Approximating Hamiltonian for Hartree-Fock solutions for nonrelativistic atoms

TL;DR

This paper introduces an algebraic Hamiltonian approximation for nonrelativistic atoms that simplifies calculations of atomic properties while maintaining accuracy comparable to traditional Hartree-Fock methods.

Contribution

It develops an algebraic Hamiltonian model whose eigenstates approximate Hartree-Fock solutions without solving complex integro-differential equations.

Findings

Accurately computes binding energies and ionization potentials.

Provides electron density distributions and scattering factors.

Achieves results comparable to standard Hartree-Fock calculations.

Abstract

In our work we construct a Hamiltonian, whose eigenstates approximate the solutions of the self-consistent Hartree-Fock equations for nonrelativistic atoms and ions. Its eigenvalues are given by completely algebraic expressions and the eigenfunctions are defined by Coulomb wave-functions orbitals. Within this approximation we compute the binding energy, ionization potentials, electron density distribution, electron density at the nucleus, and atomic scattering factors of nonrelativistic atoms and ions. The accuracy of our results is comparable with those obtained via the usage of the Hartree-Fock method but does not require solving integro-differential equations or numerically computing integrals with complex functions. This approach can serve as a good initial approximation for performing more accurate calculations and for the quantitative evaluation of physical parameters that depend on the electron density of atoms. The proposed approach is of interest for various fields of condensed matter physics, plasma physics and quantum chemistry.