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Volume 47A, number 4 PHYSICS LETTERS 8 April 1974 ISOTOPE SHIFT AND HYPERFINE STRUCTURE IN THE 2537 A LINE OF Hg BY LINE-CROSSING EXPERIMENTS IN FORWARD-SCATTERING* G. STANZEL 1. Phys. Institute, 63 Giessen, Germany Received 13 February 1974 The line-crossing effect between Zeeman components of different isotopes was studied experimentally and theoreti- cally in forward-scattered light in order to determine the isotope shift and hyperfine structure. The influence of the spectral distribution of the incident radiation was properly considered. Hanle's method [ 1] of magnetic depolarisation, also known as level-crossing technique, can be applied to forward-scattering [2] and selective reflection [3] of resonance radiation. As in these cases light scattered from different atoms is coherent, there are additional possibilities for interference. Besides the Doppler broadening of the level-crossing curves a line-crossing effect [2] of Zeeman Components of different isotopes results, determined by the isotope shift. Because of the Doppler broadening the usual condition of broad-band excitation is hardly to fulfil and the spectral distribu- tion of the incident light has to be considered carefully. Experiments in selective reflection and some other connected investigations, will be represented elsewhere [4]. Corresponding to the principal arrangement [2] for the experiments in forward-scattering, the scat. tering cell was situated between crossed polarizers in a static, longitudinal magnetic field H. The lamp, fiUed with an even mercury isotope, was situated in another magnetic field H L for shifting the frequency; the Zeeman components were seperated by a quarter wave plate and the polarizer. Especially prepared mix- tures of two different isotopes as well as natural mercury were used in the scattering cell at a total density of 5 X 1012 cm -3. In.order to receive sharp line,crossing signals, the corresponding Zeeman- components should have nearly the same intensities, determined by the transition probablities and the relative abundances. As an example a mixture of the isotopes Hg 199 and 202 shall be regarded, where there are three line- * From a thesis (D 26, Giessen) and supported in part by the Deutsche Forschungsgemeinschaft. 2 0 2 ~ _ I 1 9 9 ~ t 1 2 3 /, ROe Fig. 1. (a) Zeeman structure of the 2537-A-lineof Hg 199 and 202 (only e-components) and lamp profile p(k). (b) Experi- mental line-crossingcurve in forward-scatteringon a Hg 199 + 202 mixture with this lamb profile p(k). crossings (fig. la). With an incident line, shifted in such a.manner, that its maximum had the frequency of one of these line-crossings the cul-¢e in fig. lb was received. In this way each line.crossing could be isolated from the others. The theoretical calculation of the line-crossing curves is based on the formulas derived by Series [2]. As an example, a mixture of two different even mercurt isotopes (Hg 200 and 202) shall be regarded for densities, where the weak scattering approxima- tion is valid. Then the forward-scattered light, observed with crossed polarizers, is described by the integral over 283

Isotope shift and hyperfine structure in the 2537 Å line of Hg by line-crossing experiments in forward-scattering

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Volume 47A, number 4 PHYSICS LETTERS 8 April 1974

ISOTOPE S H I F T AND H Y P E R F I N E S T R U C T U R E IN T H E 2537 A LINE

O F Hg BY LINE-CROSSING E X P E R I M E N T S IN F O R W A R D - S C A T T E R I N G *

G. STANZEL 1. Phys. Institute, 63 Giessen, Germany

Received 13 February 1974

The line-crossing effect between Zeeman components of different isotopes was studied experimentally and theoreti- cally in forward-scattered light in order to determine the isotope shift and hyperfine structure. The influence of the spectral distribution of the incident radiation was properly considered.

Hanle's method [ 1] of magnetic depolarisation, also known as level-crossing technique, can be applied to forward-scattering [2] and selective reflection [3] of resonance radiation. As in these cases light scattered from different atoms is coherent, there are additional possibilities for interference. Besides the Doppler broadening of the level-crossing curves a line-crossing effect [2] of Zeeman Components of different isotopes results, determined by the isotope shift. Because of the Doppler broadening the usual condition of broad-band excitation is hardly to fulfil and the spectral distribu- tion of the incident light has to be considered carefully. Experiments in selective reflection and some other connected investigations, will be represented elsewhere [4].

