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

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 σ/sub m/ = 194 keV. Nuclear contributions were subjected to the constraint of charge symmetry, and Coulomb displacement energies are reproduced with σ/sub c/ = 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