JOURNAL OF THE OPTICAL SOCIETY OF AMERICA

Analysis of the Spectrum of Neutral Erbium (Er I)

NIssAN SPECTOR

National Bureau of Standards, Washington, D. C. 20234(Received 3 June 1965)

First results of a continuing analysis of Er I are given: 30 low levels belonging to 4fII5d6s2 and other oddconfigurations, as well as 138 high levels of even parity are assigned J-values. More than 300 absorptionlines are classified. The connection of the odd levels to the 4f' 26s2 configuration is established, using tran-sitions in the infrared. The energy matrices in intermediate coupling for the subconfiguration f " (41)d havebeen calculated and are given. The theoretical formulas were adjusted by a least-squares fit to 19 observedlevels designated as 4f" (4I7i, 61)5d6s2 resulting in new values for 6 electrostatic and 2 spin-orbit interactionparameters. The rms error was 186 cm-1. Calculated percentage compositions in various coupling schemesshow the J.-j type to be the best for these levels.

INDEX HEADINGS: Erbium; Atomic spectra.

INTRODUCTION

N the last few years there has been an increasinginterest in the atomic spectra of erbium. A full

description of the first and second spectra of erbiumwas undertaken by us at the National Bureau ofStandards. We are now observing, measuring, andcompiling separate line-lists for Er I and Er iI, whichtogether will include about 25 000 lines. The work inthe visible and photographic infrared regions has beencompleted, and work in other regions is now in progress.

Marquet and Davis' have recently reported somepreliminary results of their work on Er i. Their resultsare available also in Marquet's doctoral thesis, whichProfessor S. P. Davis kindly made available to us. Inthis thesis, 338 self-reversed lines and 4 low-energylevels of neutral erbium were reported. These levelswere interpreted as the 3H6, 3H6, 3H4, and 3F4 of 4f"6s 2

.

The 3f6 was assigned as the ground level of the erbiumatom.

Although 500 lines were classified in Ref. 1 as transi-tions from 170 upper levels to 7 low ones, only 79 of the338 reversals were accounted for. The bulk of theself-reversed lines remained unclassified; this suggeststhe existence of another low-lying configuration. Thefact that no other low level could be found by combina-tions with the same upper levels made it clear that theother low levels should be of opposite parity to that of4f'2 6s2, namely, odd. With the same 4f'2 core the onlyprobable odd configurations are 4f"2 5d6p and 4fp2 6s6p.Both can be eliminated as candidates competing forthe ground state. The low odd configurations, therefore,should involve the excitation of a 4f electron to aneven orbital. Reasonable possibilities are furnished by4f"I5d6s2 and 4f"15d26s. An interpolation between Ce i2and Yb i3 in which we have information about therelative positions of 4fn5d6s2 and 4fn5d'6s, indicatedthat no level of 4f 1"5d26s of Er i is to be expected withina distance of 9000 cm7- above the first level of 4fII5d6s2.

1 L. C. Marquet and S. P. Davis, J. Opt. Soc. Am. 55, 471(1965).

2 W. C. Martin, J. Opt. Soc. Am. 53, 1047 (1963).' W. F. Meggers and N. Spector (Unpublished material, 1964).

We conclude, therefore, that (a) there is a low configura-tion (say, within 10 000 cm-' from the low levels of4f"26s2) in neutral erbium which is yet to be identified;(b) this configuration is of odd parity; (c) it is, in alllikelihood, 4f"5d6s2 .

The goal of this work was to locate the lower levelsof this configuration and to interpret them.

I. THEORETICAL PREDICTIONS

One of the gaps in the description of the erbiumspectra is the lack of good Zeeman-effect data for theneutral atom, except for the patterns of 19 lines, givenby Lindner and Davis.4 However, the high J valueswith resulting small differences in the g-factors involvedin the transitions to the low 4f"5d6s2 levels, reducethe usefulness of Zeeman data for the present work.Furthermore, as we shall see later, our interpretationof these levels makes these data unnecessary for thecorrect designations of the levels.

The 4f"-5d6s2 configuration is complicated, and thestructure of its levels, even the lower ones, is notobvious. Therefore, a theoretical calculation which willpredict the arrangement of these levels is highlydesirable. We distinguish two main parts in thisconfiguration: the core 4f11 and the outer electrons5d6s2. The structure of the fn type configurations iswell-known now. Conway and Wybourne' calculated,with a high degree of accuracy, the lowest multipletsof the 4f86s2 configurations for all neutral rare-earths.For n= 11 (holmium), only the 4 levels of 4I werepredicted to lie below 10 000 cm-l. It thus seemslikely, since erbium directly follows holmium, that 41

will be the lowest parent of the 4f" core. The lowestlevels of 4f"5d6s2 will then be those based on the 41

parent. We therefore calculated the energy matricesfor that part of f~ld based on the 41 parent. There are40 possible levels in this subconfiguration, with f'sranging from 2 to 10, according to the distributiongiven in Table I.

4 J. W. Lindner and S. P. Davis, J. Opt. Soc. Am. 48, 542 (1958).5 J. C. Conway and B. G. Wybourne, Phys. Rev. 130, 2325

(1963).

