Effective potential and local density approximation approach to the binding energy of closed shell nuclei

Abstract

The ground state binding energies of closed shell nuclei such as {sup 4}He,{sup 12}C,{sup 16}O,{sup 28}Si,{sup 32}S,{sup 40}Ca, and {sup 56}Ni are calculated by using the local density approximation in the harmonic oscillator basis. Different channel effective two-body interactions are generated from the lowest order constrained variational calculation for nuclear matter with the Reid68 and {delta}-Reid68 potentials. It is shown that the unlike nuclear matter, Reid68 potential gives ground state binding energies closer to the experimental data with respect to the {delta}-Reid68 interaction. The different channel effective interactions as well as one- and two-body density distribution functions are discussed and compared with the results of other approaches such as the correlated basis function, variational fermion hypernetted chain, variational cluster Monte Carlo, Brueckner-Hartree-Fock, fermionic molecular dynamics, and coupled cluster.