Uncoupled Correlated Method for Helium Bound States

Abstract

An uncoupled correlated variational method for calculating helium bound states is proposed. The projective coordinates s = r1+r2, v = r12 r1+r2 , w = r1−r2 r12 are introduced instead of the conventional ones s = r1 + r2, t = r1 − r2, u = r12. All matrix elements of the total Hamiltonian and the weight function are expressed by simple products of three one-dimensional integrals. The variational basis is formed by a set of Laguerre polynomials with a single nonlinear parameter and two sets of Jacobi polynomials for the projective coordinates s, v, w, correspondingly. It provides a reasonable degree of convergence of the energy, E = E(N), with respect to the number N of expansion terms over the basis of the eigenvectors. In the case of infinite and finite nuclear mass, calculations give the energy of the helium ground state.