g 0.255578 0.247184 0.239142 0.231409 0.223970 0.216826 0.209973 0.203379 0.197031 0.190943 u 6.264975 6.269315 6.273052 6.276572 6.279913 6.283055 0.002839 0.005639 0.008275 0.010758
L-180-la9 g 0.185087 0.179452 0.174031 0.169012 0.164003 0.159172 0.154545 0.150088 0.145783 0.141657 II 0.013098 0.015293 0.017343 0.019287 0.021106 0.022794 0.024390 0.025864 0.027432 0.028716
LrlgO-199 g 0.137678 0.133844 0.130155 0.126795 0.123366 0.120077 0.116905 0.113835 0.110878 0.108050 u 0,02gg74 0.031025 0.032054 0.033013 0.033888 0.034699 0.035451 0.036124 0.036743 0.037324
Lz200-209 g 0.105298 0.102643 0.100291 0.097838 0.095447 0.093154 0.090945 o.o88809 0.086134 0.084743 U 0.037824 0.038285 0.038883 0.039251 0.039573 0.039856 0.040106 0.040303 0.040478 0.040636
L:210-219 g 0.082822 0.080957 0.079158 0.077408 0.075918 0.074303 0.072724 0.071184 0.069720 0.068298 u 0.040738 0.040810 0.040873 0.040904 0.041092 0.041066 0.041037 0.040981 0.040892 0.040804
Ln220-229 g 0.066905 0.065554 0.064268 0.063008 0.061785 0.060798 0.059652 0.058529 0.057458 0.056415 u 0.0406gO 0.040558 0.040409 0.040266 0.040109 0.039903 0.039905 0.039713 0.039494 0.039276
L.230-239 g 0.055392 0.054085 0.053067 0.052140 0.051418 0.050526 0.049669 0.049029 0.048224 0.047443 U 0.039052 0.038816 0.038568 0.038322 0.038079 0.037809 0.037540 0.037477 0.037214 0.036923
L.240-249 g 0.046679 0.045912 0.045181 0.044474 0.043805 0.043134 0.042664 0.042006 0.041385 0.040783 U 0.036636 0.036359 0.036092 0.035794 0.035509 0.035226 0.034926 0.034643 0.034285 0.034244
L-250-259 g 0.040204 0.039620 0.039040 0.038485 0.037944 0.037428 0.036915 0.036392 0.035894 0.035447 U 0.033970 0.033677 0.033382 0.033096 0.032793 0.032486 0.032080 0.031881 0.031595 0.031341
L=260-269 g 0.034972 0.034510 0.034078 0.033796 0.033369 0.032 i 61 0.032524 0.032109 0.031730 0.029098
0.031524 U 0.031233 0.030965 0.030695 0.030425 0.030133 0.029 68 0.029593 0.029340 0.028810
L-270-279 g 0.031166 0.030807 0.030444 0.030087 0.029731 0.029383 0.029061 0.028719 0.028371 0.028235 U 0.028533 0.028503 0.028242 0.027977 0.027709 0.027451 0.027219 0.026961 0.026691 0.026450
L.280-289 g 0.027917 0.027617 0.027339 0.027060 0.026783 0.026494 0.026177 0.025879 0.025621 0.025556 u 0.026206 0.026158 0.025900 0.025636 0.025403 0.025186. 0.024934 0.024891 0.025621 0.025556
L.290-299 g 0.025290 0.025045 0.024806 0.024575 0.024302 0.024057 0.023833 0.023801 0.023576 0.023347 L:300-300 g 0.023105
300 Atomic Data and Nuclear Data Tables, Vol. 25. No. 4duly lSB0
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
TABLE. Phase Shifts for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
Ener 'gy = 10.0 eV K=
4.518809 4.871060
25.976817 Number: gerade = 366 ungera tde = 323
1.002471 2.276483 1.571008 3.015351
3.479921 4.428468
4.614987 5.810613
0.406834
1.306385 1.273625
2.200029
4.863133
0.313737
4.144478 0.017763
6.197395
5.061653 0.165879 4.466048 5.802798 2.690902 4.687701 6.268437 3.332062 2.821604 1.900099 5.064005 0.507781 0.546090
5.514497 1.928265
4.396583 3.003742 3.453047 3.834829 2.680150 4.472349 2.061993 4.957630 1.576768 5.324090 1.201322 5.598552 0.913932 5.802377 0.695670 5.952413
0.530759 6.062071 0.406968 6.141039
LZO-g
L.lO-19
L:20-29
t=30-39
L=40-49
L=50-59
Lt60-69
L-70-79
L.ao-a9
L190-gg
L.lOO-109
L.llO-119
L=120-129
L-130-139
L1140-149
L=150-159
Lr160-169
L=170-179
L=lao-la9
L--190-199
L.200-209
L.210-219
L-220-229
L-230-239
L-240-249
L.250-259
L.260-269
L=270-279
L=280-289
L.290-299
L:300-309
L=310-319
L-320-329
l-=330-339 Ln340-349 L=350-359 L.360-365
g ”
5.939195 0.095235 3.853443 0.906035
3.059121 5.202527
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0.198939 1.214164 6.2648g3 0.112084
m;; . 4.163gii 1.199695
:%;:z .
