Hauser-Feshbach fission fragment de-excitation with calculated macroscopic-microscopic mass yields

Abstract

The Hauser-Feshbach statistical model is applied to the de-excitation of primary fission fragments using input mass yields calculated with macroscopic-microscopic models of the potential energy surface. We test the sensitivity of the prompt fission observables to the input mass yields for two important reactions, $^{235}$U$(n_\mathrm{th},f)$ and $^{239}$Pu$(n_\mathrm{th},f)$, for which good experimental data exist. General traits of the mass yields, such as the location of the peaks and their widths, can impact both the prompt neutron and $\gamma$-ray multiplicities, as well as their spectra. Specifically, we use several mass yields to determine a linear correlation between the calculated prompt neutron multiplicity $\bar{\nu}$ and the average heavy-fragment mass $\langle A_h\rangle$ of the input mass yields $\partial\bar{\nu}/\partial\langle A_h\rangle = \pm 0.1\,n/f/\mathrm{u}$. The mass peak width influences the correlation between the total kinetic energy of the fission fragments and the total number of prompt neutrons emitted $\bar{\nu}_T(\mathrm{TKE})$. Typical biases on prompt particle observables from using calculated mass yields instead of experimental ones are: $\delta \bar{\nu} = 4\%$ for the average prompt neutron multiplicity, $\delta \bar{M}_\gamma = 1\%$ for the average prompt $\gamma$-ray multiplicity, $\delta \bar{\epsilon}_n^\mathrm{LAB} = 1\%$ for the average outgoing neutron energy, $\delta \bar{\epsilon}_\gamma = 1\%$ for the average $\gamma$-ray energy, and $\delta \langle\mathrm{TKE}\rangle = 0.4\%$ for the average total kinetic energy of the fission fragments.