singlet-triplet anticrossings 3He : precise determination ... He by means of Electric Field Induced...
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Forbidden singlet-triplet anticrossings in 3He : precise determination of n1D-n3D (n = 3-6) intervals
J. Derouard, M. Lombardi and R. Jost
Laboratoire de Spectrométrie Physique (*), Université Scientifique et Médicale de Grenoble, B.P. 53X, 38041 Grenoble Cedex, France
(Reçu le 21 décembre 1979, accepté le 11 avril 1980)
Résumé. 2014 Nous avons étudié sur 3He des signaux d’anticroisement de faible largeur; dus à la conjonction des interactions de structure fine et hyperfine, ils n’ont pas d’équivalent dans 4He. Des mesures de grande précision sont rendues possibles grâce à l’utilisation d’une bobine de Bitter de grande homogénéité pilotée par RMN. Les signaux expérimentaux sont en parfait accord avec les prédictions déduites d’une diagonalisation complète du hamiltonien de Breit à l’intérieur de chaque configuration (Is, nd) de 3He; les valeurs utilisées pour les constantes radiales sont déduites de résultats expérimentaux antérieurs portant sur les intervalles de structure fine et hyperfine de 4He et 3He obtenus par différents auteurs; on trouve que ces valeurs diffèrent de moins de 1 % de celles calculées à l’approximation hydrogénoïde. Nous avons déterminé : d’abord la constante de couplage spin-orbite singulet- triplet dans le cas des états 3D : a(3D) = 650 ± 1 MHz. Ensuite, les écarts singulet-triplet pour les états nD (n = 3 à 6) avec une précision allant jusqu’à 5 x 10-5 en valeur relative; nos valeurs sont plus petites, d’en- viron 1 % que les quantités correspondantes mesurées dans le cas de 4He ; ce déplacement isotopique, dont la grandeur est inattendue, est, pensons-nous, dû à une faible interaction de configuration induite par l’interaction hyperfine.
Abstract. 2014 We have studied narrow anticrossing signals in 3He which have no equivalent in 4He because they are due to the conjonction of fine and hyperfine interactions. High precision results are obtained by the use of a high homogeneity Bitter coil driven by NMR. The experimental signals obtained are in perfect agreement with the predictions deduced from an entire diagonalization of the 3He Breit hamiltonian restricted to the (Is, nd) configu- ration. The values used for the radial constants are deduced from an analysis of previous experimental results obtained by various authors on 4He and 3He. These values are found to differ from the hydrogenic ones by less than 1 %. We have determined : first the singlet-triplet spin-orbit coupling constant for the 31-3D states : a(3D) = 650 ± 1 MHz and secondly the singlet-triplet separation of nD states (n = 3 to 6) with a precision of up to 5 x 10-5 in relative value. An unexpectedly large ( ~ 10- 3), negative isotope shift is found compared to the equivalent 4He values, presumably due to a slight configuration interaction induced by a hyperfine interaction.
J. Physique 41 (1980) 819-830 AOÛT 1980,
Physics Abstracts 32.80B - 32.60
1. Introduction. - Anticrossing phenomena  have been extensively used in the past to measure intervals between states of different multiplicity (see Refs [2, 3] and references therein). As it is well known, this occurs when two levels (e.g. singlet and triplet), weakly coupled by a perturbation, (e.g. spin-orbit) are tuned near degeneracy by the magnetic field; the resonant mixing of the wave functions which results is observed as a variation of the intensity of the light emitted by each level. This variation has a Lorentzian shape as a function of the magnetic field, the width of which is fixed by the magnitude of the,
(*) Laboratoire associé au Centre National de la Recherche Scientifique.
coupling matrix element. That width is the main limit’ for the accuracy of the method. Hence it is very interesting to search for cases where
the effective coupling responsible for the anticrossing is very weak. That has been achieved in the D states of ’He by means of Electric Field Induced Singlet-Triplet Anticrossings . The coupling between 1 D and 3D states occurs via mixing with F states and has provided experimental values for the singlet-triplet intervals which are more accurate, typically a few 10- 4 instead of a few 10-3 than the ones derived from conventional singlet-triplet anticrossings. Another situation has been reported in the case of H2 .
In 3He, the existence of nuclear spin induces some narrow singlet-triplet anticrossings [cf. Figs. 5-7] as a
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphys:01980004108081900
result of mixed spin-orbit-hyperfine 2nd order coupl- ings. The object of this paper is to study them.
