Investigation of phenomenological models for the Monte Carlo simulation of the prompt fission neutron and $\gamma$ emission

A Monte Carlo simulation of the fission fragment deexcitation process was developed in order to analyze and predict postfission-related nuclear data which are of crucial importance for basic and applied nuclear physics. The basic ideas of such a simulation were already developed in the past. In the present work, a refined model is proposed in order to make a reliable description of the distributions related to fission fragments as well as to prompt neutron and $\gamma$ energies and multiplicities. This refined model is mainly based on a mass-dependent temperature ratio law used for the initial excitation energy partition of the fission fragments and a spin-dependent excitation energy limit for neutron emission. These phenomenological improvements allow us to reproduce with a good agreement the ${}^{252}\mathrm{Cf}$(sf) experimental data on prompt fission neutron multiplicity $\overline{\nu }(A)$, $\overline{\nu }(TKE)$, the neutron multiplicity distribution $P(\nu ),$ as well as their energy spectra $N(E)$, and lastly the energy release in fission.

Figure 1

${}^{252}\mathrm{Cf}$ experimental input data from [9]. Preneutron mass yield $Y(A)$ (a) and kinetic energy [distribution width ${\sigma }_{\mathrm{KE}}$ (b) and mean value $\langle \mathrm{KE}\rangle$ (c)].

Figure 2

Schematic representation of the evaporation of the fission fragments in the ($E^{*},J$) plan. Primary fragments dissipate excitation energy $E^{*}$ through neutron emission until $E^{*}<S_n+E^{\mathrm{rot}}$ while secondary fragments dissipate energy through $\gamma$ rays.

Figure 3

Average prompt neutron multiplicity as a function of mass calculated with $R_T=1$ and $E_{\lim }^{*}=S_n$ compared with measurements from Budtz-Jørgensen and Knitter [35], Hambsch et al. [36], and Bowman et al. [37].

Figure 4

Same as Fig. 3 with $R_T=1.25$ and $E_{\lim }^{*}=S_n+E^{\mathrm{rot}}$ involving two sets of moment of inertia ($\mathcal{J}={\mathcal{J}}_{\mathrm{rig}.}$ and $\mathcal{J}=0.5{\mathcal{J}}_{\mathrm{rig}.}$).

Figure 5

Macroscopic constraints for the determination of the temperature ratio law $R_T(A)$. For mass split 78/174 the light FF is near spherical and then its temperature is lower than its heavy partner, leading to a minimum $R_T<1.$ For mass split 120/132 the situation is reversed and the heavy FF is near spherical with a higher temperature than its light partner, leading to a maximum $R_T>1.$ Finally for symmetric mass split 126/126 the temperature is the same and then $R_T=1.$

Figure 6

Same as Fig. 3 with the refined model.

Figure 7

Average prompt neutron multiplicity as a function of the fission fragment total kinetic energy compared with Budtz-Jørgensen et al. [35]. Data from Bowman et al. [37] are also reported.

Figure 8

Average prompt neutron multiplicity as a function of the fission fragment total kinetic energy $\mathrm{TKE}$ for the light, the heavy, and the pair of fragments.

Figure 9

Average prompt neutron multiplicity as a function of mass number $A$ and total kinetic energy $\mathrm{TKE}$ [$\overline{\nu }(A,\mathrm{TKE})]$. $Q_{\max }$ and $\langle \mathrm{TKE}\rangle$ are also represented to guide the eyes.

Figure 10

Prompt neutron multiplicity distributions for heavy (a), light (b), and both (c) fission fragments. The dashed line correponds to experimental data from Vorobyev [39]. The full line is the result obtained with our refined model.

Figure 11

Average center-of-mass neutron energy as a function of mass number compared with experimental data from [35].

Figure 12

Neutron spectrum compared with a Maxwellian ($T_M=1.42$) and the Manhart evaluation. The spectrum is lying between the Maxwellian and the Manhart’s evaluation above few MeV (a) and is slightly underestimated at low energies (b).

Figure 13

Ratio of the calculated neutron spectrum to the Manhart’s evaluation.

Figure 14

Total excitation energy available for $\gamma$ deexcitation $\langle E_{\gamma }\rangle$ as a function of the light fragment mass number, compared with Nifenecker’s data [50].