341

VOLUME 56, NUMBER 3 MARCH 1966

NISSAN SPECTOR

The energy matrices were calculated in intermediate coupling, i.e., both electrostatic interactions and spin-orbit interactions were included. The following formula was used for the electrostatic interactions:

WV(fld) =- 70 (6) i(U(2) ud(2 ))F2-126(55)i(U( 4) Ud ( 4 ))F4-[-9/2+3 (70)i2(U(1) *Ud(1))-15(6)1(U(2

).Ud (2)

+ (21/2) (15)2 (U(3) Ud 3

))-(9/2) (55)l(U(4) ud(4))+6 (Sf SO- 12 (70)1(V(11) * Vd (1)

+ () (2))- 42(15) (VW0 )* Vd( 3))+18(55)2(V(14) . 4Vd )]G [ 18+ ( )+ (55/2)(6)i(U(2) Ud ))-28(15) (U(3) *Ud 3 ))-18(55),1(U( 4) *Ud (4))+ 24(Sf* Sd)-18(70)2(V'"). Vd~"l)- 110(6)l(V(12 ). vd(I2))+112(15)1(V(13)- Vd(

13))+ 72 (55)l(V(14). vd(14))]G 3- [-99- (99/2) (UM') U()

- (275/2) (6)1 (U'2 )-ud 2))-(77/2) (15)(U(3) (-)) -(9/2) (55)1 (U(4 ) Ud ))+132(Sf-sd)+ 198 (V I) Vd( I))+550(6)' .(V(12). Vd (2))+ 154 (15)1(V(13). Vd (3)+18(55)1(V(I4). v (14) )]G5

For notations see Racah I1.6For the two spin-orbit matrices we used

ES14SL12LJ I Z il (sf * If) I S1'?S'L1'2L'J] =-(- 1) +L'---l'-Sl'-J * E84 (2S+ 1) (2S'+ 1) (2L+ 1) (2L'+ 1)TX (S1Lij1 V(ii) jIS'L,')W(SLS'L'; J1) . W(LLL,'L'; 21)W(SiSSi'S'; I 1),

and

ES1 SL12LJ I (Sd Id) I Sj'1S'Ll'2L'J] = (- l) H-S-+Li+si-J * 3E5 (2L+ 1) (2L'+ 1) (2S+ 1) (2S'+ 1)]-iXW('SIS'; Sll)Wk(2L2L'; Lj1)W(SLS'L'; J1) -6SjSj'5Ll-Lj1,

where S1Li designate the states of the core, and SLJare the quantum numbers of the final state. These arethe general formulas for the whole f"d configuration.We introduced L1 = 6 and Si= 3/2 in all cases, so as toobtain only those levels which result from an additionof a d-electron to the 4I parent.

TABLE I. Number of possible levels for each J-value of f'1 (41I)d.

J 2 3 4 5 6 7 8 9 10

No. of levels 1 3 5 7 8 7 5 3 1

Since it is easy, by changing the signs of the doubletensors, to obtain the electrostatic matrix elements forf3 d from those of f~ld, we calculated the coefficients ofFk and Gk'S for the 3M5G, HI, I, K, L of f3 d and obtainedthe same results given by Judd.7 In the Appendix wegive the electrostatic matrices of fl (I)d, and thespin-orbit matrices of f3 (4I)d. [For fI (4I)d, the matricesof tJ have to be multiplied by - 1.] The diagonalizationof the energy matrices was performed using parametersobtained from previous calculations made by us." Thepredicted positions of the first 10 levels are shown inFig. 1. From this we deduce that the appropriatecoupling scheme for the lower levels of 4f"5d6s 2 is

b

G G. Racah, Phys. Rev. 62, 438 (1942).7 B. R. Judd, Phys. Rev. 125, 613 (1962).8 N. Spector, "Interpretation of the second spectrum of thu-

lium," Ph.D. thesis, Hebrew University of Jerulsalem (1962)(unpublished). The values of the parameters we used were(in cm-,).

F22= 160 Gl= 200F4=7 G3=20

G5 =2

Ji-j in which the two different j's of the d electroncouple to the Ji= 72 level of the 4fll core, to give agroup of 4 and a group of 6 levels, the former being thelower. The most important information is that J= 6 isthe lowest level of this configuration.

II. EXPERIMENTAL DATA AND ANALYSIS

The use of a restricted line-list, consisting mainly oftransitions to the low levels, was considered by us as asuitable way to start the search for these levels. TheKing furnace seemed to furnish exactly this type ofline-list. We took the opportunity of C. H. Corliss' visitto Imperial College in London to obtain photographsof erbium in absorption in the King furnace, in theregion 2500-4700 A. Our measurements of the platesresulted in a list of approximately 1500 lines. Thepresence of such a number of lines in absorption, evenin this limited region of wavelength, confirmed ourconclusion mentioned in the introduction that thereexists a low odd configuration. Our list of absorptionlines included all but 22 of Marquet's 222 self-reversalsin the region where the observations overlapped, plusmany more, especially in the shorter wavelength region.

6000

tENERGY

i n (cm-')

4000

2000

fi = 22501d= 900

The values for the fd interaction were taken from fl2ds of Tm II,owing to lack of other values.

'0

FIG. 1. Predicted positions for first ten levels of 4f"5d6s2 inEr I, using parameters of Ref. 8.

342 Vol. 56

ANALYSIS OF SPECTRUM OF NEUTRAL ERBIUM

Wherever duplicate measurements existed, those ofMarquet at high precision were used in the analysis,since the plate factor on the King furnace p'ates wasonly 2.7 A/mm.

Recently, Mossotti and Fassell have publishedabsorption spectra of various rare-earths, observed inoxyacetylene flames, fed with ethanolic solutions ofperchlorate salts of these elements. They gave 106erbium lines which they attributed to the first spectrum.Only 17 of them were found in Marquet's list of classifiedlines. The authors -point out in their paper that thegiven data "should be of value in deducing the low-lyingenergy-level structure of those rare-earth systems whichare still not analyzed." Our use of them is discussedbelow.

