The congruence energy: A contribution to nuclear masses and deformation energies

The difference between measured binding energies and those calculated using a shell- and pairing-corrected Thomas-Fermi model can be described approximately by C(I) = -10exp(-4.2|I|) MeV. The authors' interpretation of this extra binding is in terms of the granularity of quantal nucleonic density distributions, which leads to a stronger interaction for a neutron and proton with congruent nodal structures of their wave functions. The predicted doubling of this congruence energy in fission is supported by an analysis of measured fission barriers and by a study of wave functions in a dividing Hill-Wheeler box potential. A semi-empirical formula for the shape-dependent congruence energy is described