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

TL;DR

This paper theoretically analyzes the charge-to-mass ratio of neutron cores and heavy nuclei, comparing different models and empirical relations, and discusses how electron penetration affects these ratios at large mass numbers.

Contribution

It introduces a theoretical relation between proton number and mass number for neutron cores, comparing it with empirical and semi-empirical models, highlighting differences at high A.

Findings

Good agreement with empirical relations for typical nuclei

Discrepancies arise for A > 10^4 due to electron penetration effects

Theoretical model extends understanding of charge distribution in large nuclei

Abstract

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.