Our first step in the analysis was to difference aselected group of lines versus the whole absorption-linelist by means of a spectroscopic-level searching programwritten by Racah'0 for the IBM 7090 electroniccomputer. This selected group consisted of all the lineswith intensity greater than a chosen value. Mossotti andFassell's lines included most of our strong absorptionlines. Because of their significance for analyses wedecided to use them as our selected group. We changedtheir qualitative intensities, however, to our numericalvalues.

The results of the first run contained many signif-icant intervals. About a dozen of them repeated morethan 8 times, within a tolerance of 0.06 cm-l; some ofthem were sums or differences of others. The outstand-ing ones were 520.45 cm-l, repeating 22 times, and729.54 cm-', repeating 19 times, both within 0.06cm-'. The lines involved in these intervals were amongthe strongest in the absorption list. There was nodoubt that these are fundamental intervals, connectedwith the lowest levels of the 4f515d6s2 configuration.From these results, we deduced the four lowest levels of4f1"5d6s2; they are 0.00, 520.45, 1444.06, and 2173.60cm-' (note: 2173.60-1444.06= 729.54). These four lowlevels were connected to about 60 upper levels, of evenparity.

We then decided to make use of Marquet's completelist, excluding all of his classified lines and about athousand Er ii lines. By using the level-searchingprogram several times (going from low levels to highones and back) we were able to find a total of 30 oddlevels and 138 upper even levels. They are given inTable 11. The connection of these levels to the ground

I V. G. Mossotti and V. A. Fassel, Spectrochim. Acta 20, 1117(1964).

10 We describe here briefly the essential features of this program:It calculates all the possible differences between the wave numbersof the lines (on a magnetic tape) and a group of levels (or lines)given on cards. Then it sorts them in increasing order, and checksfor "chains" of repeating differences bigger than a given lengthk-1 within a given tolerance A. It also calculates the Poissonprobability for a "chain" of this minimum length, to be present.Then it prints out the chains which satisfy the above minimumconditions, together with the number of fortuitous chains to beexpected by Poisson statistics.

state is discussed in the following section; the first 10of the odd levels have already been assigned J-valuesby us in a recent publication." Marquet and Behring"published the first 27 of them without any J-valueassignments. More than 1100 lines in Marquet's listwere classified by the 30 odd and 138 even levels, andwill be published elsewhere." Table III gives our wave-length measurements for 9 emission lines above 5700 A(used to establish the connection to the ground state)as well as those for more than 300 absorption lines whichwere classified with the new levels. Among them, 145were classed as self-reversed by Marquet. These,together with those classified by Marquet,' accountfor more than half of the self-reversed lines. Also, morethan half of the 87 Er i lines listed by Mossotti andFassel, which were used as our selected group, arenow classified. In the first column of Table III we giveour wavelengths for the lines. Column two gives therelative intensities of the lines, estimated visually fromour plates. The comments are: W-wide, F-faint,UR-unresolved, V-very. Columns three and four givethe energies of the even and odd levels which classify thelines, as well as their J-values.

HI. INTERPRETATION OF THE OBSERVEDLEVELS

In Sec. II we have already mentioned the two funda-mental intervals 520.45 and 729.54, which are connectedwith the lowest levels of 4f"l5d6s'. We interpret eachof them as a distance between pairs of levels withadjacent J-values.

By accepting the theoretical prediction that J= 6is the lowest level (see Fig. 1) we were able to givef-values to the first four levels. This also gave usalmost unambiguously the J-values for the upperlevels. In particular, those 19 giving the 729.54 intervalcould have J's of 8 and 9 only. A significant level at2479.34 cm-' was obtained by a special partial group ofthe J= 8,9 levels. Since the theoretical predictionassigned it a J= 10, this enabled us to distinguishbetween the J= 9 and the J= 8 upper levels. By apply-ing the J selection rules to our square-array we gavef-values to all our levels.

We now come to the question of the ground state.By searching for combinations with our odd levels, wefound a single significant level, 7176.52 cm'- below thelowest level of 4f"5d6s'. Only odd levels with Jf= 5,6,7gave transitions to this level. We had, therefore,obtained an even level with J=6, 7176.52 cm-' belowthe lowest 4f"5d6s' level. The corresponding lines onour plates were among the strongest. The final proofthat the level was 'H6 lay in the region of 8000 -10 000A. There we found six very strong lines connecting the

11 N. Spector, J. Opt. Soc. Am. 55, 567 (1965).2 L. C. Marquet and W. E. Behring, J. Opt. Soc. Am. 55, 576

(1965).13 S. P. Davis (private communication, 1965).

March 1966 343

NISSAN SPECTOR

TABLE II. Observed energy levels of Er i.

Odd parityConfiguration Designation

4f'15d6s2 (411512)dl

(411,12)d11

(411312)d2i

(41j,1 2)d,1 ?4f' 1 5d26s ?

