Nuclear Compressibility and Symmetry Energy

Abstract

A modification and generalization of the Puff-Martin model for many-fermion systems is employed to calculate nuclear compressibility and symmetry energy in order to provide a practical test of the model and at the same time obtain useful information about these interesting quantities. An alternative, heuristic, derivation of the Puff-Martin equations is presented in order to exhibit the role of the exclusion principle. The condition stated for normal nuclear matter is that the mean binding energy be minimal (with respect to variation of the Fermi momentum) rather than the Puff-Martin condition that the mean binding energy equal the "single particle" energy at the Fermi surface. These two quantities differ from each other by the rearrangement energy, which is found to be 10 Mev. Employing Puff's potential (hard-shell potential plus a separable Yamaguchi potential, acting only in relative $S$ states), satisfactory agreement is obtained with observed binding energy and density. The value of nuclear compressibility, 214 Mev, falls within the wide range of semiempirical values. The symmetry energy coefficient, 43 Mev, is larger, by 40-80%, than those usually quoted in semiempirical mass formulas. However, our value of the symmetry coefficient is the same as that calculated by Brueckner and Gammel in the absence of odd-state forces; they found the coefficient to be reduced to 26 Mev when a more realistic potential, including odd-state contributions, is employed.