Ground state of heavy closed shell nuclei: An effective interaction and local density approximation approach

We study the ground-state properties of heavy closed-shell nuclei such as ⁴⁸Ca, ⁹⁰Zr, ¹²⁰Sn, and ²⁰⁸Pb as well as ⁴He, ¹⁶O, and ⁴⁰Ca. Similar to our recent work, the local density approximation in the harmonic oscillator basis and different channel-dependent effective two-body interactions that are generated through the lowest-order constrained variational calculation for asymmetric nuclear matter with the Reid68Day, Reid68, and Δ-Reid68 potentials are used. Unlike nuclear matter, it is shown that Reid68 potential gives ground-state binding energies closer to the experimental data with respect to the Δ-Reid68 potential and there is not much difference between Reid68 and Reid68Day potentials, which have been define up to J=5. The different channel-dependent effective interactions (J>2) and one- and two-body density distribution functions are discussed and they are compared with the results of other approaches such as the Brueckner local density approximation, correlated basis function, variational fermion hypernetted chain, variational cluster Monte Carlo, Brueckner-Hartree-Fock, fermionic molecular dynamics, and coupled cluster. Finally it is concluded that the three-body force (isobar degrees of freedom) is very important for light (heavy) nuclei because in the most of recent many-body calculations, it is observed that the available two-body nuclear forces usually underbind light nuclei and overbind heavy nuclei and nuclear matter.