Correlation of isotope shifts with |Ψ(0)|2 for actinide configurations

2 See, for example, the review by H. K. V. Lotsch, Optik 32,

116 (1970); 32, 189 (1970); 32, 299 (1971); 32, 553 (1970), andreferences therein.

30. Bryngdahl, Prog. Opt. XI, 169 (1973).4 T. Tamir, Optik 36, 209 (1972); 37, 204 (1973); 38, 269

(1973). Both this reference and Refs. 2 and 3 above containexcellent descriptions of the physical phenomena involved.See also H. Kogelnik, in Integrated Optics, edited by T.Tamir, Topics in Applied Physics, Vol. 7 (Springer, NewYork, Heidelberg, Berlin, 1975), pp. 15-81.

5C. von Fragstein, Ann. Phys. (Leipz.) 4, 271 (1949); RemiH. Renard, J. Opt. Soc. Am. 54, 1190 (1964); J. Ricard,Nouv. Rev. Opt. Appl. 1, 5 (1970); the possibility of an en-ergy flow into the evanescent wave was postulated severalyears before the experiment was performed. See J. Picht,Ann. Phys. (Leipz.) 3, 433 (1929).

6IK. Artmann, Ann. Phys. (Leipz.) 2, 87 (1948).7 L. Agudin, Phys. Rev. 171, 1385 (1968).8 F. I. Fedorov, Dokil. Akad. Nauk. SSSR 105, 465 (1955).DC. Imbert, Phys. Rev. D 5, 787 (1972), and references

therein; 0. Costa de Beauregard, Found. Phys. 2, 111(1972).

100. Costa de Beauregard and C. Imbert, Phys. Rev. D 7,3555 (1973); A. Mozet, C. Imbert, and S. Huard, C. R.Acad. Sci. Paris B 273, 592 (1971). Goos and Hlinchen alsoobserved this effect with a beam linearly polarized at arbi-trary incident azimuthal angles. See Ann. Phys. (Leipz.) 5,251 (1949).

t Costa de Beauregard and Imbert (Ref. 10) claim that both thetransverse and longitudinal shifts are quantized, each havingcharacteristic eigenvalues. The longitudinal shift shouldthen be characterized by the principal linear polarizationstates, and the transverse shift, by the circular polarizationstates: K. W. Chiu and J. J. Quinn, [Am. J. Phys. 40,1847 (1972)] analyze the longitudinal shift by classical elec-trodynamics in terms of a time delay scattering process,

and also arrive at the conclusion that an incident beam ofarbitrary polarization splits exactly into p and s polarization

states. A similar conclusion was also reached by G. J.Troup et al., Phys. Rev. Lett. 28, 1540 (1972).

1 2 L. de Broglie and J. P. Vigier, Phys. Rev. Lett. 28, 1001(1972).

DAt the completion of our work we became aware of a con-current study of the longitudinal shift due to microwaves thatwas made by V. Akylas, J. Kaur, and T. M. Knassel, Appl.

Opt. 13, 742 (1974); Am. J. Phys. 44, 77 (1976). In a re-markably similar experiment, they used a paraffin prismbut a larger wavelength (3.2 cm). Their measurements wererestricted to a single angle of incidence and to illuminationwith only parallel and perpendicular linear polarization. Italso came to our attention that the Goos-Hanchen shift wasmeasured in a general study of the total reflection of micro-waves by P. Baumler, Ann. Phys. (Leipz.) 10, 409 (1963).He also used a single angle of incidence with p and s polar-izations but a shorter wavelength of 1.46 cm. The resultsof the authors above were found to be in good agreement withclassical theory.

14 Portions of the present work were presented at the SpringMeeting of the Optical Society of America, Washington, D. C.,21-25 April 1974. See J. J. Cowan and B. Anibin, J. Opt.Soc. Am. 64, 525 (1974).

15 H. Wolter, Handbuch der Physik (Springer-Verlag, Berlin,1956), Vol. 24, p. 472.

16B. R. Horowitz and T. Tamir, J. Opt. Soc. Am. 61, 586(1971).

1 7C. K. Carniglia (personal correspondence).18 M. McGuirk, C. K. Carniglia, J. J. Cowan (unpublished).1 9In the acoustical case this distance is significant [M. A.

Breazeale (personal correspondence)]. See also M. A.Breazeale, L. Adler, and G. W. Scott, J. Acoust. Soc. Am.Suppl. 57, 5-38 (1975).

Correlation of isotope shifts with I(O) 12 for actinide configurations*

K. RajnaktUniversity of California, Lawrence Livermore Laboratory, P. 0. Box 808, Livermore, California 94550

Mark FredArgonne National Labortory, 9700 South Cass Avenue, Argonne, Illinois 60439

(Received 18 April 1977)

We have used both Hartree-Fock functions and the pseud6relativistic HX functions of Cowan to examine

the relationship between observed isotope shifts and s-electron densities at the nucleus for Cm, Am, Pu, and

U. There are significant changes in relative electron densities when the relativistic correction is includedwhich greatly improve the correlation between observed isotope shifts and electron density. The improvementis especially dramatic for those configurations which fit most poorly with HF values of Il4(0)12. The slope

[S = AIS/A(4~rjop(0)Io,)] per unit effective mass difference is found to be nearly constant for the

actinides considered. This allows prediction of isotope shifts for 2 52Cf-25 0Cf which have not been measured.

Isotope shifts are also predicted for Cm, Am, Pu, and U configurations which have not yet been identified.

INTRODUCTION other. The volume shift can be written

The isotope shift (IS) of a given atomic energy level con- IS = I 21(a2 /Z) C = FC, (1)

sists of a mass shift and a nuclear volume shift. Since

the mass shift is proportional to 1/M 2, it is usually where F depends only on the electron density at the nu-

neglected for elements with Z ' 80. Consequently, one cleus, and all nuclear effects are contained in the IS

can expect actinide ISs to arise entirely from the volume constant C. 1 Since in the Slater-Condon theory all levels

effect, i. e., the change in the overlap of the nuclear and of a configuration have the same electron radial wave

electronic charge distributions from one isotope to an- functions, the IS is expected to be constant for all levels

Copyright © 1977 by the Optical Society of America 13141314 J. Opt. Soc. Am., Vol. 67, No. 10, October 1977

TABLE I. HF, HXR, and DHF values of 47r I p(0) 12 (units of a03) for U(f 3 ds2 ) and Pu(f6 s2 ).

U

Is2s

2p1 /23s

3P I/24s

4p1/25s

5PI/26s

6P1/27s

Total

DHF TotalTotal

HFa

3 076 691346 159

80 355

21576

5 220

927

73

(7 062 002)

11.24

HXR

26 898 8594120401

958 198

259 075

66255

13225

1 360

(64 634 742)

1.228

DHFb

31736 7735 405 393

589 1151 285 979

158 049

346 46242 553

84 9149 813

16 6281 6481484

(79 357 693)

1.00

HFC

3 282 529370 056. . .