4fl26s6p ? ('H6 )lP,

J99889

Level(in cm-1 )

25220.2126099.6126268.0927178.9127198.09

I6798

109586785769856776567875667

Even parityLevel

J (in cm 1)

7 27459.448 27578.767 27625.559 28043.288 28397.15

J88867

Level(in cm-')

7176.527696.978620.589350.129655.86

10557.9211401.2011557.6811799.7811887.5115083.1215185.3615846.5516070.1016501.4217297.6717347.8617456.3917796.1521168.4316321.1817029.0617073.8017157.3118335.5018774.1219201.3719326.6020166.1324943.28

Level(in cm-')

28579.0228699.8629451.9029801.2429967.87

J6787668696766865

10667986869797887768567868

same odd levels to two other even levels of 4f'2

6s2

: the3H5 at 6958.34 cm-' and the 3F4 at 5035.19 cm-l. Thisestablished the fact that the even level first obtainedwas indeed the 3H16 of 4f'2 6s2 . We have given theseresults in a previous publication." It also confirms, aposteriori, our J-value assignments to the odd levels.

IV. THEORETICAL FIT OF THE OBSERVEDENERGY LEVELS

In Fig. 1 we gave the predicted positions, calculatedwith preliminary parameters, of the first ten levels of4f"5d6s2. The same calculation yielded, as was indicatedin §1, the positions for the 40 levels based on the 4Jterm of the 4f11 core. The calculations indicated that inthe first 13 000 cm-1 of the 4f 1"5d6s2 configuration thereprobably were not more than 20 levels. Since weobserved in this region 30 instead of 20 levels it is clearthat some of these levels don't belong to 4 115d6s2 . Thepredicted structure of the ten (4 I 7x)d and the four(4 I61 )dq. levels is clearly displayed by the first 14observed levels. The only problem was the selection of

the J= 5, J= 6, and J= 7 levels. For the last two thiswas done on the basis of isotope shifts. The isotopeshifts of the lines connecting 4f "5d6s2 to 4f'26s2 isabout -48±L 1 mK, according to Marquet and Behring'2

and Wilets and Bradley. 14 There was only one each ofthe J=6 and J=7 levels, whose transitions to theground state had an isotope shift of -48± 1 mK, and weselected them for the 4f"15d6s2 configuration. Theselection of the J= 5 was more difficult. The lineat 5870 A connecting the J= 5 level at 17029.06 cm-1to the ground level was not observed by Wilets andBradley. It is a very weak line on our plates, whichmakes it unlikely to be a 4f"15d6s2 -- 4f126s2 transition.On the basis of intensities from our plates we selectedthe level at 17347.86 cm-1 as the desired J=5, eventhough the line at 5762.79 A, which connects it to theground level, was observed by Wilets and Bradley tohave a positive isotope shift of 33.2±t 1.2 mK. Recently,Haynes and Ross"1 have published their work on

'4 L. Wilets and L. C. Bradley, III, Phys. Rev. 87, 1018 (1952).15 E. Paul Haynes II and John S. Ross, Phys. Rev. 137,

B790 (1965).

Level(in cm-')

30468.4030693.2930726.7431105.6731338.4731523.7731559.8431878.7931906.7031946.4232001.4532212.4632799.5032884.8833139.8133519.7533619.3433750.6534055.2834153.7734224.0634288.4434313.1134447.7734458.0134587.8134596.4034724.9134733.2534756.5934990.2535014.7635191.4735218.6135300.4235328.6835370.3835394.6035493.3135557.1835632.61

J777667796987

10965

10767869787687889878978676

Level(in cm-')

35667.0935717.1135833.8035963.3836026.8836051.4636123.0436136.2036306.2736321.9336384.5636418.4136461.8636494.1736511.2336710.8336712.5936735.7536876.4636891.9937021.2837044.4237062.8337178.4537378.4637391.2437542.8037645.7637806.9937843.8638164.9238172.8238253.6938301.6338343.7038487.2638545.3438556.7638604.5938664.2638667.81

J88656867676867867657686567686668766888677

Level(in cm-1 )

38668.3238734.2538786.5538831.9738923.5939049.4839075.9039145.4639164.2739256.4639350.5239432.6739658.1939738.4839843.4339971.0740131.3440140.6440343.4340833.9940840.9441168.1641407.8341603.8541907.3341989.9342353.8542376.2742627.5743191.6343298.2243586.0643826.6743870.4944194.7844201.0544301.5244410.8944827.9145874.4246970.82

344 Vol. 56

ANALYSIS OF SPECTRUM OF NEUTRAL ERBIUM

TABLE III. Classified absorption lines of Er i.

Wavelength'(in A) Intensity

9927.10a9883. 1839849.38$9622.45n9523.00"8119.47a6583.48n5870.69"5726.98"5909.285855.335826.785762.775719.495348.025172.744722.714713.094710.874687.804684.734684.014640.204522.714488.854432.034418.684390.214386.374380.634359.164347.274340.924313.664306.334301.214293.164270.684269.884251.064221.074212.744197.394195.734177.794171.814170.824160.294113.274091.754070.524069.084067.414027.044009.754007.973999.043993.083982.503981.323977.573969.013961.203959.863948.053939.793938.493936.583934.893929.283919.653908.443904.603901.643899.043896.753895.343894.853881.173880.303871.753870.863869.843868.673859.313854.513852.423849.923838.503837.173832.533829.703825.053824.243823.983822.333803.733803.19

Even level(cm-,) J

303

808

808060

13

5125122

5021F31F1F122131

10211

20

111

21

1

3

122

1

1 VP

3

1

111

8

8

1 VF223

10

1W21 VW

3

1

2

213228

0

3211W12

132

695869585035695869585035

000

26268000

2609928043

00

386673154236511331393069337.39 12980129967319062980130468299673866734733306933458734733350144441031906311053530030693408403428835218315233110533619353703458732001349904190734224361363200134587

0336193221232799365113702132884345873459641168347243473343191347563313937062361363422432799349903754235014342883764536321373783638437391351913646136494432983458735394337504116834724347563754241989367123563237843

