Hyperfine Structure of Sodium

Abstract

The Brueckner-Goldstone many-body perturbation theory has been applied in a calculation of hyperfine structure (hfs) of sodium in the ground ($^{2}S_{\frac{1}{2}}$) state. Our result for $A$ (as in $A\stackrel{\ensuremath{\rightarrow}}{\mathrm{I}}\ifmmode\cdot\else\textperiodcentered\fi{}\stackrel{\ensuremath{\rightarrow}}{\mathrm{J}}$) is 857.8001\ifmmode\pm\else\textpm\fi{}6 Mc/sec, in good agreement with the experimental result of 885.8131\ifmmode\pm\else\textpm\fi{}0.0001 Mc/sec. The major contributions beyond the restricted Hartree-Fock result of 622.6430 Mc/sec arise from diagrams describing the exchange core-polarization effect. This contributes 139.6665 Mc/sec, in agreement with the existing unrestricted Hartree-Fock (UHF) and moment-perturbation (MP) results. All diagrams involving two orders of correlation interactions and associated ladders were calculated and were found to contribute 95.49 Mc/sec. Higher-order diagrams involving three or more orders of correlation interaction were investigated and found to be of minor importance in affecting the hfs constant of soidum.