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

An extension to the RACAH program is presented for calculating standard qua ntities in the decomposition of many-electron matrix elements in atomic str ucture theory. These quantities include the coefficients of fractional pare ntage, 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, resp ectively. Values for these quantities are available for all (partially-fill ed) shells (nl) with l less than or equal to 3 in LS-coupling and for all s ubshells with j less than or equal to 9/2 in jj-coupling. Different notatio ns and classification schemes are supported to characterize the antisymmetr ized states of partially-filled shells. (C) 2001 Elsevier Science B.V. All rights reserved.