Masses from Inhomogeneous Partial Difference Equations; A Shell-Model Approach for Light and Medium-Heavy Nuclei

Any mass equation M(N,Z) may be expressed as a special solution of an inhomogeneous partial difference equation. One only has to introduce an appropriate difference operator D and calculate κ(N,Z) = D M(N,Z). The inhomogeneous partial difference equation $${\text{D M}}\left( {{\text{N}},{\text{Z}}} \right){\text{ }} = {\text{ }}\kappa \left( {{\text{N}},{\text{Z}}} \right)$$ (1) contains the original mass equation as a special solution. The most general solution of eq. (1) will include solutions of the homogeneous equation which can, for example, be used to generate shell correction terms.