Proximity forces

We have generalized a theorem according to which the force between two gently curved objects in close proximity is proportional to the interaction potential per unit area between two flat surfaces made of the same material, the constant of proportionality being a measure of the mean curvature of the two objects. This theorem leads to a formula for the interaction pontential between curved objects (e.g., two smooth cylinders of mica or two atomic nuclei) which is a product of a simple geometrical factor and a universal function of separation, characteristic of the material of which the objects are made, and intimately related to the surface energy coefficient. We have calculated and tabulated this universal function for nuclear surfaces, using the nuclear Thomas-Fermi approximation. The results can be expressed by a simple cubic-exponential formula which gives the potential between any two nuclei in the separation degree of freedom. Even simpler expressions are found for the interaction energy associated with the “crevice” or neck in the nuclear configuration that would be expected immediately after contact of two nuclei. These “proximity energies” are used to supplement the usual expansion of the energy of a thin-skinned system into volume, surface, curvature, and higher-order terms. The resulting elementary formulas are tested against explicit models of interacting nuclei and against elastic scattering data, and are found to be useful for even quite small mass numbers.