86 262. . .

23 409. . .

5 773. . .

973

66

(7 538 122)

12.49

'A. Paszek (Ref. 22). bj Mann (Ref. 19). CM. Wilson (Ref. 8).

of a given configuration but will vary with configurationas I o(O)I 2 Because of this fact, ISs have proven to beinvaluable in the assignment of energy levels to con-figurations in the complex spectra of the actinides, 2-6

although, as discussed below, the constancy is some-times perturbed by IS mixing due to configuration in-teraction (CI).

The quantity I b(0)1 2 is familiar from the standardtreatment of fine structure and magnetic hyperfine struc-ture and is conventionally evaluated in terms of quantumnumbers and screening constants for the outer elec-trons. Nonrelativistically, only s electrons contributeto p(O), and the screening constant is supposed to de-scribe the modification of the outer s-electron chargedensity by other electrons. Blaise and Steudel 7 andDiringer4 have derived empirical IS screening constantsfor a number of actinide configurations, attempting totake into account the screening due to the 5f as well as7s, 7p, and 6d electrons. However, it is difficult em-pirically to disentangle the various contributions, to re-late the shifts of the i and ii spectra, and to derive shiftsunperturbed by CI.

An alternative approach was introduced by Wilson, 8

who made direct calculations of 47rl b(0)) 2 from non-relativistic Hartree-Fock (HF) radial functions. Theresults verified, in general, the expected proportionalityof IS to 4Ir1 O(O) 12 for heavy atoms and also showed thatin some cases changes in 471T (O)l 2 from one configura-tion to another could not be explained in terms of a sim-ple change in the screening of the outer s electrons.For the Pu configurations investigated by Wilson, thechange in the total value of 4irT1 0(0)12 when f 6-f 5 d orf 5p arises from changes in b(O) for the 5s and 6s ratherthan the 7s electrons. This result turns out to be as-sociated with the use of nonrelativistic radial functionssince for the pseudorelativistic functions described be-low the change is mostly in the 7s function.

As pointed out by Wilson, observed ISs of only two"pure" configurations in the same spectrum of an ele-ment enable one to use HF values of 471T (O)1 2 to cal-

1315 J. Opt. Soc. Am., Vol. 67, No. 10, October 1977

culate ISs (within a single additive constant) for all otherconfigurations in all ionization stages. In practice thisis often difficult for the actinides. There are manycases where the IS varies widely for different levels ofthe same configuration, even for different levels of thesame term. 5,6 Several workers have shown9-11 that thisis due to CI, which results in a level which is a mixtureof configurations and produces an IS which is an averageof the pure configuration ISs weighted by the percentconfiguration composition. Until recently, the largematrices involved with mixed actinide configurationshave made it impossible to make quantitative use of thisinformation. But as our ability to deal with large ma-trices increases, it is becoming feasible to include ex-plicitly some CI in the parametric analysis of actinideenergy levels. Then, using theoretical pure-configura-tion isotope shifts and the CI eigenvectors, we can cal-culate ISs for individual levels to provide an additionalcheck on the level assignments and the accuracy of theeigenvectors. Theoretical isotope shifts may also aidin the identification of the highly excited levels recentlyfound by laser spectroscopy. 12,13

In addition to aiding the analysis of complex spectra,such as that of U where CI is often very strong, we werealso interested in exploring relativistic effects on4 1T IO) 1 2. The latter have been shown1 4 to have a largeeffect on some screening ratios of Eu but have not beeninvestigated in the actinides.

CALCULATIONS

Previous methods for approximating relativistic ef-fects on I g(O)1 2 have been summarized by Shirley. 15The current calculations were carried out using the HXcode (Hartree with statistical exchange) of Cowan1 6

where relativistic corrections for s electrons can beincluded via the addition of the Darwin and mass-veloc-ity terms to the central field potential. 16-18 These cal-culations are designated as HXR.

In Table I we compare HF and HXR values of 41fI 7p(0)1 2

with the Dirac Hartree-Fock calculations of Mann19 for

K. Rajnak and M. Fred 1315

Pu

HXR

31 740 0414939582

1 153 268. . .

314 450

82 360

16 137

1 395

(76 495 184)

DHF

37 425 8866511632

756 1801 556 730

203950423 345

55 516106 178

13 11320 503

2 2501 508

(94 153 582)

1. 231 1. 00

E

x1

,;

N~

V

-1000

8,03 S ,100 5200 5300 5400 5500 5600

HF 4iThp(0)I1ot for

200

0

E

1

x

11

D~

N2

-200k

-400

-600

-800

-1000

-1200 L I L90,705,000 7000

Cm I in units of a-3a0

9000 11,000

HXR 4Tr I (0) 2 for Cm I and II in units of ao-3tot

FIG. 1. IS of 2 4 8

Cm-2 4 4

Cm vs 47r zp(0) I tot; (a) HF values of

Crosswhite (Ref. 20): (b) HXR values for Cmi and ii.

the ground configurations of U and Pu. The ratio ofDHF to HF values is 11. 2 for U and 12. 5 for Pu. (Theseare somewhat smaller than the relativistic correctionfactors of 15. 9 and 14. 3 tabulated by Shirley. 15) Forboth U and Pu the DHF value is only 1. 23 times the HXRresult. Thus Cowan' s relativistic correction has ac-counted for a large fraction of the total relativistic ef-fect.

To examine the relative effect of the relativistic cor-rection on different configurations we can compare anHXR calculation with the relativistic HF results ofCoulthard14 for Eu i. We have not tabulated them herebut the HXR changes in 4 v 1T (0)12 from one configurationto another are comparable to those given by Coulthard.

Since the spin-orbit term is neglected in the HXR ap-proximation, there is no distinction between Pl/ 2 andP3/ 2 electrons and no direct relativistic effect is in-cluded for p electrons. Examination of Coulthard' s Euresults indicate that the P1/2 contribution of the innerelectrons to 47T I b(0)I 2 depends primarily on the numberof electrons in the fN core. Thus the use of only the s-electron density is not likely to affect the relative elec-

tron densities for configurations with the same f core,but it may have some effect on the relative electron


densities for configurations with different N.

Even though the electron density of the inner p electronsremains relatively constant (- 1% of the total for U), theuse of only the s-electron density does introduce an errorin the relative electron densities of configurations withand without valence p electrons. For U and Pu the pelectron has a density which is 10%-12% of that of thecorresponding s (see Table I). One cannot just apply anapproximate correction to the electron densities of con-figurations with valence p electrons, however, since inany particular case a jj coupling CI treatment is neces-sary and the P1/2 contribution varies from one level toanother. But the contribution of P1/2 generally decreasesfor higher levels, so one would expect some decrease inIS as a function of energy for those configurations withvalence p electrons. The empirical isotope shifts re-ported here have generally been chosen from the valuesfor the lower levels of a configuration where the P1/2contribution is maximal. The possible effects of thisare discussed for particular cases.

