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Physical Review A

Multiconfiguration Hartree-Fock calculations of low-lying excited 2 Sstates in lithium

Per Jönsson, Charlotte Froese Fischer, Jacek Bieroń

Published Nov 1, 1995• 12 citations
Publisher

Abstract

The hyperfine interaction constants, specific-mass-shift parameters, and total energies for the 3s${\mathrm{}}^{2}$S and 4s${\mathrm{}}^{2}$S states in lithium were calculated using the multiconfiguration Hartree-Fock method. The configuration expansions were obtained with the active space method, where configuration state functions are generated by excitations from the reference configuration to an active set of orbitals. The active set was increased in a systematic way, allowing the convergence of the studied parameters to be monitored. The obtained nonrelativistic energies are close to the lowest-upper-bound estimates from Hylleraas calculations. Whereas the convergence rate of the hyperfine interaction constants with respect to the increasing basis in the Hylleraas calculations degrades appreciably for higher states in the Rydberg series, no such effect could be seen for the multiconfiguration Hartree-Fock calculations. The uncertainties of the calculated hyperfine interaction constants are estimated to be less than three parts in a thousand for both of the studied states. The value for the 3s${\mathrm{}}^{2}$S state is in excellent agreement with results from relativistic many-body perturbation theory calculations, but is well outside the error bars from a recent precision measurement using Stark spectroscopy.

DOI
10.1103/physreva.52.4262

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The hyperfine interaction constants, specific-mass-shift parameters, and total energies for the 3s2{\mathrm{}}^{2}2S and 4s2{\mathrm{}}^{2}2S states in lithium were calculated using the multiconfiguration Hartree-Fock method. The configuration expansions were obtained with the active space method, where configuration state functions are generated by excitations from the reference configuration to an active set of orbitals. The active set was increased in a systematic way, allowing the convergence of the studied parameters to be monitored. The obtained nonrelativistic energies are close to the lowest-upper-bound estimates from Hylleraas calculations. Whereas the convergence rate of the hyperfine interaction constants with respect to the increasing basis in the Hylleraas calculations degrades appreciably for higher states in the Rydberg series, no such effect could be seen for the multiconfiguration Hartree-Fock calculations. The uncertainties of the calculated hyperfine interaction constants are estimated to be less than three parts in a thousand for both of the studied states. The value for the 3s2{\mathrm{}}^{2}2S state is in excellent agreement with results from relativistic many-body perturbation theory calculations, but is well outside the error bars from a recent precision measurement using Stark spectroscopy.
We have performed very accurate quantum-mechanical calculations for the two lowest SSS states of the lithium atom in order to determine the transition energy. In the nonrelativistic part of the calculations performed using the variational method, we explicitly included the nuclear motion. The nonrelativistic wave function was expanded in terms of explicitly correlated Gaussian functions. Next, this wave function was used to calculate the leading ${\ensuremath{\alpha}}^{2}$ relativistic correction ($\ensuremath{\alpha}$ is the fine-structure constant) and the ${\ensuremath{\alpha}}^{3}$ QED correction. We also estimated the ${\ensuremath{\alpha}}^{4}$ QED correction by calculating its dominating component. The results obtained with Gaussians are compared with the most accurate results obtained recently with the Hylleraas-type basis functions.
A fully numerical multiconfiguration Hartree-Fock program has been modified for performance of calculations on atomic quasibound states using the complex-coordinate (dilation) technique. We present single-configuration calculations for the lowest 2^{2}2P\ifmmode^\circ\else\textdegree\fi{} states of ${\mathrm{Be}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Mg}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Ca}}^{\mathrm{\ensuremath{-}}}$, ${\mathrm{Sr}}^{\mathrm{\ensuremath{-}}}$, and ${\mathrm{Ba}}^{\mathrm{\ensuremath{-}}}$, along with results of some small-scale multiconfiguration investigations of the Mg resonance. An instability originating in difficulty satisfying orthogonality constraints prevents a full multiconfiguration treatment of this resonance. Single-configuration dilated Hartree-Fock calculations predict 2^{2}2P\ifmmode^\circ\else\textdegree\fi{} shape resonances for all these systems, though recent extensive calculations show the Ca, Sr, and Ba ions to be bound. Nonetheless, we think it is significant that the dilated numerical method can easily carry out fully variational computations on these heavy atoms, and our results, in conjunction with those of other studies, shed light on the importance of electron correlation in its effect upon the resonance parameters and its variation with progressively heavier alkaline-earth atoms. We also establish the feasibility of accounting for important correlation effects through the use of multiconfiguration approximations, though we have not attempted an accurate calculation in this work. Our Be, Mg, and Ca results agree well with previously published single-configuration dilated basis-set calculations, but no such calculations have been carried out for Sr or Ba. Finally, we investigate the dilational stability of the numerical method since this has been an important consideration in basis-set calculations. A simple exercise based on Cauchy's theorem shows that analyticity of the Hartree-Fock radial wave functions implies that the energy and other physical quantities are independent of the dilation parameter, and a high degree of such independence is demonstrated in our numerical results.
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