Affiliations: Joint Institute for Nuclear Research, Dubna, 141980, Russia
Correspondence:
[1]
The address for manuscript correspondence: O. Chuluunbaatar, LIT, JINR, Dubna, Moscow region, 141980, Russia. E-mail: [email protected]. Tel.: (096-21) 64808. Fax.: (096-21) 65145.
Abstract: An uncoupled correlated variational method for calculating helium bound states is proposed. The projective coordinates s=r1+r2, v=r12r1+r2, w=r1−r2r12 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.
