Effect of nondiagonal lowest order constrained variational effective two-body matrix elements on the binding energy of closed shell nuclei

Abstract

The binding energies of the light, the moderate and the heavy closed shell nuclei, that is, ${}^{4}\mathrm{He}$, ${}^{12}\mathrm{C}$, ${}^{16}\mathrm{O}$, ${}^{28}\mathrm{Si}$, ${}^{32}\mathrm{S}$, ${}^{40}\mathrm{Ca}$, ${}^{56}\mathrm{Ni}$, ${}^{48}\mathrm{Ca}$, ${}^{90}\mathrm{Zr}$, ${}^{120}\mathrm{Sn}$, and ${}^{208}\mathrm{Pb}$ are calculated, using all of the channels-dependent effective two-body interactions (CDEI) matrix elements, which are generated through our lowest order constrained variational (LOCV) nuclear matter calculations with the $A{v}_{18}$ $({J}_{\mathrm{max}}=2$ and $5)$ phenomenological nucleon-nucleon potential. The $\mathcal{J}$-coupling scheme is applied to construct the interaction Hamiltonian matrix elements in the spherical harmonics oscillator shell model basis. In the channels with $Jg{J}_{\mathrm{max}}$, the CDEI are replaced by the average effective two-body interactions. It is shown that the nondiagonal matrix elements with the $A{v}_{18,{J}_{\mathrm{max}}=2}$ interaction increase the binding energies of nuclei; that is, the maximum magnitude of them is about 1.49 MeV for the ${}^{56}\mathrm{Ni}$ nucleus. However, for the similar calculations with the $A{v}_{18,{J}_{\mathrm{max}}=5}$ potential, they increase the binding energies of the symmetric nuclei more than the asymmetric ones; that is, the maximum magnitude of them is about 2.74 MeV for the ${}^{56}\mathrm{Ni}$ nucleus. Owing to the huge computational time that is obviously needed for the calculation of the matrix elements of the heavy closed shell nuclei, their binding energies are evaluated only at their saturation points, which are available from our previous works.