Z. Physik A 272, 223-226 (1975) �9 by Springer-Verlag 1975

Level Crossing Investigation of the Hyperfine Splitting in the z 6Pv/2-Level of EuI

W. Lange*

Institut A f'tir Experimentalphysik der Technischen Universit~it, Hannover, Germany

Received December 11, accepted December 20, 1974

Abstract. By means of a level crossing experiment the hyperfine structure constants of the zOp7/z-level of Eu have been determined. The results are A = - 6 . 5 1 ( 6 ) M H z and B= 131.2(1.0) MHz in the isotope ~51Eu and A = -2.84(3) MHz and B= 327.5(1.5) MHz in the isotope 153Eu. Experimental data on the hyperfine splitting are available now for 11 of the 12 levels of the configuration 4fv(SS)6s6p of EuI. These data are compared with the theoretical interpretation given by Bordarier et al. [1] which was based on only 7 A-factors and B-factors. It is shown that the agreement between theory and experiment can be improved by taking into account configuration interactions.

I. Introduction

The hyperfine splitting (hfs) in the configuration 4fv(SS) 6s 6p of EuI has been analysed by Bordarier et al. [1] by means of effective tensor operator tech- niques. Their treatment was based on experimental data by MiJller et al. [2], who obtained the A- and B-factors of 7 levels by conventional optical spectro- scopic methods. Subsequently similar experimental methods were applied to the z s Ps/2 and z s P7/2 [3], which were not investigated in [2]. Furthermore, the h f s of the yS P5/2 has been determined by use of an atomic beam inside a spherical Fabry-Perot-inter- ferometer [4], and the knowledge on the y8 P7/2 has been considerably improved by a level crossing experiment [5]. It seemed desirable, however, to obtain as complete experimental information as possible, since broadly based comparisons between theory and experiment are rare in the h f s of rare earths. Hence, a level crossing experiment on the extremely narrow split z 6 PT/2-1evel was performed, leaving only the h f s of the z 6 P3/2-1evel unmeasured in the configuration 4fV(SS)6s 6p. It turned out that

* Present address: Fakult~it ftir Physik der Universit~t Bielefeld, Germany

the agreement of the results with the predicted values [1] is not very good in the z 6 P7/2, zS Ps/z and z s Pv/2; the agreement can be considerably improved, how- ever, by use of eigenfunctions which take into account configuration interactions with 4fv(sS)5d6p and 4f6(VF) 5 d 6 s 2.

II. Experimental

The experimental set-up was similar to the one described by Handrich et al. [6] which makes use of the technique of the rotating polarizer in connection with phase-sensitive detection [7, 8, 9]. Just as in [6] an atomic beam was used instead of a resonance cell. With respect to the high costs of Eu metal, the eva- poration rate was restricted to 100mg/hr; the two stable isotopes were in their natural abundancy (47.9 percent 151Eu, 52.1 percent 153Eu). As an alter- native to the hollow cathode lamp used in [6] for excitation, a r f discharge lamp was employed which provided an intense source for the intercombination line connecting the a8S7/2 ground state with the z6 g/2 ( f= 0.0072 [10]). A typical signal curve is shown

224

151 151 151 153 151

Z. Physik A 272 (1975)

I I I I 11.07

I I I = 13.08

I t ~ H EOe3 15.09

Fig. 1. Typical signal curve. Averaging time was 20min. The isotopic assign- ment of the signals is indicated in the upper region of the figure

Table 1. Observed positions of levelcrossing signals. All values have been averaged over several independent measurements. The errors given in brackets include the uncertainties of the magnetic field determination and other possible sources of systematic errors. (F, M) and (F', M') are the quantum numbers of the crossing hyper- fine Zeeman levels as determined in the analysis of the experimental results (see text). The last column gives the isotope to which the signal is attributed

H [Oe] (F, M) • (F', M') Isotope

2,65(5) (4, 3) • (5, 5) 153 7.78(5) (1, - 1)x(2, 1) 151 9.99(10) (4, 3) • (5, 5) 151

11.23(5) (2, - 1 ) • 1) 151 t2.77(5) (1,0) x (2, 2) 151 14.08(5) (2, 0) x (3, 2) 151 14.91 (5) (1, - 1) x (2, 1) 153 15.15(5) (4, 1) • (5, 3) 151 16.11 (5) (4, - 2 ) x (6, - 4 ) 151 17.08(5) (4, 0) x (5, 2) 151 18.15(5) (2, 1) x (3, 3) 151 18.81 (8) (4, 2) x (5, 4) 153 19.1 (2) (4, - l )x(5 , 1) 151 21.30(7) (3, - 1) x (4, 1) 153 22.37(7) (2, - 1) x (3, 1) 153 24.17(7) (3, 0) x (4, 2) 153 24.57(7) (3, 1) x (4, 3) 153 26.21 (7) (1, 0) x (2, 2) 153 26.89(10) (3, 2) x (4, 4) 153 27.59(10) (4, 1) x (5, 3) 153 31.57(8) (2, 0) x (3, 2) 153 35.08(10) (4, - 1) x (5, 1) 153

in Fig. 1; the height of the signal peaks corresponds to about 10- 3 of the resonance fluorescence light. The positions of the observed crossings are given in Table 1. It was not obvious in the beginning to which of the two isotopes and to which hyperfine levels the signals must be assigned. From the predictions of [1] an irregular order of the hyperfine levels in zero

