Method for Calculating Matrix Elements between Configurations with Several OpenlShells

Abstract

A simple procedure applicable to a digital computer is given for calculating matrix elements of $F$- and $G$-type operators between configurations that involve several partially filled $l$ or $j$ shells. The new procedure uses "partially coupled" basis functions, instead of traditional "uncoupled" (determinantal) or "coupled" basis functions, and may provide a simpler method for calculating configuration mixing in highly excited states of very complex atoms or for calculating nuclear shell-model energies.