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

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 ²H, ³H, ³He, ⁴He, ⁶Li, ⁶Be, ⁷Li, and ⁸Be 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.