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 ${\hat{I}}^3$-ray multiplicities, as well as their spectra. Specifically, we use several mass yields to determine a linear correlation between the calculated prompt neutron multiplicity $\bar{\hat{I}}½$ and the average heavy-fragment mass $⟨A_h⟩$ of the input mass yields $\partial \bar{\hat{I}}½/\partial ⟨A_h⟩=\pm 0.1n/f/\mathrm{u}$. The mass peak width influences the correlation between the total kinetic energy of the fission fragments and the total number of prompt neutrons emitted $\bar{\hat{I}}{½}_T(\mathrm{TKE})$. Typical biases on prompt particle observables from using calculated mass yields instead of experimental ones are: $\hat{I}´\bar{\hat{I}}½=4\%$ for the average prompt neutron multiplicity, $\hat{I}´{\bar{M}}_{\hat{I}}^3=1\%$ for the average prompt ${\hat{I}}^3$-ray multiplicity, $\hat{I}´\bar{\hat{I}}{\mu }_n^{\mathrm{LAB}}=1\%$ for the average outgoing neutron energy, $\hat{I}´\bar{\hat{I}}{\mu }_{\hat{I}}^3=1\%$ for the average ${\hat{I}}^3$-ray energy, and $\hat{I}´⟨\mathrm{TKE}⟩=0.4\%$ for the average total kinetic energy of the fission fragments.

12 pages, 8 figures, 2 tables