Abstract: | A procedure is described for the efficient evaluation of the energy matrix elements necessary for atomic configuration-interaction calculations. With the orbital configurations of an N electron system in spin state S written as the irreducible representations 21/2N?S, 12S] of the permutation group S( N ), it is possible to evaluate readily the energy matrix elements of a spin-free Hamiltonian expressed in terms of the generators of the unitary group. We show how the use of angular momentum ladder operators permits the effective generation of a basis of eigenstates of ??2, ??z as well as ??2 and ??z, for which the energy matrix elements may be evaluated with ease. |