Extension of the Hauser-Feshbach fission fragment decay model to multichance fission

The Hauser-Feshbach fission fragment decay model, ${\mathrm{HF}}^3\mathrm{D}$, which calculates the statistical decay of fission fragments, has been expanded to include multichance fission, up to neutron incident energies of 20 MeV. The deterministic decay takes as input prescission quantities—fission probabilities and the average energy causing fission—and postscission quantities—yields in mass, charge, total kinetic energy, spin, and parity. From these fission fragment initial conditions, the full decay is followed through both prompt and delayed particle emissions, allowing for the calculation of prompt neutron and $\gamma$ properties, such as multiplicity and energy distributions, both independent and cumulative fission yields, and delayed neutron observables. In this work, we describe the implementation of multichance fission in the ${\mathrm{HF}}^3\mathrm{D}$ model, and show an example of prompt and delayed quantities beyond first-chance fission, using the example of neutron-induced fission on ${}^{235}\mathrm{U}$. This expansion represents significant progress in consistently modeling the emission of prompt and delayed particles from fissile systems.

Figure 1

Multichance fission probabilities, in percentages, for ${}^{235}\mathrm{U}(n,f)$ for first- (black solid), second- (red dashed), third- (blue dotted), and fourth- (green dash dotted) chance fission, as calculated by ${\mathrm{CoH}}_3$.

Figure 2

Average excitation energy causing fission for first- (black solid), second- (red dashed), third- (blue dotted), and fourth- (green dash dotted) chance fission for ${}^{235}\mathrm{U}(n,f)$ as calculated by ${\mathrm{CoH}}_3$. The magenta dots show the average: the sum of each $m\mathrm{th}$-chance excitation energy folded with the $m\mathrm{th}$-chance fission probability, as shown in Fig. 1.

Figure 3

Black solid, pre-neutron-emission mass yields for ${}^{235}\mathrm{U}(n,f)$ with incident neutron energies of (a) thermal, (b) 6 MeV, and (c) 15 MeV, compared to experimental data [32, 34, 46, 47, 48]. Red dashed lines represent the part of the distribution coming from first-chance fission, blue dotted lines for second-chance fission, and green dot-dashed lines for third-chance fission.

Figure 4

Total kinetic energy as a function of incident energy for $\mathrm{BeoH}$ (solid) compared to experimental data [21, 22, 49, 50] for ${}^{235}\mathrm{U}(n,f)$.

Figure 5

Average prompt neutron multiplicity as a function of incident energy for $\mathrm{BeoH}$ (solid) compared to experimental data [51, 52, 53, 54, 55, 56, 57] for ${}^{235}\mathrm{U}(n,f)$.

Figure 6

(a) Average neutron multiplicity as a function of mass for $\mathrm{BeoH}$ with $R_T$ as a function of mass (solid) and with fixed $R_T=1.2$ (dashed) compared to experimental data [50, 58, 62] for ${}^{235}\mathrm{U}(n,f)$ for thermal incident neutrons. (b) Average neutron multiplicity as a function of mass for thermal incident neutrons (solid), incident neutrons at 6 MeV (dashed), and incident neutrons at 15 MeV (dotted).

Figure 7

Average $\gamma$-ray multiplicity as a function of incident energy for $\mathrm{BeoH}$ (solid) compared to experimental data [63, 64, 65, 66, 67]. A lower-bound cutoff on the outgoing $\gamma$-ray energy of $E_{\mathrm{th}}=150$ keV is included on the $\mathrm{BeoH}$ results, consistent with many experimental measurements.

Figure 8

Prompt fission $\gamma$-ray spectrum for ${}^{235}\mathrm{U}(n,f)$ for outgoing $\gamma$-ray energies (a) up to 2 MeV and (b) up to 20 MeV. Comparison between $\mathrm{BeoH}$ at thermal (black solid), $E_{\mathrm{inc}}=10$ MeV (gray dashed) and $E_{\mathrm{inc}}=20$ MeV (gray dotted), the ENDF/B-VIII.0 evaluation (red), and recent data by Makii et al. [68].

Figure 9

Independent fission mass yields (black solid) and cumulative fission mass yields (red dashed) for ${}^{235}\mathrm{U}(n,f)$ for incident energies of (a) thermal, (b) 5 MeV, (c) 10 MeV, (d) 15 MeV, and (e) 20 MeV. Note that the scale for the independent yields is on the left, and the scale for the cumulative yields is on the right.

Figure 10

Cumulative fission yields for select isotopes compared to available experimental data [69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81], (a) ${}^{87}\mathrm{Br}$, (b) ${}^{95}\mathrm{Zr}$, (c) ${}^{105}\mathrm{Ru}$, (d) ${}^{125}\mathrm{Sn}$, (e) ${}^{127}\mathrm{Sb}$, and (f) ${}^{135}\mathrm{Cs}$.

Figure 11

Average number of delayed neutrons calculated by $\mathrm{BeoH}$ (black solid) compared to experimental data [82, 83, 84, 85].