March 1966

Odd level(cm-,) J

S6SS6S

Even level(cm-,) J

Odd level(cm-,) J

9787686

7106978699796

106668897897686999686788988771096976898671088

1702917073151851734717456174371518517029174569350

170731715717347862093501932621168174561632115185117999350

15846769676969350717676967176

15846117997696

1155711557117992116886207696

118877176

171571055711401769671769655

11401105577696

10557173479655

1155771769655

24943862071767696

1140111887769693509350

1584693509350

1779693507696

1155710557862071769350

1188793508620

11887105571155710557115579350

105571055717347862093507696

1508386208620

1140115846105579350

11557

Wavelength(in A)

3794.913792.793791.553791.163784.783778.683777.763775.333774.843771.813761.993759.543756.183756.063749.033747.093738.103735.723732.963732.233729.463727.433724.963723.803721.353720.833720.213719.373716.513712.353706.523705.773704.463702.773700.993698.203697.933697.723694.903694.493693.333690.673688.093687.533684.013683.003678.583667.603666.443665.813665.123664.443663.843662.853659.563655.823653.203650.523647.643644.483641.723641.053640.213636.393636.043633.253632.453629.793629.373628.623627.823623.743621.233620.173612.833612.543612.363609.633609.373608.883607.423603.933601.753600.863600.753599.883597.943596.553596.093592.443591.143590.753589.523588.573588.353586.593586.403579.44

Intensity

1802025

1502

158

105030

150821 F

202851

101 F112

2081 VF

2010

131 F1

2501515381

401

203112

15 VW608

25208 W

31

1 W13

153

2031 VP

25103021

2002010

12

103020I F12251 VF2415

5033

30153

20

3351934055357173499043870341533702136136358333706233750342883817234313363213530038301344583866836136364613737836494387343866438667354933405534596384873632134153387863855635632388313638434733367123475636418376453866438668343133649438734391453866734447390753445837843349903501439145391643673537062388314329839256393503904935191361363521836891394323935034733391453816438172370213537039075382533539436321370624358643826391643638439658383433549344301371783501436461397383965835557441943943238487

56786789796896987689

1089876867997688S87

108787869876566887767956768796786778986687998768688877

10766689

7176769693508620

174567696

1055796559350

1055771767696

115577696965586201155776961188793509655

105579655118871179911799862071767696

1155793507176

11799115578620

1179993507696965576969350

10557115571155771769350

1155711887114017176

117997176

1055776967696

117991179993509655

1140115846117991188711557769686207696935011887117997176115571055710557935076961140110557769686209350

15846160701140186201188710557769616501935071768620

11887117997696

163211155710557

6789679108967871098778

10910

76696788668968710789886887S666977668

10S76787978766899875979876S97979869767689

NISSAN SPECTOR

TABLE III (continued).

Wavelength(in A,) Intensity

3578.23 83576.85 23576.02 13574.22 33570.55 83569.58 1 VF3568.49 83567.82 83567.33 1 VF3566.79 13565.16 1t)3565.05 13559.80 1 VIF3558.72 503556.38 203556.07 83553.05 203551.10 53548.07 83547.51 33545.88 803542.81 153539.59 803538.38 1 W3536.76 83534.35 53528.85 13526.55 13525.78 23522.52 803520.05 803516.91 103514.90 103513.05 1(0 VW3508.95 203508.82 203508.57 203507.43 13505.70 303502.78 300 VW3502.39 2 W3498.74 33495.81 13494.39 53488.53 303484.83 1 IF3480.74 403478.56 43478.07 13476.32 203472.83 53469.48 200 VW3468.46 13465.16 101)3462.24 303458.80 203454.15 1 VF3453.65 203453.08 13452.83 13448.05 83444.29 203443.20 23442.71 503442.42 23431.91 23431.07 23426.08 23424.26 153422.91 203421.55 1 F3420.95 303418.78 53414.76 33414.25 13413.68 13410.35 33409.87 153409.16 33407.95 23406.47 23395.81 53390.99 103386.53 1 VF3384.92 13383.77 153382.86 103382.08 303373.63 53369.10 1 F

Evenl level(Cin' I) J

397383935039843356673855643191351913571743870373783739135218399713671238668432983583335328387343973835370353944013140140359633984336026441944420135557370213612337062378063566739049378434358638172357174034340131382533630635833363843641840140438263737835963365113817236026394323825340343408333830140840383433764540833367354084036306384873687636891385564430137843364184083341168398433866438668370213651137044408403717841407367103816438172367353825346970

