Study of many-nucleon correlations in32S as a model for fragment shell effects in fission

Abstract

The formation and break-up of substructures is studied in 32S as a calculable microscopic model for analogous long-range many-nucleon correlations in the fission of actinides. The calculations are performed for alpha-cluster wave functions with Volkov and BrinkBoeker interaction allowing for a, 12C, 160 and 2~clustering. It turns out that the correlated motion of large magic numbers of nucleons in two groups (160+160) is energetically favorable already at relatively small deformations. In the second minimum the 160 +160 substructure occurs with high probability (about 80 %). In analogy to these results the "pre-formation" of fragments and "fragment shell" effects occuring in the fission of actinides are explained in terms of probability statements for the formation of the corresponding heavy clusters in the many-body wave function.

Comparison of cluster and shell model wave functions of deformed32S states

“…In order to carry out the program described above we expand the ACM wave functions of 32S calculated in [6] into TCSM wave functions. The TCSM wave functions we have adopted are Slater determinants of one-particle states which are generated by the potential…”

“…A similar calculation has been performed using the ACM wave functions of minimal energy [6] for the Brink-Boeker force B 1. be meaningful to look at the probability P2 which approaches 100 741 in the limit of vanishing deformation.…”

“…By summing up the energies associated with these cluster configurations in a suitable way, one gets again an approximate expression for the deformation energies of heavy nuclei as function of the deformation parameters. Besides the ground state minimum, in both cases they show a second minimum which is produced by the formation of two ~60 clusters in their ground state (see [4] and [6]). In this method one can see immediately that the first (ground state) minimum belongs to states where the * Supported in part by the Bundesrninisterium ftir Forschung und Yechnologie doubly closed shell structure of Pb (N= 126, Z=82) is practically not broken up.…”

“…An important result of these calculations was the discovery of a second minimum in the deformation energy surface which is responsible for the phenomenon of isomeric fission. A suitable nucleus for such a comparison is 31S because the general form of its deformation energy curve is determined by analogous physical facts as the deformation energy curves in the actinide region [6]. One calculates approximately the probability for the existence of different cluster configurations at the surface of the deformed nucleus.…”

“…One calculates approximately the probability for the existence of different cluster configurations at the surface of the deformed nucleus. The other calculation by Schultheis et al [6] uses a-cluster wave functions (ACM) [7] as basis 9 This approach corresponds to the calculation of deformation energies using cluster representation wave functions. Also here one obtains potential-energy curves with two minima for nuclei with N> 132.…”