Late-time emission of prompt fission $\gamma$ rays

The emission of prompt fission $\gamma$ rays within a few nanoseconds to a few microseconds following the scission point is studied in the Hauser-Feshbach formalism applied to the deexcitation of primary excited fission fragments. Neutron and $\gamma$-ray evaporations from fully accelerated fission fragments are calculated in competition at each stage of the decay, and the role of isomers in the fission products, before $\beta$ decay, is analyzed. The time evolution of the average total $\gamma$-ray energy, the average total $\gamma$-ray multiplicity, and the fragment-specific $\gamma$-ray spectra is presented in the case of neutron-induced fission reactions of ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$, as well as spontaneous fission of ${}^{252}\mathrm{Cf}$. The production of specific isomeric states is calculated and compared to available experimental data. About 7% of all prompt fission $\gamma$ rays are predicted to be emitted between 10 ns and 5 $\mu \mathrm{s}$ following fission, in the case of ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}(n_{\mathrm{th}},f)$ reactions, and up to 3% in the case of ${}^{252}\mathrm{Cf}$ spontaneous fission. The cumulative average total $\gamma$-ray energy increases by 2% to 5% in the same time interval. Finally, those results are shown to be robust against significant changes in the model input parameters.

Figure 1

Average prompt fission $\gamma$-ray spectrum (PFGS) for the spontaneous fission of ${}^{252}\mathrm{Cf}$. The high-energy tail of the calculated PFGS reproduces very well the recent measurement by Billnert et al. [31] (see inset), while the low-energy part of the spectrum shows very clear structures that can be attributed to transitions between low-lying excited states in fission fragments. $cgmf$ calculations do reproduce many of these structures reasonably well. The exact magnitude of these peaks depends on several factors, including our present knowledge of the nuclear structure of fission fragments. Note that no energy resolution broadening has been applied to the $cgmf$ results.

Figure 2

Same as Fig. 1 for the thermal-neutron-induced fission reaction of ${}^{235}\mathrm{U}$. Experimental data are from Billnert et al. [31]. The observed low-energy structures, as shown in the inset, are very well reproduced by $cgmf$ calculations. The high-energy tail would be better fit with a smaller value for the $\alpha$ spin parameter.

Figure 3

Same as Fig. 1 for the thermal-neutron-induced fission reaction of ${}^{239}\mathrm{Pu}$.

Figure 4

Top panel: Prompt fission $\gamma$-ray multiplicity distribution calculated with $cgmf$ and compared to a negative binomial distribution [35] with best-fit parameters. A double Poisson distribution as proposed originally by Brunson [34] to fit his experimental results is shown in red in the log-plot (bottom panel). The negative binomial distribution is in much better agreement with the tail of the distribution as calculated by $cgmf$ than the double Poisson distribution. The $\gamma$-ray threshold used in the $cgmf$ results is 140 keV.

Figure 5

Average prompt $\gamma$-ray multiplicity as a function of time for ${}^{252}\mathrm{Cf}$ (sf). Experimental data are from Verbinski et al. [30], Billnert et al. [31], and Chyzh et al. [33]. Valentine's data point [35] represents a weighted average of experimental data available prior to 2001.

Figure 6

Same as Fig. 5 for the thermal-neutron-induced fission of ${}^{235}\mathrm{U}$ (top panel) and ${}^{239}\mathrm{Pu}$ (bottom panel). The experimental data by Sund et al. [6] (green solid steps) were normalized to match gcmf-calculated average $\gamma$-ray multiplicity at 10 ns.

Figure 7

$\gamma$-ray spectrum in the 10–100 ns coincidence window gated on the post-neutron-emission ${}^{134}\mathrm{Te}$ fission fragment. The three $\gamma$ lines at 115, 297, and 1279 keV corresponding to the deexcitation of the 162 ns isomer in ${}^{134}\mathrm{Te}$ are clearly visible in this time range. The intensity of the 115-keV $\gamma$ line is strongly hindered compared to the two other lines due to internal conversion.

Figure 8

The distribution of prompt fission $\gamma$ rays emitted between 10 ns and 1 $\mu \mathrm{s}$ after fission, for ${}^{252}\mathrm{Cf}$ spontaneous fission, is shown as the blue histogram. Also shown are the independent fission yields (IFY), i.e., post-neutron-emission fission yields, as calculated by $cgmf$ (dashed red) and taken from the ENDF/B-VII.1 library (solid red), in arbitrary units.

Figure 9

Energy spectrum of late fission $\gamma$ rays emitted in the 10 ns to 2 $\mu \mathrm{s}$ time window following fission, in the case of ${}^{252}\mathrm{Cf}$ spontaneous fission. Experimental data are from John et al. [7].

Figure 10

Same as Fig. 9 but for all three fission reactions studied.

Figure 11

Cumulative average prompt $\gamma$-ray multiplicity as a function of time since fission for thermal-neutron-induced fissions of ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$ and spontaneous fission of ${}^{252}\mathrm{Cf}$.

Figure 12

Cumulative average prompt total $\gamma$-ray energy as a function of time since fission for thermal-neutron-induced fissions of ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$ and spontaneous fission of ${}^{252}\mathrm{Cf}$.

Figure 13

Pre-neutron-emission fission fragment mass yields for the three reactions studied here.

Figure 14

Sensitivity of the time dependence of the cumulative $\gamma$-ray multiplicity (red) and energy (blue) on the choice of the model input parameters $R_T$ and $\alpha$. The “reference” results, shown in Figs. 11 and 12, are reported here as solid lines.