768786776876610867S8767766866868

977888975

868

76786696885

688

766967888778878866676S89

8

Odd level(cm-') J

11799 611401 511887 77696 7

10557 915185 5

7176 67696 7

15846 79350 89350 87176 6

11887 78620 9

10557 915185 5

7696 77176 6

10557 911557 87176 67176 6

11887 711887 77696 7

11557 87696 7

15846 715846 77176 68620 97696 78620 99350 87176 6

10557 99350 8

15083 89655 107176 6

11799 61 1557 89655 107696 77176 67696 77696 7

11401 515083 88620 97176 67696 79350 87176 6

10557 99350 8

11401 5118S7 79350 8

11887 79350 88620 9

11799 67696 7

11799 67176 69350 87696 77696 79350 8

15083 88620 97176 6

11557 811887 710557 99350 89350 87696 77176 67696 7

11401 57696 7

11887 77176 68620 98620 97176 68620 9

17297 8

Wavelengthi(in A) Intensity

3368.18 2003366.70 203366.11 23364,29 203363.42 23354.25 23349.60 83347.27 53342.79 13339.49 203338.09 33332.18 103327.08 203323.23 203319.80 23316.15 53308.70 83292.19 13285.42 13281.20 83278.47 23271.63 23266.53 33263.79 53262.04 33246.74 33244.55 23239.51 63228.30 33227.85 83215.61 13211.94 13201.87 103201.47 23193.58 1 VF3188.59 23186.94 13185.93 23182.70 1 VF3175.32 13174.95 23174,57 33173.84 1 F3162.67 13153.83 13150.12 103141.96 13133.94 23130.04 23127.88 23127.13 23121.48 23120.04 13117.20 53098.06 13094.38 33086.01 23082.24 203078.94 203077.74 23073.80 13062.51 13053.13 103042.97 203033.57 23027.01 23016.90 13016.26 23014.17 32990.78 12971.51 22969.63 12965.55 42962.66 102920.05 102882.72 102871.62 12859.12 12851.36 12785.53 1 UR2816.48 22809.71 12801.74 202793.22 12785.53 1 UR2767.01 1 F2738.60 22731.10 32724.45 1

a These lines were observed by us in emission and were used to establish the connection to the ground state.

346 Vol 56

Even level(cm-') J37378 837391 739049 836891 738343 845874 737542 638478 939256 738556 837645 837178 738668 839432 838734 837843 837391 737542 639049 838164 839843 838253 838301 737806 738343 845874 739432 838556 838664 738668 838786 638301 739843 838923 643191 639049 838545 739075 643298 640833 738664 738667 643298 638786 643586 839432 841168 839075 643826 739658 639145 743826 739738 743870 643826 744194 644194 640131 743870 639658 644410 844201 844301 844410 840131 742376 840833 740840 640343 544827 644201 840840 641407 644301 843586 842376 841989 743586 844410 843586 843191 644201 844301 844410 843586 843826 744201 844301 843870 6

Odd level(cm-') J

7696 77696 79350 87176 68620 9

16070 67696 78620 99350 88620 97696 77176 68620 99350 88620 97696 77176 67176 68620 97696 79350 87696 77696 77176 67696 7

15083 88620 97696 77696 77696 77696 77176 68620 97696 7

11887 77696 77176 67696 7

11887 79350 87176 67176 6

11799 67176 611887 77696 79350 87176 6

11887 77696 77176 6

11799 67696 7

11799 611557 811887 711799 67696 7

11401 57176 6

11887 711557 811557 811557 87176 69350 87696 77696 77176 6

11401 510557 9

7176 67696 7

10557 99350 87696 77176 68620 99350 87696 77696 78620 98620 98620 97696 77696 77696 77696 77176 6

ANALYSIS OF SPECTRUM OF NEUTRAL ERBIUM

TABLE IV. Parameters for 4f"15d6s2.

Results from least-squaresParameter (in cm'-)

F0 16666 =1±139F2 130 14F4 16 ±4CG 98 ±t21G3 14 ±9G5 4.8±t0.9

2577 ±39805 ±44

rms error 186in percent of total width 1.7%

'9

INI

, 7 I

\I \ - ,'

15

tENERGY 13

in (1OOOcm')

isotope shifts.but the line ata positive isotc

We diagonalcalculation weparameters whtion between tF0 , F2 , F,, G,,-?f, pd. Fromclear that thcoupling, and 1best to describa least-squaresthe 19 observe(ful. The resulTable IV. Intheir percentscoupling, andobserved levelhlevels of 4fl(4)only the first .We see that altto distinguish

,I

I? -

ENERGY 13

in (1000-]cm

II

These lines were not given in their paper,5763 A was found on their plates to haveope shift of 34.2 4 1.2 miK.1'

4 5 6

FIG. 3. Low observed

8 9 lo

J -

4f"15d6s` levels of Er i in J1 -l coupling.

ized the energy matrices of f Id. In this configurations; and the 4I4, in the 4fll core is heavilyincluded eight parameters: six Slater mixed with the TF42, as indicated by Wybourne.'7

ich account for the electrostatic interac- Therefore, there is no point in giving our results for thehe fll core and the 5d electron, namely, case of 4L1,, which do not take this mixture into account.G3, G, and two spin-orbit parameters The rms deviation is 186 cm-', which is 1.7% of the

the eigenvectors of these matrices it was total width. For the first time in the spectra of neutral,re was a serious departure from L-S rare-earths it was possible to perform a meaningful:hat the Ji- j coupling scheme was the least-squares on the f-d electrostatic interaction param-e the structure of the levels. Therefore, eters. Recently, Smith and Wybourne" calculated theadjustment of these eight parameters to f-d interaction in Eu i, but they did not allow the threeI energy levels of 4f"5d6s 2 was meaning- exchange parameters GI, G3, G5 to vary independently.ting adjusted parameters are given in Instead they had only one parameter, X (fd), which wasTable V we give the predicted levels, a linear combination of the Gk's. Its value was 595 cm'-.ge composition in JA-j and J,-I and 698 cm-l for f7 ds and f 7dp, respectively. We geta comparison with experiment for the 19 for X(fd) 780 cm-' which seems reasonable, in the;. Although the calculations gave all 40 light of their results. From Table V we see that the1)5d6s2 configuration, we give in Table V designations in Jf-l and f 1 -j are both satisfactory.30, omitting those ten based on the 4141. On the whole, the Ji-j coupling designations areready the levels based on 4I[6 are difficult better for the lower levels and for the higher J's. Fromfrom those belonging to overlapping Figs. 2 and 3 we see that J 1 -j notations are much

preferable for the (417)d levels, but Jr-I is not badeither for the (016)d ones. We also give in Table V thecalculated g-factors for the levels. A value for the firstobserved g-factor of g6= 1.340 was given by Lindner

