Perturbative Studies of theS2Lithium Atom: Total Energy and Hyperfine Interaction

Abstract

Double perturbation theory has been applied to the calculation of the total and hyperfine interaction energies of ground-state lithium. The effective one-electron potential used contains only the Coulomb terms which arise from the $1s$- and $2s$-electrons, multiplied by a factor of $\frac{2}{3}$ for correct asymptotic screening. The first-order perturbed wave functions in correlation and the hyperfine interaction are obtained by a numerical finite-difference solution of their respective two- and one-particle inhomogeneous differential equations. Convergence of both expansions is rapid, giving a total energy of -7.4793 ± 0.0038 a.u. and a spin density at the nucleus of $(2.850\mathrm{}\pm 0.076)a_0^{-3\mathrm{}}$, in good agreement with their accurate counterparts: -7.47807 a.u. and $2.9096a_0^{-3\mathrm{}}$.