Inverse methods are applied to the nuclear bound-state problem. Considering only the self-interactions of these states analytical solutions results for potentials and densities. The simplest possible approximation to the full expression yields immediately [FORMULA OMITTED] = 〈r2(Ai)〉 − 〈r2 (A0)〉 ~ − [B (Ai) − B (A0)] for the differences in the squared nuclear radii as functions of the respective binding energies per nucleon, B (Aj).