In contrast to ’He [5-15], very few spectroscopic measurements already exist on D levels of ’He. Apart from some determinations of the hyperfine structure of nID states , and one interval in the n 3D struc- ture , an accurate measurement of some intervals in the 3 3D states [16, 17] was achieved only very recently. However, when we started our experiments, our
aim was to improve the experimental values of the singlet-triplet intervals of D levels, the exchange energy in He. In fact the comparison with other accurate measurements already existing for 5D and 6D states in ’He showed a systematic difference. There exists a relatively large isotope shift (about 10-3). Apart from a very small mass effect ( 10-4) such an effect was unexpected. A tentative explana- tion is developed in the last sections.
2. Experiment. - 2.1 ANTICROSSING SET-UP. - The principle of the experiment is similar to that of reference ; the intensity and polarization of lines emitted by anticrossing states, singlet or triplet are recorded as a function of the magnetic field. As in reference , the observation of n 1- 3D
anticrossings for n 5 requires magnetic fields of several tesla which cannot be attained by classical electromagnets. Thus the experiments were carried out in a Bitter coil at the Service National des Champs Intenses (C.N.R.S. Grenoble).
3He is contained in a sealed Pyrex cell and is excited by a triod system . The measurements were made at two pressures, 10 mtorr and 100 mtorr. The electrons were produced by an indirectly heated cathode (S - 1 cm’) and accelerated parallel to the magnetic field at 30 to 40 eV energy by a grid placed at about 2 mm from the cathode ; the resulting current collected at the anode was 15 to 25 mA. The anode was at the same potential as the grid and 3He emission spectra were taken in the grid anode space which is about 1 cm long. Some space charge electric fields should however exist and induce slight Stark shifts ; however, as specified in section 5, several runs were performed in different conditions of pressure, current intensity and voltage, and the corresponding dis- persion of results was found small in face of the other sources of uncertainty.
Light emitted by the He atoms perpendicularly to the magnetic field, reflected by a small mirror placed at 450 was collected by a 2 m fused silica light pipe which was fed into a polychromator built in our laboratory  from a Jobin-Yvon HRS 2 monochro- mator. Singlet and triplet lines corresponding to the same (ls, nd) configuration could be then recorded simultaneously. The light was detected by thermoelec- trically cooled and magnetically shielded Hamamatsu R 268, R 269 and R 374 photomultipliers. The signal was digitized by a DANA 160 000 points voltmeter
and fed into a multichannel analyser also built in our laboratory. A laboratory-made multiplexer was used to store simultaneously the two signals, singlet and triplet, on adjacent channels of the multichannel analyser and restitute them during readout. An expe- rimental curve consisted of 200 points accumulated in 10 to 30 passes of 40 s each.
2.2 FIELD CONTROL AND SWEEP. - For large (and not too precise) magnetic sweeps, a (also laboratory- made) step generator was used to drive the field and trigger the multichannel analyser. The magnetic field was produced by a 5 MW Bitter
coil which provided a field of up to 13 tesla with a homogeneity of about ± 10-5 in a sphere of 8 mm diameter. Of equal importance in setting the possible accuracy of the experiments is the time stability of the field. Several kinds of instability éxist. First a jitter of the order of 10-5 in relative units. Second a drift of the current of 10-5 in 20 min. Third a drift of up to 10-4 in relative units which is due to the non-
independence of two Bitter coils which are operated simultaneously ; the coupling comes from the fact that the cold part of the cooling water circuits are common. When the second Bitter magnet goes from zero to full current, the temperature of the cooling water in our coil increases by 7 °C, which corresponds to a thermal dilatation of 10-’ and thence a 10-’ decrease of the field for constant current. To remedy that, in high precision measurements,
the field was locked onto a NMR magnetometer which corrected for the drift (but nor for the jitter) so that the final accuracy was of the order of 10-5 in relative units. The principle of the NMR system is the same as the
one used by R. S. Freund and T. A. Miller at the Bitter Magnet Facility of MIT . We have only changed the way of making thé probes and made some modi- fications in order to use it to lock the field on the NMR
signal at any NMR frequency, conveniently, without tuning or adjustment. The heart of the system is the magic tee 6 (Fig. 1) :
When the two proton probes 7 and 8 are carefully matched as explained below, the output of the tee is more than 40 dB b