Imposing Fermi momentum cut-off on the channel- and density-dependent effective interaction and the ground-state properties of closed shell nuclei

Abstract.

The ground-state properties of light-moderate symmetric closed shell nuclei, i.e. ⁴He, ¹²C, ¹⁶O, ²⁸Si, and ⁴⁰Ca, and moderate-heavy asymmetric ones, i.e. ⁴⁸Ca, ⁹⁰Zr, and ¹²⁰Sn, are calculated using the channel- and density-dependent effective interaction with the imposed Fermi momentum cut-off (CDDEI+FMC). CDDEI+FMC are generated through the lowest-order constrained variational (LOCV) nuclear matter calculations with the $Av_{18}(j_{max}=2)$ nucleon-nucleon bare potential. FMC is considered by defining the maximum value of the relative quantum numbers according to the last shell in the ground state of a nucleus. The Hamiltonian matrix of the truncated effective interactions is diagonalized in the harmonic oscillator basis, regarding the nucleon configurations. The FMC effect on the different interaction channels is considered by comparing the contributions of each channel in the binding energies of the sample nuclei. CDDEI+FMC are replaced by the density-dependent average effective interactions with the imposed FMC (DDAEI+FMC) for the channels with $j > j_{max}$. For the light nuclei, the results show that the nuclei are more binding relative to the CDDEI-FMC case. The ⁴He nucleus is about 1.4MeV more binding per nucleon, and the root mean square of its radius equals the experimental data exactly. For the moderate-heavy closed shell nuclei, there are no significant differences between the results of the two cases, both with FMC and without it.