Simulation of symmetric nuclei and the role of Pauli potential in binding energies and radii

It is shown that the use of a density dependent effective Pauli potential together with a nucleon-nucleon interaction potential plays a crucial role to reproduce not only the binding energies but also the matter root mean square radii of medium mass range spin-isospin saturated nuclei. This study is performed with a semiclassical Monte Carlo many-body simulation within the context of a simplified nucleon-nucleon interaction to focus on the effect of the genuine correlations due to the fermionic nature of nucleons. The procedure obtained is rather robust and it does not depend on the detailed features of the nucleon-nucleon interaction. For nuclei below saturation the density dependence may be represented in terms either of the nucleon number, $A$, or the associated Fermi momenta. When testing the simulation procedure for idealized "infinite" symmetric nuclear matter within the corresponding range of densities, it turns out that finite size effects affect the Pauli potential strength parametrization in systems up to about 120 particles while remaining approximately stable for larger systems.