The effect of Fermi momentum cutoff on the binding energy of closed shell nuclei in the LOCV framework

Abstract

The ground state binding energies of the light symmetric closed-shell nuclei, i.e., 4He, 12C, 16O and 40Ca and the heavy asymmetric ones, i.e., 48Ca, 90Zr and 120Sn are calculated in the harmonic oscillator (HOS) basis, by imposing the relative Fermi momentum cutoff of two point-like interacting nucleons on the density dependent average effective interactions (DDAEI). The DDAEI are generated through the lowest order constrained variational (LOCV) method calculations for the asymmetric nuclear matter with the operator and the channel dependent type bare nucleon-nucleon potentials, such as the Argonne \(Av_{18}^{j_{\max } = 2}\) and the Reid soft core, Reid68, interactions. In the framework of harmonic oscillator shell model, the cutoff is imposed by defining the maximum value of the relative quantum numbers (RQNmax) in two ways: (1) The RQNmax of the last shell and (2) the RQNmax of each shell, in the ground state of the nucleus. It is shown that present results on the binding energies and the root means square radius are closer to the corresponding experimental data than, our previous works with the same DDAEI potentials, but without the cutoff constraint. However, for the light symmetric nuclei, the second scheme gives less binding energy and larger root mean square radius compare to the first one. While the situation is reversed for the heavier nuclei.