Validity of the Concept of the Core Polarization Effect in Hyperfine Structure

Abstract

The core polarization effect in hyperfine structure is discussed by a semiempirical evaluation of 16 recently calculated values of the Fermi contact term for the ground state of lithium. The analysis proceeds by an investigation of the manner in which the various wave functions approximate eigenfunctions of ${\mathbf{S}}^2$, in conjunction with an examination of the one-electron orbitals employed. The concept of core polarization by non-$s$ electrons is shown to be valid, while if the polarizing electron is an $s$ electron, no definite conclusion concerning core polarization can be made. Finally, it is proposed that for all cases of a single polarizing electron, the following many-electron, approximate unrestricted Hartree-Fock wave function may be used: $\phi =A_p\left\{B_1\right[\Pi \stackrel{}{i}\left[U_{n\left(i\right)l\left(i\right)\mathrm{}}\alpha {{U_n}^{\prime }}_{\mathrm{}\left(i\right)l\left(i\right)\mathrm{}}\beta \right]]U_{N,L}\alpha +B_2[U_{N,L}\alpha \Pi \stackrel{}{i}\left[U_{n\left(i\right)l\left(i\right)\mathrm{}}\beta U_{n^{\prime }\mathrm{}\left(i\right)l\left(i\right)\mathrm{}}\alpha \right]\left]\right\},$ where $N$, $L$ are the quantum numbers of the polarizing electron and $B_1=-B_2$ if $L=0\mathrm{}$. Two tests of the validity of this wave-function approximation are proposed.