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

We determine theoretically the relation between the total number of protons Np 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 Np versus A relations: the empirical one, related to the Periodic Table, and the semi-empirical relation, obtained by minimizing the Weizsäcker 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 ∼ 10; 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.