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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 andneutron cores with the model recently proposed by Ruffini et al. (2007) and wecompare it with other $N_p$ versus $A$ relations: the empirical one, related tothe Periodic Table, and the semi-empirical relation, obtained by minimizing theWeizs\"{a}cker mass formula. We find that there is a very good agreementbetween all the relations for values of $A$ typical of nuclei, with differencesof the order of per cent. Our relation and the semi-empirical one are inagreement up to $A\sim 10^4$; for higher values, we find that the two relationsdiffer. We interprete the different behaviour of our theoretical relation as aresult of the penetration of electrons (initially confined in an externalshell) 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.

On the Mass to Charge Ratio of Neutron Cores and Heavy Nuclei