Nuclear Characteristics and Empirical Mass Sum Rules

The Garvey-Kelson mass sum rule is known to be violated when $Z=N=\mathrm{odd}$, $Z=N+1=\mathrm{even}$, or $Z=N+1=\mathrm{odd}$ nuclei are considered. This violation is a result of the lack of cancellation of certain two-body matrix elements. These matrix elements can be calculated assuming various models of the nuclei involved, e.g., deformation, level orderding, etc., and the amount by which the sum rule is violated empirically can then be used to distinguish the most appropriate model. The results of this empirical determination of nuclear characteristics agree quite well with the results of more involved calculations and conform to the generally accepted picture of nuclei in the $s-d$ shell.