  We determine theoretically the relation between the total number of protons
$N_{p}$ and the mass number $A$ (the charge to mass ratio) of nuclei and
neutron cores with the model recently proposed by Ruffini et al. (2007) and we
compare it with other $N_p$ versus $A$ relations: the empirical one, related to
the Periodic Table, and the semi-empirical relation, obtained by minimizing the
Weizs\"{a}cker mass formula. We find that there is a very good agreement
between all the relations for values of $A$ typical of nuclei, with differences
of the order of per cent. Our relation and the semi-empirical one are in
agreement up to $A\sim 10^4$; for higher values, we find that the two relations
differ. We interprete the different behaviour of our theoretical relation as a
result of the penetration of electrons (initially confined in an external
shell) inside the core, that becomes more and more important by increasing $A$;
these effects are not taken into account in the semi-empirical mass-formula.