Both HF and HXR values of 4;TI 0(0)I for each ns shelland 47T I0(0)1 2ot are given in tables along with empiricaland predicted IS values for Am, Cm, Pu, U, and Cf.Plots of observed IS versus 47r1 g(o)I 2ot are shown inFigs. 1-5. Because of the effects of configuration in-teraction, the choice of empirical values is somewhatarbitrary and is discussed below in detail for individualactinides. Figures 1, 3, and 4 compare HF and HXRresults for Cm, Pu, and U, respectively. The relativepositions of most configurations remain unchanged butthere are some significant systematic differences be-tween the HF and HXR results.

Cm

We begin with Cm where CI is expected to be less ofa problem than in the lighter actinides and where someHF calculations are available for comparison with theHXR results. Since for the inner electrons changes inHXR values of F4TI 0, (0)1 from one configuration to an-other are < 0. 03 a 3/

12 only average values are given inTable II. The HF values of Crosswhite2 0 and the cur-rent HXR results for 47r1 IP(0)1 2otl are given in Table IIIand plotted against empirical isotope shifts for 246Cm-244Cm in Figs. l(a) and l(b). Empirical values were

C

x

N

1000

800

600 [

400

200

0

-2001

83,274,400 76,000 78,000 80,000

HXR 4irI4(0)1t2t for Am I & Am II in units of aO3

FIG. 2. IS of 2 4 3 Am- 24 1Am vs HXR values of 47r I b(0)1 2Ot for

Ami and ii.


d 2 2/- (b) d2-

d7s8s -d 0^ s2

7s 8 sA / ds -

3 '- d3

ds / ds-

2? 5 CmlI Cm 11

/ * Of 7

7 A A f8

I - I d 2 I

s7d 7s\ s 2 -

S s Am I Am II-s f6 -

d7 -A A f

- , I I I -

II

TABLE II. HXR values of V47I 0bs(0) I (units of a-3/2) for innerelectrons.

Is 2s 3s 4s

Cf 6667.38 2672.96 1296.07 682.04Cm 6125.65 2435.95 1179. 18 618.20Am 5873.88 2326.46 1125.18 588.73Pu 5633.85 2222.51 1073.89 560.76U 5186.41 2029. 88 978. 88 509. 99

chosen from the data of Worden and Conway, generallyfor the lower levels of the configuration where the levelsare more likely to belong to a single configuration.There are cases where it is difficult to arrive at a "pureconfiguration" IS. For f 7 dsp error bars are used inFig. 1 to indicate the range of observed values sincethere seems to be no criterion for picking a particularone. The HF points in Fig. 1(a) show a great deal ofscatter. There are two possible reasons for this: (1)the relative values of 4ir1 p(0)1 2 are not appropriate be-cause of the neglect of relativistic effects or (2) the ex-perimental ISs are not those of "pure" configurations.In the latter case, we can, by consideration of the par-

E

S

400 -(a)

0 ds2

-d 21 /s s-400 T d/2 tdsp

-800 / d2p

7,061,700 1800 1900 2000

HF 4Tr 1(0) Itot for

1 ' i 'I I I400 ds (b) .

dsp0- d 2sp

-400 - ds{ S2dE\

-800 -d2

,S d

dp / U I

-1200 ?A2 .S

2100 2200

U I

U 1 1-0 f2 _

o f3 _

A f4,U- I d/4 i01 , I

64,631,500 2500 3500 4500 5500

HXR 41r1i(0)12o tfor U I and II in units

A

6500

of a0 3

1000L

800

600

400

200

0

7,537,900 8100

HF 4,1I(0)1ttot

1000

800

600

400

200

76,491,000 3000

8300 8500

in units of a-3

5000 7000

HXR 4nrl(O)jt for Pu I in units of a0

d 2s

. 800 - (c) d /

x 600 ds

- 400 - osp

' 200 -

v, 0 dI I I

76,491,900 2000 3000 4000 5000 6000

FIG. 4. IS of 235

U-23 5

U vs 47r O(0) I 2to; (a) HF values of Paszek(Ref. 22) for UI; (b) HXR values for UI and II.

ticular configurations involved, sometimes determinewhether the observed value is an upper or lower bound.The possible shifts resulting from CI are indicated byarrows in Fig. 1 (upward arrow if the observed valueis a lower bound and vice versa). Since the uncertaintyin the experimental values varies considerably frompoint to point, no attempt was made to do a least-squaresfit to the data. The "best" line was drawn to take intoaccount the bounds indicated and to fit the most reliableof the experimental values.

In the HF case, Fig. 1(a), CI could inprinciple accountfor all significant deviations from the line except for theconfigurationf 7 d3 and perhapsf7d2 p. In these cases CI

E

12

�3

1�

7000 8000

HXR 4ni p(0)~tot for Pu II in units of aO3

FIG. 3. IS of 2 40PU-

239pU vs 47r ti(o) 12t; (a) HF values of Wil-

son (Ref. 18) and Paszek (Ref. 22) for PuI and ii; (b) HXRvalues for PuI; (c) HXR values for PuIs.


3000 5000 7000

HXR 4TrIpl (0)l2t0 for Cf I & II

FIG. 5. Predicted IS of 25 2Cf-255 Cf from HXR values of4mr I p(0) I 2 t and assumption of slope = 0. 23. Both Cf I and iIpoints are based on defining the IS of f s 2 as zero.


E11

2

1;�

81

I2 I I I 2 Pu I- (a) 52 o d2

d2

s ds5s2 7

S *dsp Pu I Pu II

dp p P f4

&d2 0 0 f5-

-A A f 6 -I I I

I

1

2

13�

8

�20o

I I I

(b) ds2

A 'a SPs2

s s8s

0 f5 -A f6

I . I I I

TABLE 111. Values of 47r I (0) I 2ot (units of a-3) and isotope shifts (246-244) for Cmi and CmiI.

Cmi HXR v'; I Op8(O) I 47r I O() I 2 IS x 10 cm-

Configuration 5s 6s 7s 8s HXR HFa Expt. b Calc. (HXR)

f 8s2 319. 755 141. 622 40.471 90708535 8035307 - 250 - 240f 87s8s 319.752 141.600 45.778 15.656 90 707 349 - 400 - 500.fsp 319. 753 141. 595 43. 292 ... 90 707 005 8035232 - 480 - 590f 8 p2 319.750 141.572 90 704 997 * -1050fads 319.760 141.653 40.243 ... 90706937 8035189 - 600 - 600f 8dp 319.758 141.620 * - 90705210 8035124 * -1000f 8d2 319.763 141.671 * 90 705 307 8035113 ... - 975f 7s 2p 319.801 143.465 47.396 * 90710216 8 035 564 130 150f 7 s 2 8s 319.802 143.480 49.676 16.730 90 710 782 ... 275f 7dS2 319. 805 143.430 43. 926 * 90709741 8035474 0 35f 7d7s8s 319.805 143.435 48.332 16.150 90708254 8035293 - 200 - 300f 7dsp 319.805 143.428 46.104 ** 90 707 916 8035392 - 300 - 380f 7d2S 319. 809 143. 425 43. 073 ... 90707793 8035203 - 350 -355f 7d2p 319.808 143.407 ... ... 90 705 843 8035262 - 700 - 850f 7d3 319.813 143.429 ... ... 90 705 982 8035246 -650 - 825fGd2s2 319.895 145.510 46.539 90710996 ... 290

