Properties of prompt-fission $\gamma$ rays

In a Monte Carlo Hauser-Feshbach statistical framework, we describe spectra, average multiplicities, average energy, and multiplicity distributions of the prompt $\gamma$ rays produced in the thermal neutron-induced fission of ${}^{235}\mathrm{U}$ and ${}^{239}\mathrm{Pu}$, and the spontaneous fission of ${}^{252}\mathrm{Cf}$. Comparisons against recent experimental data show reasonable agreement in all cases investigated, after adjustment of the initial spin distribution in the fission fragments. In particular, when we include in the calculation the Doppler broadening we obtain a qualitatively good description of the measured low-energy spectra, where contributions from collective discrete transitions in specific fragments can be identified. At higher energies, both the calculated neutron and $\gamma$-ray spectra are softer than experimental data. The impact of selected model parameters on the prompt neutron and $\gamma$-ray spectra is analyzed. Finally, we present the prompt $\gamma$ spectrum and multiplicity distribution for the neutron-induced fission of ${}^{235}\mathrm{U}$ for 5.5 MeV neutron incident energy, just below the threshold for second-chance fission.

Figure 1

Prompt $\gamma$ average multiplicity (a) and laboratory energy (b) as a function of the initial fragment. We present the ratio of the respective quantities for $R_T=1$ to $R_T\left(A\right)$. In both calculations, the angular momentum distribution is set by $\alpha =1.5$. A ratio of 1.0 would represent a perfect agreement between the two calculations.

Figure 2

Same as in Fig. 1, but for prompt neutrons.

Figure 3

The prompt neutron average multiplicity (a) and energy (b) as a function of the initial fragment mass, for five values of the $\alpha$ parameter. As in Fig. 1, we plot the ratio of the results for $\alpha =0.5,1.0,1.5,2.0$ to the ones for $\alpha =1.7$. In all calculations, the same $R_T\left(A\right)$ was used.

Figure 4

Same as in Fig. 3, but for prompt $\gamma$ rays.

Figure 5

The prompt $\gamma$ multiplicity distribution in MCHF for five values of the $\alpha$ parameter compared against the parametrized model (PM), the Valentine model [43], and the negative binomial model with the parameters fitted to our $\alpha =1.7$ calculation.

Figure 6

The prompt $\gamma$-ray energy spectrum calculated with MCHF, plotted as a ratio of the spectrum obtained with $\alpha =0.5,1.0,1.5,2.0$ to the result of $\alpha =1.7$.

Figure 7

Dependence on average $\gamma$-ray multiplicity (upper panel) and average $\gamma$-ray energy of the threshold energy $E_{\mathrm{cut}}$ used in the calculation. The ENDF data was obtained by integrating the evaluated spectrum combined with the evaluated multiplicity. The filled area shows the spread in our calculations for different $\alpha$ parameters.

Figure 8

The prompt $\gamma$ spectrum for ${}^{235}U(n_{\mathrm{th}},f)$ (upper panel). Our calculation with $\alpha =1.7$ is compared against the experimental spectra obtained by Verbinski [12] and Oberstedt [14], as well as against the parametrized model of Jandel et al. [16]. In the lower panel we present, in linear scale, the low-energy part of the spectrum, where discrete transitions play a major role.

Figure 9

The prompt $\gamma$-ray energy spectrum decomposed into contributions from the continuum-to-continuum, continuum-to-discrete, and discrete-to-discrete transitions.

Figure 10

The average $\gamma$-ray multiplicity (a) and average $\gamma$-gamma energy (b) as a function of mass for ${}^{235}\mathrm{U}(n_{\mathrm{th}},f)$.

Figure 11

The prompt $\gamma$ spectrum in the thermal neutron-induced fission of ${}^{235}\mathrm{U}$, for multiplicities $2,4,6,\cdots ,20$. We compare our results for $\alpha =1.7$ against the parameterized model.

Figure 12

Comparison between the prompt $\gamma$ spectra for the induced fission of ${}^{235}\mathrm{U}$ by thermal neutrons (continuous line) and by neutrons with 5.5 MeV incident energy.

Figure 13

Comparison between the prompt $\gamma$ multiplicity distribution for the induced fission of ${}^{235}\mathrm{U}$ by thermal neutrons (continuous line) and by neutrons with 5.5 MeV incident energy.

Figure 14

The prompt $\gamma$ spectrum for ${}^{239}\mathrm{Pu}(n_{\mathrm{th}},f)$. Our calculation with $\alpha =1.5$ is compared with the experimental spectrum measured by Verbinski et al. [12], as well as with the parametrized model of Jandel et al. [15]. In the lower panel, we present, in linear scale, the low-energy part of the spectrum, where discrete transitions can be identified as in Fig. 8.

Figure 15

The prompt $\gamma$ multiplicity distribution in MCHF for $\alpha =1.5$ compared with the parametrized model (PM), Valentine model [43], and the negative binomial model with the parameters fitted to our optimal calculation (see Table 1). We also show the multiplicity distribution for $\alpha =1$, which gives the best agreement with the parametrized model and Valentine's evaluation.

Figure 16

(a) The average prompt $\gamma$ spectrum for the spontaneous fission of ${}^{252}\mathrm{Cf}$. Our calculation with $\alpha =1.7$ is compared against the experimental spectra obtained by Verbinski [12] and Billnert [13], as well as against the parametrized model (PM) of Jandel et al. [15, 16]. (b) In the lower panel, we present, in linear scale, the low-energy part of the spectrum, where discrete transitions play a major role.

Figure 17

The prompt $\gamma$ multiplicity distribution in MCHF for $\alpha =1.7$ parameter compared against the parametrized model (PM), Valentine parametrization, and the negative binomial model with parameters fitted to our calculation (see Table 1).

Figure 18

The average $\gamma$ multiplicity (a) and average total $\gamma$ energy per fission (b) as a function of fragment mass for ${}^{252}\mathrm{Cf}$ (sf).