Solving one-dimensional penetration problem for fission channel in the statistical Hauser-Feshbach theory

TL;DR

This paper develops a method to solve the Schrödinger equation for one-dimensional potentials to calculate fission transmission coefficients, integrating them into the Hauser-Feshbach model, and successfully reproducing experimental fission cross sections.

Contribution

It introduces a novel approach to compute transmission coefficients for fission channels using quantum mechanics within a one-dimensional model, enhancing the accuracy of reaction predictions.

Findings

The model reproduces experimental fission cross sections well.

Resonance-like structures are observed in transmission coefficients.

Quantum effects are evident in double-humped fission barriers.

Abstract

We solve the Schr\"{o}dinger equation for an arbitrary one-dimensional potential energy to calculate the transmission coefficient in the fission channel of compound nucleus reactions. We incorporate the calculated transmission coefficients into the statistical Hauser-Feshbach model calculation for neutron-induced reactions on $^{235,238}$U and $^{239}$Pu. The one-dimensional model reproduces the evaluated fission cross section data reasonably well considering the limited number of model parameters involved. A resonance-like structure appears in the transmission coefficient for a double-humped fission barrier shape that includes an intermediate well, which is understood to be a quantum mechanical effect in the fission channel. The calculated fission cross sections for the neutron-induced reactions on $^{235,238}$U and $^{239}$Pu all exhibit a similar structure.