  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.