CmiI

Configuration 5s 6s 7s 8s HXR HFa Expt. a Calc. (HXR)

f8s 319.752 141.601 46.401 * 90 706 988 *.. - 730 - 730

f8p 319.749 141.578 ... -*- 90704708 ... ... - 1250

f8d 319.757 141.620 ... - 90 704 913 ... - 1193 - 1200

f7s2

319.801 143.487 50.204 *.. 90 710 397 ** 0 70f 7sp 319.801 143.508 51.617 * 90 707 969 -440 - 490f

77s8s 319.802 143.541 54.090 24.500 90708721 * - - - 325

f7p

2 319.801 143.541 ... ... 90705241 ... ... -1140

f 7ds 319.804 143.439 48.898 * 90 707 866 * -510 - 515f 7dp 319.804 143.444 * 90705387 . * -1100f

7d

2 319.808 143.409 ... .. 90 705 556 -981 -1050

f6 dS2

319.895 145.614 52.534 * 90 711709 ... ... 390f 6 d2 s 319.895 145.521 51.040 *.. 90708857 ... ... -290

aFrom H. M. Crosswhite (Ref. 21). bExperimental data from Ref. 5.

probably results in an empirical value which is too high,yet the points are already below the line. CI would haveto be very strong to bring the f 7 d2 s and f 7 d7s8s pointsclose to the line. Intuitively, one would expect f8 s 2

with two 7s electrons to have a larger electron densitythanf7 d7s8s orf7 dsp. This is not in accord with the HFresults. The calculated electron density for f 8 ds isless than that for some configurations with no s elec-trons.

Figure 1(b) shows the corresponding HXR results forCm i and ii. The major differences between the HF andHXR calculations are that the addition of the relativisticcorrection increases 47r 10(0)1 2 of f 8ds with respect tothat of f 7d 2p and of f 82 with respect to that of f 7dsp andf 7d2 s. The deviations from the "best" line (slope = 0. 23)are now in a direction which could be accounted for byCI in all cases. For any combination (N, N') configura-tions containingfNsN' all have very similar electrondensities. In contrast to the HF case, the major dif-ferences in electron density are in accord with qualita-tive expectations based on simple screening arguments.For example, f electrons screen the outer s electronsmuch more heavily than p or d electrons, so that theelectron density increases with decreasing number off electrons. The 6d and 7p seem to have nearly the sameeffect on a single s electron, so that f Nsp has only a


slightly higher electron density than fvds. Including theP1/2 density would increase this difference, however.

With the exception of f77s2p, an increase in the elec-tron density of (200-250)a; 3 (- 10% of the 7s density) dueto the 7Pi,2 electron would improve the agreement inFig. l(b) and change the predicted isotope shifts by- 0. 050 cm' . This is of the same order as the errorsinvolved in arriving at the empirical values.

The configurationf 7 d3 seems to be badly perturbed.The isotope shift is predicted to be - 0. 800 to - 0. 850cm , whereas the range of measured values is -0. 53to -0. 69. The perturbation thus appears to be largerthan is apparent from the range of measured values.The deviation of f 7d 2p could be due either to CI or toneglect of the p1/2 density.

Predicted isotope shifts for configurations which havenot yet been identified are indicated in Table Iml. Sincethe choice of a "best" line in Fig. 1 is somewhat arbi-trary, it should be noted that these predictions are prob-ably better in the intermediate range than they are forconfigurations with very high or very low isotope shiftswhich are more sensitive to a slight change of slope.

Since all isotope shifts for a given ionization stage aremeasured with respect to an arbitrary zero, there is no


TABLE IV. HXR values of 47r I 0(0) I 20t (units of a- 3) and isotopeshifts forAmi and AmIi.

Ami 47 1+(O) Ii lo,1 cm-,

Configuration 5s 6s 7s 8s 471 I O(0) 1 2,t Expt. a calc.

f7

S2

302. 950 134. 170 38. 873 * 83277 978 600 650

f7sp 302. 947 134. 140 41. 518 * - 83276578 380 360

ft7s8s 302.947 134.143 43.935 15.079 83276905 450 425

f'ds 302.955 134.203 38.503 ... 83276488 300 340

f's7d 302. 947 134. 147 44. 096 * 83276638 400 375

f6S2p 302.996- 135. 929 45.387 * 83279480 * 975

feds2

302.998 135.890 42.050 * 83 279 062 850 890

f6dsp 302.994 135.966 49.175 83277596 * 575

f6d2

S 303.001 135.882 41.163 83277276 ... 505

Amii

f7s 302.946 134.144 44.534 ... 83 276 716 400 430

j p 302.944 134.120 *-- ... 83 274 450 *-- -100f

7d 302.952 134.163 *-- ... 83274648 -10 - 50

f6s2 302.994 135.952 48.113 ... 83279707 ... 1040

ftsp 302.994 135.973 49.438 83277460 * 540

f ds 302.997 135.899 46.850 83277336 * 525

aExperimental data from Ref. 3.

reason to expect values for different ionization stages

to fall on the same line. The lines should be parallel,

however. The Cm ii data fit on a line parallel to the

Cm i line but about 0. 130 cm-' below it. The scatter is

somewhat less for Cm II in accord with the expectation

that CI is less important in the second spectrum.

Am

Since no HF results are available for Am, only HXR

electron densities are plotted against 2 4 3

Am-2 41

Am ISs

in Fig. 2. Calculated values of 4vr1 0(0) I t2t and empiri-

cal isotope shifts from the work of Fred and Tomkins3

are given in Table IV. The experimental data are sparse

but the points fall reasonably close to a line of slope S

= 0. 22. The two Am iI points included in the figure fit

well on the Ami line. Predicted ISs for configurations

which have not yet been identified are indicated in Table

IV. Many of the values are similar but they do allow

identification of some of the levels in Ref. 3.

The pattern of electron densities is the same as in

the HXR calculations for Cm. For a givenfN core, the

isotope shift decreases with decreasing number of selectrons as expected. The isotope shift increases withdecreasing N as the shielding of the outer s electronsdecreases.

Pu

Figure 3(a) shows the best estimates2 1 of 2 4 0 Pu-2 39 Pu

isotope shifts versus the HF electron density at the nu-cleus calculated for Pui and iI by Wilson 8 and byPaszek. 22 Although the points for f 5s2p and f 5 dsp fallsomewhat far from the line, the agreement is fairlygood for Pui. For Puii there is considerable scatter,but if the fI5s 2 and f5 dsp points are disregarded, the Puiline represents the Puii data fairly well. Figure 3(b)shows the Pui plot using HXR electron densities. Theagreement for f 5s2 p and f 5dsp is considerably improved.