Corresponding to the principal arrangement [2] for the experiments in forward-scattering, the scat. tering cell was situated between crossed polarizers in a static, longitudinal magnetic field H. The lamp, fiUed with an even mercury isotope, was situated in another magnetic field H L for shifting the frequency; the Zeeman components were seperated by a quarter wave plate and the polarizer. Especially prepared mix- tures of two different isotopes as well as natural mercury were used in the scattering cell at a total density of 5 X 1012 cm -3. In.order to receive sharp line,crossing signals, the corresponding Zeeman- components should have nearly the same intensities, determined by the transition probablities and the relative abundances.

As an example a mixture of the isotopes Hg 199 and 202 shall be regarded, where there are three line-

* From a thesis (D 26, Giessen) and supported in part by the Deutsche Forschungsgemeinschaft.

2 0 2 ~ _ I 1 9 9 ~ t

1 2 3 /, ROe

Fig. 1. (a) Zeeman structure of the 2537-A-line of Hg 199 and 202 (only e-components) and lamp profile p(k). (b) Experi- mental line-crossing curve in forward-scattering on a Hg 199 + 202 mixture with this lamb profile p(k).

crossings (fig. la). With an incident line, shifted in such a.manner, that its maximum had the frequency of one of these line-crossings the cul-¢e in fig. lb was received. In this way each line.crossing could be isolated from the others.

The theoretical calculation of the line-crossing curves is based on the formulas derived by Series [2]. As an example, a mixture of two different even mercurt isotopes (Hg 200 and 202) shall be regarded for densities, where the weak scattering approxima- tion is valid.

Then the forward-scattered light, observed with crossed polarizers, is described by the integral over

283

Volume 47A, number 4 PHYSICS LETTERS 8 April 1974

Table 1 Isotope shift and hyperf'me structure in mK of the 2537 A line of some Hg isotopes related to flg 198.

Isotope Schweitzer [5] this work

200 -160.29 t 0.15 -160.1 ± 0.3 100F= 1/2 -513.99 ± 0.43 -513.8 ± 1.1 199 F-- 3/2 224.40 ± 0.23 224.5 ± 0.6 2-2 -336.96 ± 0.15 -336.9 ± 0.4

/"'\

1 2 3 /-, S 6 7

the angular optical frequency k:

+oo

I±(H) o: f p(k)lFl(H, k)+F2(H ' k)l 2 dk _ o o

where p(k) is the spectral distribution of the incident radiation; F12, related to atoms of the isotope 1 or 2 respectively, is written in terms of the plasma dispersion function [2].

Supposing a Gaussian lamp prof'de with a half- width of 2A D, and an isotope shift of 7& (Doppler width A D = 2 lx/Tn~A), computer solu- tions o f the integral led to line-crossing curves, shown in fig. 2, which principally agreed with experimental curves. Only when the incident line has its maximum at the frequency of the line-crossing the corresponding curve 1 allows a precise determination o f the isotope shift, otherwise the signal (curve 2) becomes broader and shifted.

In table 1 the isotope shift and hyperfine structure of some mercury isotopes is given, determined by this line-crossing experiments in forward-scattering, compared with those values of Sehweitzer [5], determined by an interferometric method. Comparing tl~a accuracy, in this work mainly influenced by Doppler broadening, it can be concluded that line-

Fig. 2. Theoretical line-crossing curves in forward-scattering on a mixture of two even mercury isotopes: (1) with a shifted line of the lamp centred between the two isotopes, (2) with an unshifted line of one of the isotopes.

crossing experiments in forward-scattering on an atomic beam should give more precise results than the other method, where an atomic beam for reduction of the Doppler width was already used. That means, line-crossing experiments do have a chance for a precise studying of isotope shift and hyperfine struc- ture, although objections recently have been made [6].

The author is grateful to Professor W. Hanle for many helpful discussions. At this opportunity the 50th anniversary of Hanle's publication [1 ] is reminded.

References

[1] W. Hanle, Z. Physik 30 (1924) 03. [2] R.Q. Hackett and G.W. Series, Opt. Comm. 2 (1970) 93;

A. Corney, B.P. Kibble and G.W. Series, Proc. R. Soc. A293 (1966) 70.

[3] G. Stanzel, Phys. Lett. A41 (1972) 335. [4] G. Stanzel, to be submitted to Z. Physik (1974). [5] W.G. Sehweitzer Jr., J. Opt. Soc. Am.53 (1963) 1055. [6] D.A. Church: and T. Hadeishi, Phys. Rev. A8 (1973) 1864.

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