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Physical Review A

Level shifts ofmsnsRydberg states induced by hyperfine interaction in odd alkaline-earth isotopes

R. Beigang, Andre Timmermann

Published Mar 1, 1982• 38 citations
Publisher

Abstract

High-resolution two-photon spectroscopy was applied to investigate the msns $^{1}S_{0}$ Rydberg states of the alkaline-earth elements Ca, Sr, and Ba. It is shown for $^{43}\mathrm{Ca}$, $^{87}\mathrm{Sr}$, $^{135}\mathrm{Ba}$, and $^{137}\mathrm{Ba}$ that the hyperfine interaction causes a level shift between odd- and even-mass isotopes. A theoretical interpretation is presented which relates the energy-level shift for odd isotopes to the singlet-triplet separation which in turn is a function of the principal quantum number, and good agreement with the experimental results is found.

DOI
10.1103/physreva.25.1496

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High-resolution two-photon spectroscopy was applied to investigate the msns 1S0^{1}S_{0}1S0​ Rydberg states of the alkaline-earth elements Ca, Sr, and Ba. It is shown for 43Ca^{43}\mathrm{Ca}43Ca, 87Sr^{87}\mathrm{Sr}87Sr, 135Ba^{135}\mathrm{Ba}135Ba, and 137Ba^{137}\mathrm{Ba}137Ba that the hyperfine interaction causes a level shift between odd- and even-mass isotopes. A theoretical interpretation is presented which relates the energy-level shift for odd isotopes to the singlet-triplet separation which in turn is a function of the principal quantum number, and good agreement with the experimental results is found.
In extremely high Rydberg states of odd alkaline-earth isotopes, the Fermi constant a ms is comparable to the energy separation between levels belonging to different principal quantum numbers n and hyperfine interactions dominate the structure of the levels. The multichannel quantum defect theory of fine structure has been developed and applied to hyperfine structure and thus the HFS can be analysed directly by MQDT. A two-channel quantum defect model for extremely high Rydberg msns 1 S 0 and msns 3 S 1 series in odd alkaline-earth isotopes for F=I is described. The U i(F)i matrix is given analytically and the relationship between the eigenquantum defects of HFS and the quantum defects of fine structure is derived. The HFS of two extremely high Rydberg 5sns 1 S 0 and 3 S 1 series in 87 Sr has been calculated by the model and an excellent agreement between the theoretical and experimental results has been achieved. The HFS of extremely high Rydberg msns 1 S 0 and 3 S 1 series in 43 Ca, 135 Ba and 137 Ba are also analysed by the model.
Doppler-free two-photon spectroscopy was applied to excite hyperfine-induced transitions from the $5{s}^{2}^{1}S_{0}$ ground state to the F=IF=IF=I component of the hyperfine multiplet of the 5sns3S15sns^{3}S_{1}5sns3S1​ Rydberg series of 87Sr^{87}\mathrm{Sr}87Sr (n=50,…,85n=50,\dots{},85n=50,…,85). The experimental data confirm the interpretation of hyperfine-induced singlet-triplet mixing which is related to the singlet-triplet energy separation.
The MQDT of hyperfine structure is greatly simplified in extremely high Rydberg states. A four (or three)-channel quantum defect model is derived for the hyperfine structure of extremely high Rydberg states of msnd configuration in odd alkaline-earth isotopes, in which the transformation matrix U i(F)i' is given analytically except for one parameter which measures the mixing of singlet 1 D 2 and triple 3 D 2 induced by spin-orbit interaction in even isotopes, and in which the four eigen quantum defects mu i' (i'=1, 2, 3, 4) are related to the quantum defects of the fine structure in even isotopes by mu i' =mod( delta i' ). This model has been used to interpret the observed sublevel structure of 5snd (n>100) configurations in 87 Sr. An excellent agreement between the theoretical and experimental results was achieved.
Calcium Rydberg levels are of significant interest for efficient and isotope-selective resonance ionization of trace radionuclides such as calcium-41 ( 41 Ca). In this study, we report novel, to our knowledge, measurement data on the energy level shifts of 43 Ca for 4sns 1 S 0 and 4s(n−1)d 1 D 2 (n=40, 45, 50, 55, 60) Rydberg levels due to hyperfine-induced singlet–triplet mixing specific to isotopes with an odd mass number. Both 3 S 1 and 3 D J triplet signals corresponding to forbidden transitions were enhanced for 43 Ca at the high principal quantum numbers n=55 and 60, indicating a mixing of singlet components to some extent.
High-resolution two-photon resonant three-photon spectroscopy was applied to investigate the 3 snf\mathrm{snf}snf Rydberg series of Mg. Hyperfine-induced level shifts were detected for the 1,3F^{1,3}F1,3F states of the odd isotope 25Mg^{25}\mathrm{Mg}25Mg. From these measurements the hyperfine coupling constant a3s{a}_{3s}a3s​ of the 25Mg+^{25}\mathrm{Mg}^{+}25Mg+-ion ground state was derived.