A generalized any‐particle propagator theory: Calculations of nucleon's binding energies

Abstract Generalized one‐particle propagator calculations were performed for fermions in atoms: neutrons, protons, and electrons. For this purpose, multicomponent Hartree‐Fock equations were implemented using Gaussian basis sets where, for nucleons, we consider a non‐Coulombic interaction, through a two‐term Yukawa scalar potential and the interaction between electrons and the electrons with positive charge (protons) through a Coulombic potential. The strategy for evaluating the required interaction integrals follows Obara‐Saika and Head‐Gordon recurrence relations combined with the generalized Boys function suggested by Ten‐no. Calculations on the isotopes 2 H, 3 H, 3 He, 4 He, 6 Li, 6 Be, 7 Li, and 8 Be were realized to test the accuracy of Koopmans' approximation and a second‐order generalized one‐particle propagator. Yukawa potentials were parametrized to reproduce nuclear properties as kinetic energies and radial distributions of density. These potentials produced the reference nuclear Hartree‐Fock calculations on which fully ab initio propagator calculations were performed for these non‐Coulombic potentials. This allowed us to explore the electronic structure of isotopes in an extended nucleus context.