Hyperfine interaction in excited states of sodium: $S$ states

The direct and exchange-core-polarization (ECP) contributions to the hyperfine interaction in the excited states, $3s$ to $10s$, of the sodium atom are obtained from first-principles one-electron calculations. The exchange-core-polarization results indicate that this effect is a nearly constant fraction of the direct effect for all the excited states considered. Using the difference between experiment in the two states where data are available and the total theoretical one-electron contribution as a measure of the correlation effect, we find a significant decrease in the percentage importance of the correlation effect in going from the ground $3s$ to the excited $4s$ state. Physical explanations are offered for this behavior and the near constancy of the fractional ECP contribution.