A MODEL STUDY OF FINITE-RANGE 3-BODY INTERACTIONS

An interaction consisting of a two-body attractive Gaussian and three-body repulsive Gaussian is applied to study the ground state and four-particle excitation state of 4He. This may be regarded as an extension of the Skyrme interactions (T. H. R. Skyrme, Philos. Mag., 1 (1956), 1043; Nucl. Phys., 9 (1959), 615; D. Vautherin and D. M. Brink, Phys. Rev. C, 5 (1972), 626) all of which have zero range three-body terms. Up to a certain point, increasing the range a3 of the three-body term results in a deeper and sharper minimum for the energy of the four-particle excitation. However if a3 becomes too large relative to the two-body range a2, a phenomenon, which we call pseudo-collapse, comes into play. In contrast to the above, when an interaction consisting of a short range two-body repulsion and long range two-body attraction is used, there is no relative minimum in the energy of the four-particle excitation. Thus, not all states obtained in usual shell model calculations may really exist. © 1990.