Maple procedures for the coupling of angular momenta. III. Standard quantities for evaluating many-particle matrix elements

Abstract

An extension to the Racah program is presented for calculating standard quantities in the decomposition of many-electron matrix elements in atomic structure theory. These quantities include the coefficients of fractional parentage, the reduced coefficients of fractional parentage as well as reduced and completely reduced matrix elements for several operators within the two most frequently applied coupling schemes, namely LS- and jj-coupling, respectively. Values for these quantities are available for all (partially-filled) shells (nl) with l⩽3 in LS-coupling and for all subshells with j⩽9/2 in jj-coupling. Different notations and classification schemes are supported to characterize the antisymmetrized states of partially-filled shells.