Equivalent results for Puii are shown in Fig. 3(c). Aline with the same slope (s=0. 152) as for Pui, and 0.110cm-' above it, represents the data as well as any other.


f 5 s2 fits very well. The agreement for f 5sp is stillpoor, although better than in the HF case. The devia-tion is in the wrong direction to be explained by neglectof the Pj/2 density.

The shifts in relative electron densities in going fromthe HF to the HXR calculations are similar to those forCm. For Puii, f 4 d 2s had the higher electron density inthe HF case, but is much lower than that of f 5S2 in theHXR calculation. Similarly, the electron density of f 6shas greatly increased with respect to that of f 5dp andf 5sp in going from the HF to HXR calculation. Theseshifts result in the same pattern of relative electrondensities as for Am and Cm.

Table V shows the HXR values of 4771 p(0)I 2tt as wellas empirical and predicted isotope shifts. The con-figurations f4d2s2 and f6 dp of Pui are seen to be badlyperturbed as indicated by the wide range of experimen-tal isotope shifts. 21

U

Since CI is so strong in U i, it is difficult to find manyreliable isotope shifts for pure configurations. Thosechosen are shown in Table VI. The choice was based onan attempt to pick out the unperturbed levels-with somehelp from CI least-squares fits to experimental levels

f22 2 32~_p+fSfor the configurationsf d s +f p of452 (Ref. 23). Di-rections expected for the pure configuration values areagain indicated by arrows in Fig. 4, while the errorbars indicate the range of observed values where thereis little reason for choosing a particular one.

For f 2d2s2 the highest positive IS was chosen, that ofthe 5L6 level at 11 503 cm-'. The CI calculation showsthis level to be _ 99% f 2d2s2. Those configurations whichwere neglected in the CI calculation all have negativeisotope shifts and would lower the observed value. Thus

TABLE V. HXR values of 47r I t(O) 1 2t (units of a-3) and isotopeshifts for Pui and Puii.

Put 7 I p (0) I 47r I t(0) 2tot IS X 103 cm-t

Configuration 5s 6s 7s 8s Expt. CaIc.

f6

S2 286. 984 127. 033 37.346 * 76 495 184 465 525

ftsp 286.982 126.999 39.819 ... 76493891 '340 335

ft7s8s 286.981 127.000 42.164 14.525 76494179 340 360

ftds 286.990 127.068 36.865 * 76 493 812 250 305

f6dp 286.987 127.025 ... ... 76492365 '290 80

fPStp 287.025 128.707 43.454 * 76 496 549 -690 725

f5Sp2 287.025 128.727 45.423 * 76494767 * 450

f5ds

2 287.028 128.663 40.256 * 76496150 655 655

ft

dsp 287.028 128.661 42.223 * 76 494 619 470 430f

5d

2s 287.031 128.653 39.351 * 76494509 490 420

f'd2p 287.030 128.634 * ... 76 492 880 * 160f4d

2s2 287.111 130.587 42.588 76497233 5 3 5a 840

Pull

fGs 286.981 127.000 42.741 76493882 380 425

ftp 286.978 126.974 * 76491966 250a 80

ft

d 286.987 127.019 * 76492126 80 150a S2 287.026 128.730 46.099 76496768 900 920

fAsp 287.026 128.751 47.341 76494723 430 550f ds 287.028 128.672 44.884 76494609 550 545f

tdp 287.027 128.677 * 76492517 3 3 0 b 225

f 5d2 287.030 128.634 * 76492653 240 245

f 4ds 287.111 130.600 46.794 76495469 815 675

aObviously perturbed.bIS is correct but level identification is questionable.


TABLE VI. 47r I ?0(0) I 2t (in units of a- 3) and isotope shifts for Ur and ii.

U I HXR -47 $Iz(0) I 47r (0)Itt IS x Io cm-,

Calc.Configuration 5s 6s 7s 8s HXR HFa Expt. (HXR)

f 2ds2 p 257.475 116. 893 41.727 64 635 999 7 062 219 590f 2dsp2 257.477 116. 924 43.336 * 64 634 359 7 062 046 - 80f 2d2s2 257.471 116. 779 38.957 * 64 635 612 7 062 134 450 455f2d2sp 257.472 116. 787 40.543 * 64 634 176 7 062 048 -170 -170f 2 d2 7s8s 257. 472 116. 789 42.404 14. 143 64 634 457 ... - 475f 2 d3 7s 257.471 116. 722 37.741 64 634 045 ... ... -240f 2d3p 257.471 116. 711 ... 64 632 572 -860f 3 s2p 257.399 115.052 39.761 64 635 089 7 062 063 150 200f 3ds2 257.400 114. 998 36. 867 * 64 634 742 7 062 002 60 60f 3 dsp 257. 399 114. 995 38. 631 * 64 633 443 7 061906 - 400 - 490f 3 d7s8s 257. 399 115. 001 40. 652 13. 826 64 633 721 7 061937 - 350 - 375f 3 d7s8p 257.399 115.003 40.812 64633516 ... *-- -460f 3 s2 7d 257.399 115.069 41.966 * 64 635 336 ... 300f 3d2s 257. 402 114. 983 35. 975 * 64633344 7 061855 -525 -525f3 d2p 257.401 114.962 ... ... 64 631987 7 061790 - 950 - 1120f3

P3 257.405 114.981 ... 64 632 093 ... ... - 1070

S4 s 2 257.366 113.555 34.473 * 64633961 7 061837 -350 - 275

f4 p2 257.540 118.604 ... ... 64631585 ... -1280f 4 sp 257.364 113.509 36.603 * 64 632 850 7 061774 -665 - 745f 4 ds 257.372 113.600 33.866 64 632 702 7 061729 ... - 810f 4dp 257.369 113.539 ... ... 64631581 ... ... -1280

UrI

5f 2 6d7s2 257.476 116.916 44.118 64 636 196 ... - 50 b 4255f 26d27s 257.472 116.796 42.865 64634153 **- 400 -4805f26d3 257.470 116.705 * 64 632 368 * -1380 -12605f 37s2 257.400 115.076 42.247 64635293 * 0 05f 37s7p 257.401 115. 101 43.340 64633564 - 650c - 7605f 36d7s 257.399 115.006 41.151 64633429 ... - 800 -8005f 3 6d7p 257.399 115.014 64631708 * * 1 1 2 5 d -12305f3 6d2 257.400 114.959 64631785 ... -1290 -12005f47s 257.363 113.503 39.322 64 632 857 ... -- - 1050

CRange: - 600 to - 950.dRange: - 950 to - 1350.

the chosen value of 0. 450 cm-' is a minimum.