1.792886 2.291756
1.352204
5.084765
3.491200
4.944259 0.0805ao 5.692202 0.130634 4.965253 5.708009 3.087006 4.559821 0.299527 3.190044 3.070436
1.757537 5.260294
0.373975 0.700161
5.395120 2.048488
4.294318 3.096928
2.239886 4.752823
2.245989 3.285574 5.286757 5.725087 0.131346 0.024905 0.087945 5.453010 5.608864 3.474063 4.429772 0.606589 3.047435 3.313481 1.615493 5.451932 0.241409 0.850499
5.277383 2.165719 4.193810 3.187735
3.072705 5.985340
2’6265%: . 5.470086 0.204258 0.170621 0.626504 0.038192 5 -929594
5 '550%: . 4.297742 0.906592 2.904370 3.550867 1.474063 5.639019 0.110140 0.997187 5.161297 2.280032 4.095074 3.276213
54-93;90:;; . :%E: . 6.034124 3.078227 0.223165 2.896915 6.058414 1.446178
5.056437 5.280672
0.225417
0.330309
5.445348
4.356836 2.486071
6.187626
6.136766 3.755058 0.212546 3.432173 5.978275 1.870707
4.936205 5.617585 3.613786 2.306064 2.186417 4.657066 0 .-I78894 0.226412 5.758041 1.678590
4.606394 2.810012
%::;43 2.821720 4.358223 2.174249 4.871044
1 .664296 5.258930 1.268704 5.549924 0.965317 5.766398
0.734591 5.926029 0.560155 6.042913 0.429035 6.127274
0.784571 0.230615
0.321908
4.620858 3.325252 6.225485
6.192598
4.416067 0.193320 3.955117 5.892981 2.285541
4.813229 5.946785
3.473357 2.566855 2.043093 4.862966 0.642775 0.388201
5.635477 1.804991
4.500613 2.908125
;:X;o" 2.750151 4.416063
2.117444 4.914944
1.619971 5.291976 1.234562 5.574598 0.939270 5.784662 0.714850 5.939430 0.545262 6.052647 0.417840 6.134272
g ”
B ”
3.758890 0.745774 5.916887 2.385159 0.224733 2.349039 6.133094 1.011721
5.173709 4.935868 3.891471 1.765797 2.473658 4.230265 1.054257 6.173963 6.007772 1.416130
4.823193 2.606088
3.809425 3.528236 2.969656 4.237730 2.292013 4.779485
1.756395 5.189910 1.339767 5.498329 1.019599 5.728155
0.775752 5.897937 0.591214 6.022475 0.452397 6.112555 0.347864 6.177151 0.269346 6.222900 0.210427 6.254893 0.166084 6.276795
0.132574 0.008269 0.113033 0.025920
0.094559 0.031523 0.080579 0.034608 0.068828 0.035936 0.060719 0.037211 0.054495 0.036567 0.049706
0.216817 1.788230 6.202030 0.567104
:-:sB198;: . 4.028423 1.486049 2.617362 4.009138 1.193366 5.999940 6.134868 1.279924 4.934186 2.500150 3.902882 3.446414 3.046058 4.175000
2.353016 4.731761
1.804221 5.153896
g ”
2.329975 4.446203 0.916078 0.060633 5.882148 1.548992
4.713924 2.709354
: ::A,",:: 2.894886 4.298793 2.232431 4.825905
1 .709765 5.224916 1.303768 5.524505 0.992090 5.747566 0.754886 5.912206
0.575463 6.032859 0.440551 6.120037
0.338959 6.182481 0.262736 6.226709
0.205401 6.257481 0.162302 6.278588
0.129663 0.009422 0.110816 0.026609
0.092852 0.031943
0.079251 0.034786 0.067798 0.035986 0.059886 0.037158
0.053853 0.036367 0.049191
g ”
B ”
1.333325 5.821657 6.263401 1.140301 5.046896 2.391489 3.998094 3.362426 3.124103 4.110556
2.415466 4.682697
1.853254 5.116833 1.414687 5.443604 1.076927 5.687524
g ”
8 u
g ”
4.527119
2.007871
0.148161
4.999130
0.001734
1.534656 5.355282 1.168953 5.621803 0.889275 5.819559 0.677008 5.964995 0.516713 6.071188
0.396397 6.147582 0.305804 6.202028
0.237825 6.240395
0.186662 6.266895
t3 ”
2.479381 4.632256
0.376147
1.903526 5.078705
6.160017
1.453638 5.415020 1.106779 5.666271 0.841970 5.852373 0.641236 5.989241 0.490047 6.088560