Table2. Hyperfine constants of the z6PT/z-level. The values have been determined with g j = 1.798, calculated from intermediately coupled eigenfunctions [11]. The experiment gives only IAI, kBI and the sign o f A/B. The sign of B was taken from the theoretical prediction [1]. All values are given in MHz, with three times the statistical error given in brackets

tSlEu 153Eu

A = -6.51 (6) A = - 2.84(3) B = 131.2(1.0) B =327.5(1.5)

magnetic field is expected. In fact, it was found in the course of the evaluation that the hyperfine levels F = 4 and F = 6 are nearly coincident in the isotope 151Eu, because the A-factor is very much smaller than the B-factor. Under such conditions even the qualitative distribution of the crossings depends critically on A/B. It turns out, however, that only the combination of A- and B-factors given in Table 2 is consistent with the observed positions of the crossings and the known ratios of the nuclear moments [11, 12]*

III. Discussion of the Results

While the experimental values of the B-factors are in reasonable agreement with the predicted values (111.6 MHz [1] and 113.4 MHz [5], resp., for 151Eu), there seems to be total disagreement in the A-factors (32.7 MHz and 16.2MHz [1], calculated with two different sets of intermediately coupled wavefunctions [-1]). The difference between the values obtained by use of two very similar sets of eigenfunctions [1] indicates that the A-factors depend very sensitively

* The positions and shapes of the crossings were computed by means of a computer program kindly sent by Prof. W. Happer

W. Lange: Level Crossing Investigation 225

Table 3. Theoretical and experimental A-factors and best values of the radial parameters. In contrast to Table 2 all values are given in 10 3cm-1

Level Calc. with eigenfunctions Exper. Ref.

[ I ] [15]

3/2 - 71.64 - 76.04 - - z 6 P 5 / 2 - - 17.88 - 1 9 . 7 9 -19.72(5) [2]

7/2 1.26 0.19 - 0.217(2) this work

5/2 - 22.89 - 20.29 - 20.337 (60) [3] zSP 7/2 - 9.35 - 8.05 - 7.943(26) [3]

9/2 21.78 22.89 22.18(11) [2]

7/2 32.53 32.06 32.32(2) [2] z~~ 9/2 34.07 34.13 34.138(8) [2]

l 1/2 30.08 30.69 31.13(10) [2]

5/2 - 3.47 - 4,93 - 5.25(5) [4] ySp 7/2 - 7.03 - 7,51 - 7.30(1) [5]

9/2 - 7.93 - 8,24 - 7.68(11) [2]

af -- 1.7(1.4) -- 2,4(4) a, 322(21) 336(6) bp 15.9(7.3) 16.0(2.3) cp 24.1 (17.3) 27.5(5.0)

on the coupling scheme; for example, it is found in a simple calculation that an A-factor in the order of -900 MHz would be expected in pure LS-coupling, with the radial parameters of the hfs taken from [1]. In [1], the radial parameters @, a s and bp of the effective tensor operator

O=-af. S f+a s �9 s+ap. s+bp" I - 101/2 "Cp" (s C12)) (l)

are determined in a least squares fit to the measured A-factors, while ap/bp and cp/bp a r e calculated by means of Casimir's relativistic correction factors. This procedure was repeated, using the 11 A-factors now available. With this amount of experimental data, it seemed appropriate to let one additional parameter be free; since the contribution of the last term of O greatly exceeds that of ap. s, Cp was chosen as fourth parameter. The results are shown in column 2 of Table 3. The mean square deviation between experi- mental and calculated values is 1.3mK ( l m K ~ 10 - 3 cm-t). There is poor agreement for the z 6 P5/2, Z6 P7/2, Z8 P5/2, 2.8 P7/2 and yS P5/2 levels.

