A Method to Calculate Fission-Fragment Yields $Y(Z,N)$ versus Proton and Neutron Number in the Brownian Shape-Motion Model. Application to calculations of U and Pu charge yields

Abstract

We propose a method to calculate the two-dimensional (2D) fission-fragment yield $Y(Z,N)$ versus both proton and neutron number, with inclusion of odd-even staggering effects in both variables. The approach is to use Brownian shape-motion on a macroscopic-microscopic potential-energy surface which, for a particular compound system is calculated versus four shape variables: elongation (quadrupole moment $Q_2$), neck $d$, left nascent fragment spheroidal deformation $\hat{I}{\mu }_{f1}$, right nascent fragment deformation $\hat{I}{\mu }_{f2}$ and two asymmetry variables, namely proton and neutron numbers in each of the two fragments. The extension of previous models 1) introduces a method to calculate this generalized potential-energy function and 2) allows the correlated transfer of nucleon pairs in one step, in addition to sequential transfer. In the previous version the potential energy was calculated as a function of $Z$ and $N$ of the compound system and its shape, including the asymmetry of the shape. We outline here how to generalize the model from the "compound-system" model to a model where the emerging fragment proton and neutron numbers also enter, over and above the compound system composition.