Theoretical Study on Scission Configurations of FissioningPu240andPu242

The scission configuration is described by two interacting fragments in a single-particle model with pairing correlations and studied as function of two parameters. One parameter is the distance between the fragment centers of mass and the other parameter is the mass ratio of the two fragments. The scission-point region can be conveniently studied in this molecular model, particularly because extensive knowledge about the fragment structure is incorporated. Level schemes, equilibrium deformations of the fragments, total energies, and charge distributions are studied for the compound systems ${}_{}{}^{240}{}_{}{}^{}\mathrm{Pu}$ and ${}_{}{}^{242}{}_{}{}^{}\mathrm{Pu}$. The scission configurations are characterized by an approximate cancellation of the attractive nuclear force and the repulsive Coulomb force between the fragment. The proton numbers of the fragments turn out to be a rather good quantum number at scission. The results support the existence of a potential barrier at the scission point (scission barrier). It is shown that the calculated energies of the scission configurations can account for the asymmetry in the fragment-mass yield with its maximum at the heavy-fragment mass $A_1\approx 140$. The decrease of the total energy for $A_1\approx 140$ is due to single-particle states which have a small angular momentum component along the symmetry axis and — because of their prolate density distribution — give large contributions to the binding energy between the fragments. The 50-proton shell closure has its greatest influence on the scission configuration around $A_1=130\mathrm{}$, whereas the 82-neutron shell closure is most effective around $A_1=135\mathrm{}$.