- -. -and Davis, Ref. 4. The agreement between this valueand the calculated one is not satisfactory. From morerecent observations that we made on the Zeeman effectin erbium we derived the value of g6= 1.306, which isin much better agreement with the calculation. The

--- - second observed g-factor is taken from Ref. 4. Thedisagreement between g-values from Ref. 4 and calcu-lated ones has already been demonstrated in Ref. 1,where the authors discuss it in the case of 'H6 . Theyfail to mention the 'F 4, however, where the disagreement

4 5 -- is even more noticeable.We have thus accounted for all the levels of 4f 1"5d6s'

J-h

.----- ------ up to 20 000 cm-' (with the exception of J==4).PIG. I. Low observed 4J'/ddOsG levels ot Er i in JA-j coupling.

"6 J. S. Ross (private communication). We are grateful toProfessor Ross for supplying us with the data on this line prior topublication.

17 B. G. Wybourne, Spectroscopic Properties of Rare Earths(John Wiley & Sons, Inc., New York, 1965), p. 46.

1" G. Smith and B. G. Wybourne, J. Opt. Soc. Am. 55, 121(1965).

March 1966 347

I

\-

NISSAN SPECTOR

TABLE V. Energy levels, g factors, and percentage compositions for 4f"Q(4I)5d6s2.

Designa- Percentage composition Observed Calculated O-Ction J in J,-j coupling in J 1 -l coupling (cm-') (cm-) (cm-') gobs gealc

( 417)dil 6 93% (417 )d 1 92% '174i)[5-14] 7177 7349 -172 1.340 1.312

(QI7j)dj 7 78% (4171)d 1 ±+18% (417,)d2, 90% (t7htE61] 7697 7916 -219 1.254 1.265(QI7j)dij 9 58% (417,)d1 1 +31% (4I6j)d2, 28%0Izo[910+41%(4I7I)L84] 8621 8651 -30 1.163

(4I71)dij 8 75% (41

7)dj 1+20% (4I6 j)d2, 63% 1(4178E]+36% (4I7AE71] 9350 9097 253 1.185

('I7j)d2j 10 100%o (4 17j)d2j 100% (4IO[94] 9656 9269 387 1.200(4

171)d,1 9 88% (4171)d21 55% (4I7i)[84]+38% (4[71)[94] 10 558 10 610 -52 1.174

(417)d2i 5 81% (417,)d2j 78% (QI70)[5-]-+21% (4I[)E41] 11 401 11 491 -90 1.216

(4I71)d21 8 94% (417j)d2j 64% (0I70[7A]+33%(4I7j)[81] 11 558 11 607 -49 1.182(417j)d2j 6 79% (1I71)d2j 75% ( 4l7v)E61] 11 800 11 811 -11 1.191(4171)d21 7 75% (417,)d21 +18% (4171)d11 83% (417)[721] 11 888 11 959 -71 1.151(41o1)dlj 8 95% (4101 )di1 81% (0Iro)[84] 15 083 15 058 25 1.056(4 IEj)djj 5 81% (4 I61 )d1j+18% (417 1)d23 61% (416)[ 41]+ 2 1%(4 I7O[E5-1 15 185 15 213 -27 1.189(4161)dtj 7 90% (41b)dli 65% (41Gi)[7!]+24%Q(4IG[6A] 15 847 15 744 102 1.073(QIo)dj1 6 79% (4-16 )dij 62% (QI6o)[54]+21%(CI6[6l] 16070 15 946 124 1.152(4181)d2j 9 62% (401 8 )d2 1 +37%(4

17j)dij 62% (41j)0[821+34% (417)[92] 16 501 16493 8 1.1294 83% (4161)d21 81% (416) E4l]+18%I(4 [323L] 16948 1.081

(4 I*j)d2j 8 76% (QIoi)d2j+22% (4Q7 )d11 83% ( 2I6E)[74] 17 298 17 222 76 1.129(41o)d2d 5 84% (4I,,)d2i 66% (41io)[5] 17348 17349 -1 1.101(4To)d2d 6 80% (

416 1)d21 68% (4I6i)[64]+19% (4IGi)[52] 17 456 17 623 -167 1.057(1IG6 )d21 7 93% (Q11 )d21 68% (4I61 )[61J+26% (OIGE)C74] 17 796 17 882 -86 1.121

7 90% (4151)dil 91% (1I5i)[71] 20 261 0.9316 80% (QI,1 )dj1 84% (4kT,)[64] 21196 0.9234 72% ("I,1 )dj1 67% (4 Ig)[44]+18%( 4 I45[34] 21 329 0.9563 88% (Q151)d2} 87% (415)[32] 21 748 0.8285 83% (41z6)d,1 78% (IO)[54] 21 990 0.9164 75% (I%1)d4, 63% (MI51) 34]+22% (4f,5')[441] 22 513 1.0038 97%C/ (4115)d21 97% (41,50T74] 22 795 1.0325 78% (4151)d21 70% (4J5)[E42] 23 095 0.9917 94% ('I 16)d23 93% (%Ij)[61] 23 265 1.0356 81% ("I6 )d21 83% (4I)[E51] 23 687 1.009

The odd level at 24943.28 cm-1 was assigned a J= 7,and may belong to 4f"26s6p. The transition from it tothe zero level, at 4007.97 A, is the widest and strongestabsorption line on our plates. Meggers, Corliss, andScribner"9 give this line as the strongest erbium line inthe range of their observations. We confirmed itsf-value by transitions to high even levels (above 40 000cm-1) of J-values 6,7,8. Although these transitions fallin the range covered by Marquet's observations, theydo not appear in his line-list. They were recorded,however, on our emission plates, as lines of relativeintensity 1. This level is designated as fJ2(3H 6 )sp('P1 ) 7

which indicates that some of the uninterpreted oddlevels around 17 000-19 000 cm-1 belong to the fQ2(3H6 ).Spe3 P) group.

