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Physical Review A

Calculations of high Rydberg states for the lithium atom

Chao Chen, Xiao-Ying Han, Jiaming Li

Published Apr 14, 2005• 8 citations
Publisher

Abstract

We present calculations of high Rydberg states for the lithium atom by two different theoretical methods. The first method is based on the $R$-matrix theory to obtain the energy levels and the quantum defects for the $1{s}^{2}nd\phantom{\rule{0.2em}{0ex}}^{2}D$ and $1{s}^{2}nf\phantom{\rule{0.2em}{0ex}}^{2}F$ states and their adjacent continuum states. Then the quantum defect functions of the two channels are obtained which vary smoothly with energy based on quantum defect theory. The second method is based on the full core plus correlation method. Our results are compared with data in the literatures; especially the results of the $R$-matrix method are in excellent agreement with microwave measurements for the lithium atom.

DOI
10.1103/physreva.71.042503

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We present calculations of high Rydberg states for the lithium atom by two different theoretical methods. The first method is based on the RRR-matrix theory to obtain the energy levels and the quantum defects for the 1s2nd2D1{s}^{2}nd\phantom{\rule{0.2em}{0ex}}^{2}D1s2nd2D and 1s2nf2F1{s}^{2}nf\phantom{\rule{0.2em}{0ex}}^{2}F1s2nf2F states and their adjacent continuum states. Then the quantum defect functions of the two channels are obtained which vary smoothly with energy based on quantum defect theory. The second method is based on the full core plus correlation method. Our results are compared with data in the literatures; especially the results of the RRR-matrix method are in excellent agreement with microwave measurements for the lithium atom.
Asymptotically exact calculations (with n → ∞) for the positions of the Rydberg states 4f14 6s1/2nlj of Yb have been carried out. The calculations have been performed by using the relativistic-perturbation theory with a model zeroth-order approximation. The proposed approach is more universal than the usually applied quantum-defect method, and, in contrast to the latter, it does not require the availability of experimental data about the low-lying states of the considered Rydberg series. It is shown that singlet–triplet splitting increases with increasing nuclear charge, and, for sufficiently heavy atoms, this splitting may exceed the distance between adjacent Rydberg states of the same series. The results have made it possible to change the accepted interpretation of the experimental spectrum. The difference between the theoretical and experimental quantum-defect spectrum monotonically decreases as n increases and is about 0.2 for n = 45.
Using a laser-excitation, optical-detection scheme, we have observed microwave transitions from the nd\mathrm{nd}nd to the nf\mathrm{nf}nf and ng\mathrm{ng}ng orbital levels in lithium states with principal quantum number nnn from 7 to 11. These measurements yield precise values for the ddd, fff, and ggg state fine-structure intervals as well as $d\ensuremath{-}f$ and $d\ensuremath{-}g$ energy separations. Within the accuracy of these measurements, the fine structures are found to be hydrogenic. The dipole polarizability of the Li+{\mathrm{Li}}^{+}Li+ core is determined from the $d\ensuremath{-}f$ and $d\ensuremath{-}g$ energy splittings. The $d\ensuremath{-}f$ intervals are compared to pseudopotential calculations.
There has been increasing interest in the energy spectrum of highly excited Rydberg states. The energy spectra of the sss, ppp, and ddd highly excited Rydberg states of a rubidium atom have been measured by different groups. However, there is a discrepancy between the reported data concerning the energy levels of highly excited sss and ddd states of Rb. We address this issue by performing accurate calculations of Rb(ns,np,ndns,np,ndns,np,nd) energy levels using the parametric one-electron valence potential [Marinescu, Sadeghpour, and Dalgarno, Phys. Rev. A 49, 982 (1994)] with spin-orbit coupling. We compare results with reference data from the National Institute of Standards and Technology and from available experiments. This enables us to recommend energy levels of highly excited Rydberg states of Rb that can be used as reference values.
The techniques of many-body Green's function theory have been applied to the calculation of properties of the lithium atom. Using basis set expansion techniques and a second-order expansion of the self-energy, Dyson's equation was solved, and the first-order reduced density matrix and the first ionization potential for the lithium ground state were computed. The natural spin orbitals of s symmetry were in excellent argeement with those computed from wavefunctions. The ionization potential was within 0.01 eV of the exact experimental result.
We report a measurement of the fine structure interval of the 7Li^{7}\mathrm{Li}7Li 10p10p10p atomic state with a precision significantly better than previous measurements of fine structure intervals of Rydberg 7Li^{7}\mathrm{Li}7Li ppp states. Our result of 74.97(74)74.97(74)74.97(74) MHz provides an experimental value for the only n=10n=10n=10 fine structure interval which is yet to be calculated. We also report a measurement of the absolute energy of the 10p10p10p state and its quantum defect, which are, respectively, $42379.498(23){\mathrm{cm}}^{\ensuremath{-}1}$ and 0.04694(10)0.04694(10)0.04694(10). These results are in good agreement with recent calculations.