Relativistic treatment of one- and many-electron contributions to hyperfine interactions in excitedSstates of rubidium atoms

Abstract

The hyperfine structure of the rubidium atom in the excited $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, and $8{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ states has been studied using the relativistic many-body perturbation procedure. The contributions from the different mechanisms, namely, the direct, the exchange core polarization (ECP), and the correlation effect are evaluated relativistically for each excited state. The contributions from these effects add up to net totals of 820 ± 16, 320 ± 6, and 156 ± 3 MHz, respectively, for the $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, and $8{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ multiplet excited states, in excellent agreement with the experimental values of 809.1 (5.0), 318.1 (3.2), and 159.2 (1.5) MHz, respectively, similar to the situation for the ground $5{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$ state found in an earlier investigation. The contribution from the ECP effect as compared to direct remains constant at about 16% as we go from the ground to the higher excited states. The correlation contribution, however, decreases dramatically as a ratio of the direct, from 32% in the ground state to 18, 14, and only 9%, respectively, in the excited multiplet states $6{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, $7{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$, and $8{}_{}{}^2{}_{}{}^{}S_{\frac{1}{2}}^{}{}_{}{}^{}$. The physical reasons for the observed trends in the contribution from the ECP and correlation effects is discussed, as is the implications of our results for the expected trends for these contributions in related systems like the ground and excited states of other alkali-metal atoms and noble-metal atoms, and the Knight shifts in nuclear magnetic resonance experiments on alkali metals.