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

TL;DR

This paper introduces a novel method using Brownian shape-motion to calculate detailed 2D fission-fragment yields, including odd-even effects, for uranium and plutonium, enhancing understanding of nuclear fission processes.

Contribution

The paper extends previous models by incorporating proton and neutron numbers of emerging fragments into the potential-energy calculations and enabling correlated nucleon pair transfers.

Findings

Method successfully calculates Y(Z,N) with odd-even staggering effects.

Application to U and Pu yields demonstrates improved predictive capability.

Generalization from compound system to fragment-specific properties achieved.

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 $\epsilon_{\rm f1}$, right nascent fragment deformation $\epsilon_{\rm f2}$ 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.