The lowest level of f 4S2 has an observed IS of - 0. 310cm-' (Ref. 5). Preliminary calculations2 3 show that thislevel is about 10% f 2d 2 s2. If these are the only two con-figurations involved, a value of - 0. 395 cm-' for thepure f 4S2 IS is necessary to obtain agreement with theobserved IS. Since it is possible that there are alsoadmixtures of other configurations with negative isotopeshifts, such asf3 dsp andf4 ds, a conservative value of- 0.350 cm-1 was chosen. The resulting prediction ofan IS of - 0. 275 cm-' indicates that interaction withf 4ds, which has a large negative IS, may be important.

CI calculations2 3 indicate an IS of about 0. 150 cm-' isappropriate for f 3s2p. But interaction with f 3 dsp wasnot included in the calculations. The effect of f 3dspwould be to lower the observed IS so that the true. valuemay be somewhat higher than 0. 150 cm-.

The IS of the lowest level, 5L6 of f 3ds2, has been de-fined as 0 and all other isotope shifts are measuredrelative to that. Several other low levels of f 3ds2 havesmall positive isotope shifts ranging up to 0. 060 cm-Since the primary interaction is with f3d 2s, which hasa large negative IS, only a small admixture of f 3d2s


would be necessary to account for the observed value of0 for the ground level and an IS of 0. 060 cm-' has beenchosen for f 3ds2.

The IS of the lowest level (- 0. 565 cm'1) has beenchosen for the configuration f 3d 2s. Any admixture off 3ds2 would mean that the true value should be morenegative. Admixture with f 4

Sp, which begins at - 23000cm , would have the opposite effect.

The most negative observed shift (- 0. 950 cm-) waschosen for f3 d2 p. Any CI would mean that this is anupper bound.

Five levels have been identified as belonging to theconfiguration f 3 d7s8s. Three of these have isotope shiftsof about - 0. 375 cm-1 and the other two have shifts ofabout - 0. 500 cm-'. The - 0. 375 cm-' value has beenused since it seems to be in accord with the calcula-tions. If all five of these levels really belong to thesame configuration, there must be a strong perturba-tion of some of them.

One level of f 2 d 2sp has been identified with IS- - 0. 170 cm- . This is in good accord with the HXRcalculations.


'A. Paszek (Ref. 23).bMeasured for only one level.

TABLE VII. Effective mass difference and slope from plot ofIS vs HXR values of 4ir I 7[(0) I tot

Element AM S S/AM

U 3.194 0.429 0.13Pu 1. 194 0.152 0.13Am 2.000 0.216 0. 11Cm 2.000 0.231 0. 12Cf 2.000 0.23 0. 12 (assumed)

The empirical values are plotted against the HF elec-tron densities of Paszek 2 2 (Table VI) in Fig. 4(a). Thereis considerable scatter. The point for f3dsp is belowthe line, but the true value is likely to be lower than in-dicated, certainly not higher. f 3ds2 is above the line andthe true value may be higher than indicated. The pureconfiguration value for f 3d 2p may be lower than indi-cated, and it is already well below the line. There isvery little difference in the total electron densities forf4 s2 and f 3 d 2p despite the difference of two s electrons.

The HXR results [Fig. 4(b)] remove all of these dif-ficulties. The points forf 3 dsp andf 3 d 2p are above theline and f 3ds2 is below as expected. The one bad pointis f 4 ds where the, entire range of observed values for thefour levels recently identified by Blaise and Radziemski 5

is shown by the error bars. If the identification is cor-rect, CI must be very strong. HFR calculations 24 doindicate strong interaction between f 4 ds and f 2 d3s whichis predicted to begin at about the same energy. Thepredicted IS of f 2d 3 s is - 0. 240 cm-, whereas that forf 4 ds is - 0. 800 cm-'. Even the lowest observed IS of- 0. 560 cm-' for f 4ds is much greater than the predictioxand there are no observed isotope shifts anywhere near- 0. 800 cm 1 . So we conclude that either the identifica-tion of the f 4ds levels is incorrect or that the observedlevels are all greatly perturbed. The predicted IS off2 d3 s is the same as the resultant IS for many levelswhich are highly mixed. Consequently, isotope shiftsalone do not allow one to pick out levels of this con-figuration. Detailed energy level calculations are alsonecessary. Inclusion of a correction for the 7 Pa/2density would improve the agreement for all configura-tions but f 3s 2p.

The current results can be used to identify the begin-ning of one new configuration. There is one odd levelat 27 930. 942 cm 1 with a measured IS of +0. 125 cm-f,J= 6, g= 0. 835. All other levels in this region havenegative shifts (Ref. 5). This IS is somewhat uncertainbecause it results f rom a single measurement, but assum-ingthat it is correct, we are led to conclude that the levelbelongs to the configuration f3 s2 7d. There are onlytwo odd configurations, other than the ground f3 ds2 ,predicted to have positive isotope shifts: f 3s27d (0. 300cm 1) andf 2 ds2 p (0. 590 cm-1 ). Both should have a 5L6ground level with gLS = 0. 714. The calculated center ofgravity for f3s 2 7d is 30700 cm-' above that of f3 ds2 .Brewer 25 predicts that f 2ds2p begins at 24000 cm-.The low IS does indicate strong CI, but the level is muchmore likely to belong to f 3s27d than to f 2ds2p. The onlyother possible explanation for a positive IS is that onehas suddenly found a pure f 3ds2 level at 28000 cm- and


that all lower ones are more strongly perturbed thanpreviously recognized. This does not seem very likely.One level of the analogous configuration f 7 s7d has beenidentified at 35 000 cmn1 in Am i.

There is not much basis for drawing a line through theU ii points in Fig. 4(b), but if the f2 ds2 point is regardedas badly perturbed, a line parallel to the U i line and0. 300 cm-' below it fits fairly well. The point for f 2ds2of U ii is so far off the line that the identification of thatconfiguration becomes questionable. But there is nolow even configuration with an IS near zero. If the ex-perimental number is correct, one can only concludethat the level is nearly a 50-50 mixture of the configura-tions f 2 ds2 and f 2 d 2s.

COMPARISON OF DIFFERENT ELEMENTS

The slope, S= AIS/A[47r1 (0)I ti, per unit mass dif-ference and the effective mass differences AM, 26 aregiven in Table VII. Because of the phenomenon of odd-even staggering, there is some uncertainty in the assign-ment of the AM. Experimental data for Pu indicate thatthe shifts of the odd isotopes correspond to a mass about20% closer to the next lower even isotope. This meansthat AM for Pu 240-239 is 1. 194. Assuming the stagger-ing in U is the same as that measured for Pu, AM forU 238-235 is 3. 194. Since AM is large, in this case asmall error in the assumed staggering would not greatlyaffect AM/S.

AM has been assumed to be 2 for Am 243-241 and Cm244-242. Since the nuclear spins and moments of thetwo isotopes are the same in both cases, 27 there is noreason to expect the effective AM to be appreciably dif-ferent from 2.

