Magnetic Hyperfine Structure and Core Polarization in the Excited States of Lithium

The magnetic hyperfine splitting constants, $a_J$, from theoretical calculations on the $3{}_{}{}^2{}_{}{}^{}S$, $2{}_{}{}^2{}_{}{}^{}P$, $3{}_{}{}^2{}_{}{}^{}P$, and $3{}_{}{}^2{}_{}{}^{}D$ excited states of the Li atom are reported. The wave functions were calculated using the author's GF method, which corresponds to optimizing the orbitals of a Slater determinant after spin projection. Thus the wave functions include core polarization, but no appreciable correlation. For the $2{}_{}{}^2{}_{}{}^{}P$ state we calculate $a_{\frac{1}{2}}=0.2206\mathrm{}$ a.u. (45.74 Mc/sec for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$) which is in good agreement with the experimental value, 0.2227 ± 0.0017 a.u. (46.17 ± 0.35 Mc/sec for ${}_{}{}^7{}_{}{}^{}\mathrm{Li}$), and the value from configuration interaction calculations, 0.2206. Thus for the Li atom core polarization accounts for most of the error in the Hartree-Fock values of $a_J$. These calculations yield $〈\frac{1}{r^3}〉$ and spin density, $Q\left(0\right)\mathrm{}$, in agreement with other accurate theoretical calculations, and in disagreement with the values found using level crossing experiments, indicating that the interpretation of the level crossing experiments in terms of $〈\frac{1}{r^3}〉$ and $Q\left(0\right)\mathrm{}$ may not be correct. It is found that for both the unrestricted Hartree-Fock and GF methods the use of a different Hamiltonian for each electron leads to virtual orbitals which are good approximations to the actual orbitals of excited states.