Hartree-Fock Calculation for Finite Nuclei with a Nonlocal Two-Body Potential

Abstract

An application of the Hartree-Fock (HF) method to calculation of the structure of finite nuclei is presented. The nonlocal, separable potential of Tabakin is used as the two-body interaction. The calculation is carried out by writing the HF equations in an oscillator basis and applying the Moshinsky transformation to relative coordinates. The closed-shell nuclei ${\mathrm{O}}^{16}$ and ${\mathrm{Ca}}^{40}$ are considered. Under the assumption that they are spherical, their binding energy per particle is found to be -2.41 and -3.74 MeV for ${\mathrm{O}}^{16}$ and ${\mathrm{Ca}}^{40}$, respectively. Possible reasons for the large discrepancy with the experimental binding are discussed. The single-particle energies show better agreement with data, but have too much spin-orbit splitting, namely, 10.2 MeV for $1p$ states in ${\mathrm{O}}^{16}$, and 11.13 and 14.59 MeV, respectively, for the $1p$ and $1d$ states in ${\mathrm{Ca}}^{40}$. The rms radii for ${\mathrm{O}}^{16}$ and ${\mathrm{Ca}}^{40}$ were found to be 2.38 and 2.96 F, compared with experimental values of 2.64 F and 3.52 F, respectively. Corrections for Coulomb force and center-of-mass motion have also been calculated.