It is difficult to tell if there is a real trend in S/AM,but as a first approximation, we can consider it to beconstant within the uncertainties in obtaining S. Thismeans that the variation in the nuclear factor C in Eq.(1) is approximately accounted for by just the effectivemass difference. On this basis we can assume a slopefor Cf and use calculated values of 4r I (0)1 2ot to predictisotope shifts for configurations of 252Cf-250Cf. With theassumption that the IS of the ground configurations fl

0s 2

is 0, these are plotted on the same line in Fig. 5 andpredicted isotope shifts are given in Table VIII.

The results presented here could also be used to cal-culate shifts for different pairs of isotopes than thoseconsidered in this work.

An analysis similar to that presented here but basedonly on HF calculations has been carried out by Champeaulfor Ce i and ii. The Ce i and ii lines do not have thesame slope and for Ce i 4f 26s 2 has a lower electron den-sity than 4f 5d 26s. For Ce iI 4f2 6s has a lower electrondensity than 4f 6d 2. An HXR calculation reverses theordering of these electron densities in Ce iI but not inCe I. If Ce were completely analogous to the actinideconsidered here, reversal would occur in both cases.With the HXR calculation, the fit is improved for Ce iI,where it was poor in the HF case; and it is possible tofit the Ce i and Ce II data with parallel lines.


(units of a30) and isotope shifts

CfI v4rI (0) I IS

Configuration 5s 6s 7s 4ir l (0) I 2t Calc.

f10S2 356. 114 157. 610 43. 906 107 795 204 0ftisp 356.111 157.586 47.098 107793411 -425POP2 356. 108 157.565 ... 107 791013 - 975

fl 0ds 356. 117 157. 640 44.064 107 793 337 - 440fl 0dp 356.116 157.613 * 107 791273 - 920f9S'p 356. 163 159. 619 51. 683 107 797 197 460

f3dS2 356. 168 159. 592 47.969 107 796 682 340f 9 dsp 356. 167 159. 591 50. 366 107 794 484 - 170f9d2s 356. 172 159. 593 47. 226 107 794 380 - 190

Cf II

fl 0 s 356. 110 157.594 50.395 107 792 344 - 670flop 356. 107 157. 573 * * * 107 790 664 - 1055fl

0d 356. 115 157. 618 ... 107790926 - 990

f9S2 356.163 159.641 54.658 107 797 399 505

f9sp 356. 163 159. 661 56.263 107 794 546 - 150f9p2 356.162 159.693 ... 107791242 - 925f 9ds 356. 167 159. 603 53. 285 107 794 375 - 200f9d2 356.171 159.580 * 107 791655 - 1075

If we compare the relativistic and nonrelativistic HFelectron densities of Coulthard14 and Wilson 28 for Eu,we find a large increase in the electron density of f7 S2

relative to that of f 7sp, which is similar to that observedin the actinides. Unfortunately, electron densities werenot calculated for Eu configurations analogous to theactinide ones for which the largest differences betweenthe relativistic and nonrelativistic values occur.

CONCLUSIONS

The relationship between observed isotope shifts andcalculated s-electron densities at the nucleus (with andwithout the inclusion of a relativistic correction) havebeen examined for Cm, Am, Pu, and U. While there arecases where the HF values of 47r1 Ip(0)120t show the ex-pected proportionality to observed isotope shifts, thereis frequently considerable scatter, some of which can-not, even in principle, be explained by effects of CI onthe observed isotope shifts. In the HF case, there areexamples where for the same fN core higher electrondensities occur for configurations with fewer s elec-trons.

When the relativistic correction is included (HXR),electron densities increase by a factor of - 12, but therelative values for some kinds of configurations areshifted dramatically. The result is that for a given fNcore, electron densities do increase with increasingnumber of s electrons. Configurations containing fN-lS2

have slightly higher electron densities than those con-taining fNs.

In all cases it is possible to fit HXR points for the firstand second spectra on lines of the same slope. Thismakes it possible to relate both sets of isotope shifts tothe same zero, which may prove to be useful in the iden-tification of Rydberg series where the observed IS of thehigher members of the series should approach that ofthe series limit.

The slope, iMS/A(47r I j(0)1 2ot), per unit mass is con-


TABLE VIII. HXR 47r 1 ()I totfor CfI and CfoI.


stant within the uncertainties in the present analysis.This allows calculated values of 471d gp(O)1 2ot to be usedto predict isotope shifts for other actinides. Such pre-dictions have been made for Cf.

ACKNOWLEDGMENTS

We are indebted to R. D. Cowan for providing his HXcode and to P. Renard for conversion to the LLL ma-chine. We also wish to thank H. M. Crosswhite, A.Paszek, and J. Mann for permission to use their un-published calculations and M. Wilson, B. Shore, and Y.K. Kim for helpful discussions. L. Radziemski, J.Blaise, E. Worden, and J. Conway have been mostgracious in providing and discussing data in advance ofpublication.

*Work was performed under the auspices of the U. S. ERDAunder contract No. W-7405-Eng-48.

tPermanent address: Kalamazoo College, Kalamazoo, Mich.49007.

'See, for example, D. N Stacey, "Isotope shifts and nuclearcharge distributions," Rep. Prog. Phys. XXIX, Part I, 171-213 (1966).

2J. Blaise, M. Fred, S. Gerstenkorn, and F. S. Tomkins,"Isotope shifts and classification of the arc and spark spec-tra of Pu, " paper given at meeting of European Group forAtomic Spectroscopy, Hanover, July 14-17 (1970).

3M. Fred and F. S. Tomkins, "Preliminary term analysis ofAmi and Amii spectra," J. Opt. Soc. Am. 47, 1076-1087(1957).

4M. Diringer, "Etude du d6placement isotopique de l'uranium(235-238). Contribution aL la classification des spectres d'arcat d'6tincelle de l'uranium, " These, Facult6 des Sciences,Univ. of Paris (1964); Ann. Phys. (Paris) 10, 89-120 (1965).

5J. Blaise and L. J. Radziemski, "The energy levels of neutralatomic uranium (Ui)," J. Opt. Soc. Am. 66, 644-659 (1976).

6E. F. Worden and J. G. Conway, "Energy levels of the firstspectrum of curium, Cm I," J. Opt. Soc. Am. 66, 109-121(1976).

7J. Blaise and A. Steudel, "Isotopieverschiebungskonstantenvon Th, U, Pu, and Am," Z. Phys. 209, 311-328 (1968).

8M. Wilson, "Ab initio calculation of screening effects onI o(0) 1 2 for heavy atoms," Phys. Rev. 176, 58-63 (1968).

9P. Brix and K. H. Lindenberger, "Konfigurationsmischungund isotopieverschiebung im gadolinium II-spektrum, " Z.Phys. 141, 1-5 (1955).

10J. Bauche, "Etudes theoreques sur la partie 6iectronique dud6placement isotopique dans les spectres atomiques, " These,Facult6 des Sciences d'Orsay, Univ. de Paris (1969).

"0R. J. Champeau, "D6placement isotopique dans les spectresd'arc et d'6tincelle du c6rium, II. Deplacement isotopique'4 0Ce-0 4 2 Ce etude des facteurs electroniques," Physica 62,225-238 (1972).

