Uncoupled correlated calculations of helium isoelectronic bound states

An uncoupled correlated variational method for the calculation of helium is oelectronic bound states is proposed. New projective coordinates s = r(1) r(2), nu = r(12)/r(1)+r(2), w + r(1)-r(2)/r(12) are introduced instead of the conventional ones s = r(1) + r(2), t = r(1) - r(2), u = r(12). All matr ix elements of the total Hamiltonian and the weight function are expressed as simple products of three one-dimensional integrals. The variational basi s is formed by a set of Laguerre polynomials with a single nonlinear parame ter and two sets of Jacobi polynomials for the projective coordinates s, nu , w, respectively. It provides a reasonable rate of convergence of the ener gy, E = E(N), with respect to a number N of the basis components of the eig envector. The proposed method yields the best available energies for the is oelectronic ground states of the helium atom. New estimations of the isotop e helium ground states are also presented.