One- and Two-Center Expansions of the Breit-Pauli Hamiltonian

Abstract

The orbit‐orbit, spin‐spin, and spin‐orbit Hamiltonians of the Breit‐Pauli approximation are expressed in terms of irreducible tensors. One‐ and two‐center expansions are given in a form in which the coordinate variables of the interacting particles are separated. In the one‐center expansions of the orbit‐orbit and spin‐orbit Hamiltonians the use of the gradient formula reduces some of the infinite sums to finite ones. Two‐center expansions are discussed in detail for the case of nonoverlapping charge distributions. The angular parts of the matrix elements of these Hamiltonians are evaluated for product wavefunctions