12 L. R. Carlson, J. A. Paisner, E. F. Worden, S. A. Johnson,C. A. May, and R. W. Solarz, "Radiative lifetimes, absoip-tion cross sections, and the observation of new high-lying oddlevels of 238U using multistep laser photoionization, " J. Opt.Soc. Am. 66, 846-853 (1976).

13R. W. Solarz, C. A. May, L. R. Carlson, E. F. Worden,S. A. Johnson, J. A. Paisner, and L. J. Radziemski, Jr.,"Detection of Rydberg states in atomic uranium using time-resolved stepwise laser photoionization," Phys. Rev. A 14,1129-1135 (1976).

14M. A. Coulthard, "Relativistic contributions to screeningratios in europium," J. Phys. B 6, 23-29 (1973).

15D. A. Shirley, "Application and interpretation of isomershifts," Rev. Mod. Phys. 36, 339-350 (1964).

16R. D. Cowan, "Atomic self-consistent-field calculationsusing statistical approximations for exchange and correla-tion," Phys. Rev. 163, 54-61 (1967).

17H. A. Bethe and E. E. Salpeter, QuantumMechanics of One-and Two-Electron Atoms (Springer-Verlag, Berlin, 1957),Sec. 13.

t8 The code provides two methods for dealing with numericalderivatives near the origin which result in total s-electrondensities differing by 15%. The option IREL=2, which givesthe lower total electron density, has been used throughoutsince it comes closer to reproducing DF results for the outershells where differences between configurations arise. Thedifferences in predicted IS values are < 0. 025 cm-1, which iswell within the uncertainties ot the present analysis. If ab-solute electron densities are desired for nuclear studies,these differences should be resolved by use of a finite ratherthan a point nucleus.

19J. Mann (private communication).20H. M. Crosswhite (private communication).21 J. Blaise and M. Fred (unpublished).22A. Paszek (private communication).23K. Rajnak (unpublished).24K. Rajnak, "Hartree-Fock calculations for many configurations

of Ui," Phys. Rev. A 14, 1979-1988 (1976).25 L. Brewer, "Energies of the electronic configurations of the

lanthanide and actinide neutral atoms," J. Opt. Soc. Am. 61,1101-1111 (1971).

26The effective mass difference is one measure of the differ-ence in volume of the two isotopes.

27T. E. Manning, M. Fred, and F. S. Tomkins, "Nuclear mo-ments of 2 4'Am and 2 43 Am," Phys. Rev. 102, 1108 (1956).

28M. Wilson, "Ab initio calculation of core relaxation andscreening effects on I 0(0) 12 for Sm and Eu, " J. Phys. B 5,218-28 (1972).

Absorption spectrum of Ag I between 1540 and 1850 A

C. M. Brown* and M. L. GinterInstitute for Physical Science and Technology, University of Maryland, College Park, Maryland 20742and E.O. Hulburt Center for Space Research, Naval Research Laboratory, Washington, D. C. 20375

(Received 26 May 1977)

The high-dispersion absorption spectrum of Agi has been photographed in the 1540-1850 A region.Observations include the 5s 2SI/2-np 2P 3/21 /2 transitions for n = 7 through n = 71, the5s 2S112-4d 9 5s5p 4P32.112, 4F3 '/2,D3/2, 4D/ 2 transitions, and the electric-quadrupole transitions5s 2 SI12-nd 2 D3/2,5/2 for n = 7 through n = 12. The iiseries is 61 106.56+0.06 cm- .

Although the spectrum and electronic structure of Agihave been studied extensively, 1-7 little data exist for thehigher excited (Rydberg) levels near the lowest ioniza-tion limit. The 1540 -1850 A region in the spectrum ofAgi is particularly important to the characterization ofsuch levels because it contains most of the possibletransitions between the 4d'05s 2S1/2 ground level of Agiand the excited energy levels converging on the 4d'0 'S0ground level of Ag ii. The present work fills the gap iilour experimental knowledge of Agi by reporting an ex-tensive and highly resolved absorption spectrum of silvervapor in the 1540-1850 A region.

The apparatus used in the present work has been dis-cussed in detail, 8 and the experimental arrangementsand procedures are similar to those employed in ourprevious studies8 -15 on the absorption spectra of neutralatoms in the vacuum ultraviolet. Briefly, silver16 wasplaced in an evacuable King furnace system with a 122-cm-long hot zone and heated to temperatures in the range- 1200-1550 °C. Absorption spectra were obtained froma single pass through the furnace using a microwave-ex-cited xenon lamp8 to provide background continua. Spec-tra were photographed on Kodak SWR plates using thethird order of a 6. 6 m spectrograph with a reciprocaldispersion of -0.41 A/mm. Most of the experimentswere performed with flowing argon in the furnace atpressures less than -0.1 Torr, although in a few casesargon pressures as high as 10 Torr were employed.The wavelength uncertainty in sharp, unblended lines is


inization potential of Agi determined from the np 2P

estimated to be ± 0.001 A, corresponding to i0.06 cm-1

at 1500 A and ± 0.04 cm-' at 1800 A. The wavelength ofdiffuse or blended lines is more uncertain.

The wavelengths and wavenumbers of the absorp-tion lines observed in the 1540-1850 A region in ourexperiments are listed in Table I. Table I also in-cludes the assignments of the electric dipole allowedtransitions 5s2 S/ 2 -np 2P3/2,1 2 (n,=7-71) and 5S 2S- 2

4d9 5s5p4 P/12 ,31 2, 4 F31 2, 4Dl 22 ,142, and the electric-

quadrupole allowed transitions 5S S112 - nd2 D5 / 2 , 3 /2 (n =7

- 12). The relative transition intei.sities listed in thetable are based on visual estimates from photographicemulsions and are intended only as a qualitative guide tothe reader.

Lines of the 5s 2 S/ 2 -p2 P 1 2 series are perturbed in

both energy and intensity in the region around n = 17 bythe 4d95s5p 4 P /2 level (see Fig. 1). It is also evidentfrom Fig. 1 that the rapid decrease in the n/ 2 P91 2 , 2

P3 /2

spacing with increasing n leads to the coalescing (withinour resolution) of the 5s 2 S-np

2P3 / and 5s 2 S2 2 -np 2

pt 2

series for n-21. The 5s2 S /2 -np2 P3/2 series also isperturbed in the region around n = 10 by the 4d9 5s5p 4

PI /2

level. The intensity perturbation is particularly strik-ing because we find no transition (see Table and Fig. 2)to the 10p

2PS,2 level at 58 849.83 cm-1 reported by

Rasmussen, 5 even though the vapor density of atomicsilver was sufficiently high to observe well-developedelectric-quadrupole transitions in the same energy re-

Copyright O 1977 by the Optical Society of America 1323

Correlation of isotope shifts with |Ψ(0)|2 for actinide configurations

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Transcript of Correlation of isotope shifts with |Ψ(0)|2 for actinide configurations