Atomic Bethe-Goldstone Calculation of the Hyperfine Structure ofLi(2 P2)

A variational formulation of Brueckner's theory has been applied to the calculation of hyperfine parameters for the $2{}_{}{}^2{}_{}{}^{}P$ excited state of atomic lithium. The hierarchy of $n$th-order (or $n$-particle) Bethe-Goldstone equations defined previously has been modified so that complete electronic configurations occur at each level of the hierarchy. Thus ${\overrightarrow{\mathrm{L}}}^2$, ${\overrightarrow{\mathrm{S}}}^2$ eigenfunctions could be used throughout the calculations, although for practical reasons such functions are not explicitly constructed. Each net increment of any mean-value electronic property defined within the hierarchy is shown to be equivalent to a sum, to infinite order, of a certain well-defined set of linked diagrams in the many-particle perturbation theory. Computed results are in excellent agreement (within roughly 1%) with experimental data and with a previously published accurate perturbation calculation.