0.386124
1.955057 5.039482 1.493625 5.385584
6.153904
1.137450 5.644370
0 .a65298 5.836218 0.658871 5.977178 0.502988 6.080018
1.376736 5.471369 1.047877 5.708147
0.624089 0.607411 6.000675 6.011749
0 -464594 6.104822
0.357018 6.171632 0.276233 6.219021
0.215599 6.252208 0.169934 6.274924
0.135498 0.007075 0.114262 0.025167
0.096281 0.031103 0.080788 0.034376
0.069883 0.035865 0.061548 0.037231 0.055148 0.036638 0.050259
0.283311 6.214991
0.366445
0.220925 6.249418
0.173913
6.165926
6.273008
0.138539 0.005829 0.116476 0.024405
0.098074 0.030635
0.083300 0.034153
0.070935 0.035758
:-00;5:;: . 0.055845 0.036726 0.050791 0.035619 0.046899 0.043943 0.040406 0.037484
0.298093 6.206506 0.232032 6.243515 0.182283 6.269026
0.144867 0.003156 0.116468 0.014473 0.100661 0.029641 0.086168 0.033633 0.073164 0.035551 0.064165 0.037268
0.290591 6.210825 0.226400 6.246526 0.178056 6.271086
0.141666 0.004521 0.118867 0.023573 0.098780 0.030169 0.084705 0.033889 0.072052 0.035676
0.063256 0.037255 0.056527 0.036833
0.045582 0.042779 0.039467 0.036669
0.256241 6.230322 0.200516 6.259969 0.158616 6.280269
0.126901 0.010524 w.108697 0.027292 0.091214 0.032305 0.077982 0.034983 0 .o67922 0.036026
0.059101 0.037120 0.053202 0.036404 0.048646
0.249925 6.233802
0.195767 6.262369 0.155034 6.281882
0.124207 0.011602
fy6;:;
0.08g608 0.032678 0.076752 0.035168 0.066957 0.036073
0.243790 6.237160 0.191149 6.264677 0.151546
0.121541 0.012620 0.104557
0.000244
0.028530
0.088053 0.033028 0.075524 0.035305 0.065980 0.036084 0.058718 0.037035 0.051962 0.036211 0.047677
g ” g ” B ” 8 ” g ” I3 ” 8 ” is ” B ” B B
0.118966 0.013579 0.102580 0.029112
0.074342 0.035448 0.065066 0.037248
0.052596 0.036271 0.048153
0.046456 0.043512 0.040112 0.037120
0.051387 0.036142 0.047170 0.051937 0.051312
0.035999 0.035871 0.046716 0.046222 0.043533 0.043125 0.041059 0.040748 0.037958 0.037745
0.044720 0.044325 0.043915 0.042093 0.041731 0.041408 0.038876 0.038608 0.038242
0.046034 0.045162 0.042443 0.039219 g
B
301 Atomic Data and Nuclear Data Tables. Vol. 25. No. 4, Juty 1980
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302 GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.ooOl-10 eV
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.OOOl- 10 eV
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
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306 GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.tNlOl- 10 eV
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, O.OOOl- 10 eV
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
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GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
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GEOFFREY HUNTER and MARY KURIYAN hoton Scattering by H Atoms, 0.0001-10 eV
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
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310 GEOFFREY HUNTER and MARY KURIYAN Proton Scattering by H Atoms, 0.0001-10 eV
GRAPHS. Differential Cross Sections for Scattering of Protons by Hydrogen Atoms See page 291 for Explanation of Table and Graphs
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