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

We solve the Schr\"odinger 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, 238U and ^239Pu. 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, 238U and ^239Pu all exhibit a similar structure.