The Bethe-Weizsäcker Mass Formula and Lennard-Jones N-N Potentials

Abstract

An elementary derivation of the Bethe-Weizsäcker semiempirical nuclear mass formula which is in the spirit of current views of nuclear structure, is given. Lennard-Jones potentials are assumed to act between nucleons. Thus the major interaction between nn, pp, and np pairs is taken of the form −gsol;r3+hsol;r4, where r is the separation distance between nucleons, and g and h are constants. An additional “symmetry” interaction of the form −s/r3 is assumed for np pairs. Summing the potential energy over all nucleon pairs and using the Fermi statistical estimate of the kinetic energy, the Bethe-Weizsäcker semiempirical mass formula is obtained directly. The constants of the mass formula are discussed in relation to the N-N interaction and are found to be quite plausible.