Nuclidic mass relationships and mass equations

Generalized nuclidic mass relationships represent a link between mass equations and mass relationships. They are partial difference equations which can be used recursively. The quality of mass predictions, particularly for very neutron-rich or proton-rich nuclei, depends essentially on our knowledge of the effective neutron-proton interaction $I_{\mathrm{np}}$. The transverse and longitudinal mass relationships of Garvey and Kelson which are special cases contain small systematic errors due to the assumed independence of $I_{\mathrm{np}}$ on the neutron excess or the nucleon number. Information about the dependence of $I_{\mathrm{np}}$ on $T$ and $A$ has been extracted from the experimental masses by a variety of ${\chi }^2$ tests and was found in partial disagreement with macroscopic and microscopic theories. Several procedure have been devised to test theoretical expressions for $I_{\mathrm{np}}$ for their compatibility and consistency with the experimental masses.