Variational description of the 3-body Coulomb problem through a correlated Eckart-Gaussian wavefunction

Abstract

The quantum mechanical problem posed by the internal motion of three particles subject to Coulomb interactions is variationally solved by means of an Eckart-Gaussian (EG) ansatz that exhibits an exponential behavior with respect to the radial coordinates {r1,r2}, and a harmonic Gaussian-type dependence on the interparticle distance r12, thereby providing explicit correlation. The proposed wavefunction is of the form (e-α1r1-β1r2 + e-β2r1-α2r2) rl12 e-γ(r12-u0)2, through which ground state energies are calculated for a few two-electron atoms-considering finite nuclear mass effects-and molecular ions corresponding to electronic and mesonic systems. The physical interpretation and advantages of the EG wavefunction are discussed in terms of the relative masses of the particles in the analyzed systems. A useful application of the variational method is presented where the underlying structure of the 3-body wavefunction combines an atomic-and a molecular-like description of the system. The obtained energies agree with the exact results within 10-4-10-2 Hartrees.