Nuclear mass relations and equations

Abstract

Relations among the masses of neighboring nuclei provide an accurate and convenient method for the estimation of unknown masses. A set of such relations is "derived" and their structure as partial difference equations is discussed. These considerations lead to a set of mass equations (solutions of the difference equations) that can be ordered such that each successive member gives a potentially more nearly accurate representation of nuclear ground-state energies as functions of $N$ and $Z$. The first two members of this ordered set are the mass equations considered originally by Garvey et al. The results obtained by fitting the third member of this set to the known masses are discussed in this paper. This third mass equation is shown to satisfy the principle of charge symmetry to a good approximation. As a consequence, it gives predictions for the masses of proton-rich nuclei.