Nuclear diffuseness as a degree of freedom

The response of the nuclear energy to changes in neutron and proton surface diffusenesses is investigated using the Thomas-Fermi model. Algebraic expressions are provided for the energy cost of changing the two diffusenesses away from their equilibrium values. This will make it possible to generalize the macroscopic-microscopic calculations of nuclear masses and deformation energies by the inclusion of the neutron and proton diffusenesses as degrees of freedom (to be varied along with the shape degrees of freedom). One result, which is suggested by the relatively low cost in macroscopic energy of increasing the diffuseness of a heavy nucleus by 10% (about 4 MeV), is that superheavy nuclei near $Z=126,\hspace{0.5em}N=184\mathrm{}$ may have a fair chance of becoming stabilized by shell effects. An appendix introduces an improved measure of surface diffuseness, with certain advantages over the conventional Süssmann width b.