Mass predictions, partial difference equations and higher‐order isospin effects

Abstract

The Garvey‐Kelson mass relation has been extended by introducing inhomogeneous source terms to improve problems with long‐range extrapolations. Such mass relations are third‐order partial difference equations with solutions representing mass equations. It was found that inhomogeneous source terms based on shell‐dependent Coulomb and symmetry energy terms are not sufficient to improve upon extrapolations. However, contributions from higher‐order perturbations in isospin (mostly cubic) have a significant effect. A many‐parameter mass equation was constructed as the solution of an inhomogeneous difference equation with properly adjusted shell‐dependent source terms. The standard deviation for reproducing the experimental mass values is σm=194 keV. Nuclear contributions were subjected to the constraint of charge symmetry, and Coulomb displacement energies are reproduced with σc=41 keV. Mass predictions for over 4000 nuclei with A≳16 and both N≥Z and N<Z (except N=Z=odd for A<40) are reported.