Maple procedures for the coupling of angular momenta. VIII. Spin-angular coefficients for single-shell configurations Original Research Article

Matrix elements of physical operators are required when the accurate theoretical determination of atomic energy levels, orbitals and radiative transition data need to be obtained for open-shell atoms and ions. The spin-angular part for these matrix elements is typically based on standard quantities such as matrix elements of the unit tensor, the (reduced) coefficients of fractional parentage as well as a number of other reduced matrix elements concerning various products of electron creation and annihilation operators. Therefore, in order to facilitate the access to the matrix elements of one- and two-particle scalar operators, we present here an extension to the Racah program for the full set of standard quantities and the pure spin-angular coefficients in LS- and jj-couplings. A flexible notation is introduced for defining and manipulating the electron creation and the electron annihilation operators. This will allow us to solve successfully various angular momentum problems in atomic physics.