$^{235}$U(n, f) Independent Fission Product Yield and Isomeric Ratio Calculated with the Statistical Hauser-Feshbach Theory

TL;DR

This paper introduces HF$^3$D, a statistical Hauser-Feshbach model for predicting fission product yields and isomeric ratios in neutron-induced fission of $^{235}$U, aligning well with experimental data and extending to higher energies.

Contribution

The paper presents a novel Hauser-Feshbach based model capable of calculating fission yields and isomeric ratios for over 500 fission fragment pairs, validated against experimental data.

Findings

The model accurately reproduces experimental independent fission product yields at thermal energies.

Calculated isomeric ratios are generally lower than previous models like Madland-England.

Most isomeric ratios remain constant across increasing incident neutron energies.

Abstract

We have developed a Hauser-Feshbach fission fragment decay model, HF$^3$D, which can be applied to the statistical decay of more than 500 primary fission fragment pairs (1,000 nuclides) produced by the neutron induced fission of $^{235}$U. The fission fragment yield $Y(A)$ and the total kinetic energy TKE are model inputs, and we estimate them from available experimental data for the $^{235}$U(n$\rm_{th}$,f) system. The model parameters in the statistical decay calculation are adjusted to reproduce some fission observables, such as the neutron emission multiplicity $\overline{\nu}$, its distribution $P(\nu)$, and the mass dependence $\overline\nu(A)$. The calculated fission product yield and isomeric ratio are compared with experimental data. We show that the calculated independent fission product yield $Y_I(A)$ at the thermal energy reproduces the experimental data well, while the calculated isomeric ratios tend to be lower than the Madland-England model prediction. The model is extended to higher incident neutron energies up to the second chance fission threshold. We demonstrate for the first time that most of the isomeric ratios stay constant, although the production of isomeric state itself changes as the incident energy increases.