Value of interparticle interaction potential as a variable in solving many-body Schr\"{o}dinger equation

Abstract

A many-body wave function is approximated by a product of two functions: the wave function $\phi$ depending on the particle coordinates and the function $\chi$ depending only on the value of interparticle interaction potential. For the given $\phi$ an ordinary linear differential equation for $\chi$ is derived by averaging the Hamiltonian over the constant interparticle interaction potential surface. Generalized Hartree-Fock equations containing correlation effects are obtained. To test the proposed technique the ground $1^{1}S_0$ and excited $2^{3}S_1$ states of two-electron ions from H$^-$ up to Ne$^{8+}$ are calculated. In all cases the calculated energies are more accurate than those obtained with the Hartree-Fock theory even taking as $\phi$ the symmetrized product of electron wave functions in the Coulomb field of nucleus complitly disregarded the electron-electron interaction. Variation of factors in the one-particle wave function exponents leads to the results close to those of configuration interaction approach.