The hyperfine interaction in the configuration 4fT(sS)6s6p is mainly due to the term as. s of O, of course. Since there is consider- able mixing between the (sS)6s6p(3p)zs+lPj "triplet" states and some mixing between the (83)6 s 6p(1P) 8ps ,, singlet" states and the triplet states, there are contributions of the type

<(83, 3p)28+l ps Ifsll (83, 3p)28+1 pd>, <(83, 3p)28+1Ps Ilsll(ss, IP)SPs> and <(88, 3p)28+1 pj ilsl I (83. 3p)2s'+1 pj>,

which are in the order of several 100 MHz each, but which nearly cancel in the case of the z6PT,z; thus the off-diagonal elements of s

are the cause of the strong dependence of the A-factors upon the coupling coefficients. Hence, one might suspect that the differences between theory and experiment are mainly due to imperfections of the eigenfunctions.

It has been pointed out previously [13] that details of lifetimes in the configuration 4fT(SS)6s6p of EuI cannot fully be accounted for by use of the eigen- functions of [13. On the other hand, eigenfunctions which include configuration mixing with 4f7(83) 5 d 6p [14] and in addition with 4f6(TF)5 d 6 s 2 [15] are now available, which allow a better description of the life- times [-13]. The use of these eigenfunctions in con- nection with the magnetic hfs has been briefly dis- cussed in [-3]; they have also been used in the descrip- tion of the quadrupole interaction in [5]. There are admixtures of the perturbing configurations in the order of I percent in the triplet states and of more than 20 percents in the singlet states. A full treatment of the influence of theses admixtures, which surely are not the only ones, becomes rather complicated and introduces a number of new parameters. On the other hand, with the hfs being governed by the interaction of the 6 s electron with the nucleus, it should be a good approximation to neglect the immediate contri- butions of the perturbing configurations and to take only into account the modifications on the coupling coefficients within the configuration 4f7(83) 68 6p. In this way the perturbations are treated by renormali- zation. The result of this procedure, using the eigen- functions of [15], is given in column 3 of Table 3. The mean square deviation has been reduced now by a factor of 3.6 to 0.36 mK, which may be regarded as a good value. All major disagreements vanished, with the largest deviation found in the z 8 P9~2 (0.7 mK). Simultaneously, the margins of error of the radial parameters are reduced, of course, and a comparison between theoretical predictions and the results of the fitting procedure makes sense. The result bp= 16.0(2.3)mK is in reasonable agreement with the prediction bp= 17.4 mK obtained from the spin-orbit- coupling constant [1]. The result cp/bp=l.72(55) agrees within the limits of error with the relativistic prediction %= 1.34. bp [1] (unrelativistically: cp=bp). The agreement found in the highly perturbed vSp- levels is somewhat surprising, since the treatment of the perturbations is very crude; it might be suspected that inaccuracies in the description of the A-factors of the y8p-levels might be absorbed in the radial parameters. Hence, another run was performed in which the ySp-levels were omitted; the result was similar. It may be summarized that the magnitude of the 11 A-factors known in the configuration 4fV6s6p can be excellently interpreted in the manner described

226 Z. Physik A 272 (1975)

by Bordarier et al. [1], provided that the eigenfunctions are renormalized in order to take into account con- figuration interactions.

The author is most grateful to Prof. A. Steudel, Hannover, for his interest in this work and to Dr. G. Smith, Oxford, for sending details on his eigenfunctions.

References

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2. Miiller, W., Steudel, A., Walther, H.: Z. Physik 183, 303 (1965) 3. Krtiger, H.D., Lange, W.: Phys. Lett. 42A, 293 (1972) 4. Kuhl, J.: Z. Physik 242, 66 (1971) 5. Champeau, R.J., Handrich, E, Walther, H.: Z. Physik 260, 361

(1973) 6. Handrich, E., Steudel, A., Wallenstein, R., Walther, H.: J. Physi-

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8. Handrich, E., Kretzen, H., Lange, W., Steudel, A., Wallenstein, R., Walther, H.: Proc. Int. Conf. Opt. Pumping and Atom. Line Shape, Warszawa 1968

9. Saloman, E.B., Baghdadi, A., Halpern, J.B.: Rev. Scient. Instr. 41, 1148 (1970)

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1 I. Baker, J. M., Williams, F. I.B.: Proc. Roy. Soc. (London) A 267, 283 (1962)

12. Evans, L., Sandars, P.G.H., Woodgate, G.K.: Proc. Roy. Soc. (London) A 289, 114 (1965)

13. Lange, W., Luther, J.: unpublished data 14. Smith, G, Collins, B.S.: J. Opt. Soc. Am. 60, 866 (1970) and

private communication by Dr. G. Smith 15. Smith~G., Wilson, M.: J. Opt. Soc. Am. 60, 1527 (1970) and

private communication by Dr. G.Smith

Dr. Wulfhard Lange Fakult~it fiir Physik der Universit~it Bielefeld D-4800 Bielefeld Viktoriastr. 44 Federal Republic of Germany