In conclusion it may be indicated that an improve-ment in the fit of the energy levels can be obtained bycalculating the complete 4f"5d6s 2 configuration, thustaking into account the interaction of the 41 and the

19 W. F. Meggers, C. H. Corliss, and B. F. Scribner, Tables ofSpectral-Line Intensities (National Bureau of Standards Mono-graph 32, 1961).

rest of the 4f"l core. This, as well as the extension of theline list and a description of the Zeeman effect oferbium is now in progress.

APPENDIX: ENERGY MATRICES FOR f"Q(J)d

Electrostatic

3G:- (70/11)F2 + (476/33)F4 + (2756/99)Gi

+ (7664/99)G,+ (656/99)G5

3H: (5/1ll)F,-(408/ll)F4+(364/l1)G,

+ (716/11)G3+ (504/11)G5

II: (5l11l)F24-(408/ll)F4+ (l40/ll)Gj

+ (1220/33)G,+ (5264/33)G5

3K: 4F 2 - 17F 4+ (200/3)G3+ (1064/3)G 5

3L: - 4F2+3F 4+ (40/3)G3+ (1624/3)G5.

For the quintets the7coefficients of F2 and F4 areidentical with those of the corresponding triplets, andall the coefficients of the Gk's vanish.

Vol. 56

ANALYSIS OF SPECTRUM OF NEUTRAL ERBIUM

Spin-Orbit

Following convention we give the matrices of fl( 41)d for Pf and rd. In order to get the corresponding matricesof f"1 (41)d, the sign of those for ?f should be reversed. Those-for vd are the same. Owing to the symmetry ofthe matrices, only their upper triangles are given.

f0 (4 I)d: NATRICES FOR Cf

J-75H

5I 5I 36 51

J I10 I SliT1 5 fT1 0 0 0 04 52 26

51 65 13 2455 2 5 oi5O0- - - O

2 8 14 21 1 365

.313 r5-5 3 FT iiii 0 014 3~ 5 455

3G 5G 5H 115 23 F221 FS95 4i-535 7 45- r 1T 336 336 46 8012 20 30 69 455 3 195

_ fT-~ -i~i-i2 9 0 21 J-2 112 240 80TO 10 5G 4 345 3

33 16 1610 2 33

163.5

3 G 56 3H 5H 3I 5I 5 K

h 7I 423! '0 0 0 0

3 10 22 330

7 A 62 46006 0 0 010 110 110

II uI[Ii 254 -5 5231 024 40 264 264

33 5IT 15 3003 040 1144 1144

65 134105 4100124 168 91

11l7 . 2 l4556 91

237

f 3 lI4 d: MATRICES OF Cd

J.9

J-436 56 3H 5H 5I

7 7477 I i-T o12 -60 6 10

21 7 12i 21 ¶ o10 330 110

- - - IIF 5 i-I

4 20 44

5 44

134

J-85I 36 5 -

3L

5L

39 TiO 3 5 0

115 23 i2 5f i946 112 16 80

115 fi _9

112 16 80

-5 85

I 8 1 6 .

- 916.

J-6 5G 3H 5

H 3I 5I 3K 5K 5L J-5 3G 56 3H 5H 31 51 5K

4 I3 -2I 0 0 0 o 2 3IT Ji 303 0 0 05 110 110 5 5 11 0 -1 10

I 4105 sl 550 -15 0 0 2 0 0 5 0 0 08 40 104 1144 5 110 110

3 5J 9 5 T54 0 0 0 I 3- 5 5 541 040 104 1144 40 40 88 88

1 65 ~343 o 3 15W Y 3 153003

J2 56 56 91 91 40 1144 11447 3 1I195 2 2fl5 0 1 3 i 341001

56 455 455 8 56 91

J=10 5L 5 15 -255 9 r214514 28 20 56 91

25 13- 5

.9

J_7 5H 31- 5 I 3K sKI 15P 3 s F3-. o Oo ~

4 52 263 3 2155 2F12155

28 14 35 4551 355 -311215514 35 455

5 5iT112 112

152

11 2

J-9 5K 3L 'L

5 3 i 4f

8 4 8

l I T

2 43

a

J-3 3G 5G 5H

1 3 F 5f2 10 10

7 l2110 10

10

L 5 L J-4 3G 'G 3H 5H 5 I J I 3 Ks 5s 3L 5L

O 7O ~- 14-m 3 F7 3 F115 5 ° 50 _ _ __ - -10 10 10 10 14 35 35

O 0 3 7I 2 0fi 0 5 15l2 311 3 Fi510 i10 - 110 16 112 16 80

O 0 3 3 15li1 25 3T7 TI 9920 20 44 112 16 80

8 0 80 16 IC- 3{i 5 44314 55 3v1i95

80 80 169 3T 416 16

1116

March 1966 349

J'63t L 1

J