Improvements to the macroscopic-microscopic approach of nuclear fission

TL;DR

This paper enhances the macroscopic-microscopic approach to nuclear fission by improving microscopic calculations, introducing a deterministic fission dynamics method, and enabling simultaneous mass and charge distribution predictions, leading to more accurate results.

Contribution

The work introduces key improvements to the mac-mic model, including refined microscopic calculations, a new deterministic fission dynamics method, and quantum mechanical particle number projection for better yield predictions.

Findings

Accurate prediction of odd-even staggering in fission yields.

Successful modeling of charge polarization in neutron-induced fission.

Enhanced agreement with experimental data for ${}^{233}$U and ${}^{235}$U fission.

Abstract

The well established macroscopic-microscopic (mac-mic) description of nuclear fission enables the prediction of fission fragment yields for a broad range of fissioning systems. In this work, we present several key enhancements to this approach. We improve upon the microscopic sector of nuclear potential energy surfaces by magnifying the resolution of the Lipkin-Nogami equations and strengthening the Strutinsky procedure, thus reducing spurious effects from the continuum. We further present a novel deterministic method for calculating fission dynamics under the assumption of strongly damped nucleonic motion. Our technique directly determines the evolution of the scissioned shape distribution according to the number of random walk steps rather than the statistical accumulation of fission events. We show that our new technique is equivalent to the Metropolis random walk pioneered over the past decade by Randrup and colleagues. It further improves upon it, as we remove the need for altering the nuclear landscape via a biased potential. With our final improvement, we calculate fission fragments mass and charge distributions using particle number projection, which affords the simultaneous calculation of both mass and charge yield distributions. Fission fragments are thus calculated from the quantum mechanical $A$-body states of the potential energy surface rather than the collective mass asymmetry variable ($\alpha_{\rm g}$) of the Finite-Range Liquid-Drop Model (FRLDM) used in past work. We highlight the success of our enhancements by predicting the odd-even staggering and the charge polarization for the neutron-induced fission of ${}^{233}$U and ${}^{235}$U.