A 4-dimensional Langevin approach to low-energy nuclear fission of $^{236}$U

TL;DR

This paper introduces a four-dimensional Langevin model for low-energy nuclear fission of uranium-236, accurately reproducing key observables and enabling detailed correlation analysis among fission parameters.

Contribution

The novel 4D Langevin model independently treats fragment deformations and incorporates microscopic potential energy calculations, advancing the understanding of fission fragment behaviors.

Findings

Successfully reproduces TKE(A) and its standard deviation

Reveals different deformation behaviors for light and heavy fragments

Enables multi-parametric correlation analysis among fission observables

Abstract

We developed a four-dimensional Langevin model which can treat the deformation of each fragment independently and applied it to low energy fission of 236U, the compound system of the reaction n+$^{235}$U. The potential energy is calculated with the deformed two-centerWoods-Saxon (TCWS) and the Nilsson type potential with the microscopic energy corrections following the Strutinsky method and BCS pairing. The transport coefficients are calculated by macroscopic prescriptions. It turned out that the deformation for the light and heavy fragments behaves differently, showing a sawtooth structure similar to that of the neutron multiplicities of the individual fragments $\nu$(A). Furthermore, the measured total kinetic energy TKE(A) and its standard deviation are reproduced fairly well by the 4D Langevin model based on the TCWS potential in addition to the fission fragment mass distributions. The developed model allows a multi-parametric correlation analysis among, e.g., the three key fission observables, mass, TKE, and neutron multiplicity, which should be essential to elucidate several long-standing open problems in fission such as the sharing of the excitation energy between the fragments.