Improved modeling of photon observables with the event-by-event fission model freya

The event-by-event fission model $\mathtt{FREYA}$ has been improved, in particular to address deficiencies in the calculation of photon observables. We discuss the improvements that have been made and introduce several new variables, some detector dependent, that affect the photon observables. We show the sensitivity of $\mathtt{FREYA}$ to these variables. We then compare the results to the available photon data from spontaneous and thermal neutron-induced fission.

Figure 1

The ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ photon spectrum from $\mathtt{FREYA}$ calculated as in Ref. [2] without GDR form factor or RIPL-3 lines, with GDR but without RIPL-3 lines, and including both, as in the current version of $\mathtt{FREYA}$. Panel (a) shows the spectrum over the entire energy range, while panel (b) shows the low-energy spectrum for photon energies less than 1 MeV. The calculated results in this and all subsequent figures are based on one million events and the associated sampling errors are shown. The spectra are normalized to the fission photon multiplicity.

Figure 2

The calculated fragment mass dependence of (a) the average total photon energy, $E_{\gamma }\left(A\right)$, and (b) the average photon multiplicity, $N_{\gamma }\left(A\right)$, for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ obtained with $\mathtt{FREYA}$ for three different model scenarios: (1) without GDR form factor or RIPL-3 transitions, as in the earlier $\mathtt{FREYA}$ [2]; (2) with the GDR form factor but without RIPL-3 lines; and (3) including both, as in the improved $\mathtt{FREYA}$. Here and in subsequent figures, $A$ is the mass number of the primary (i.e., pre-evaporation) fission fragment.

Figure 3

The energy per photon as a function of fragment mass for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$, $E_{\gamma }\left(A\right)/N_{\gamma }\left(A\right)$, obtained with $\mathtt{FREYA}$ for three different model scenarios: (1) without GDR form factor or RIPL-3 transitions, as in the earlier $\mathtt{FREYA}$ [2]; (2) with the GDR form factor but without RIPL-3 lines; and (3) including both, as done in the improved version of $\mathtt{FREYA}$.

Figure 4

The total photon energy $E_{\gamma }$ (a) and the photon multiplicity $N_{\gamma }$ (b) as functions of total fragment kinetic energy TKE calculated for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ with $\mathtt{FREYA}$ for three different model scenarios: (1) without GDR form factor or RIPL-3 transitions, as in the earlier $\mathtt{FREYA}$ [2]; (2) with the GDR form factor but without RIPL-3 lines; and (3) including both, as done in the improved version of $\mathtt{FREYA}$.

Figure 5

The photon multiplicity distribution $P_{\gamma }\left(N_{\gamma }\right)$ for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ obtained with $\mathtt{FREYA}$ in three different model scenarios: (1) without GDR form factor or RIPL-3 transitions, as in the earlier $\mathtt{FREYA}$ [2]; (2) with the GDR form factor but without RIPL-3 lines; and (3) including both, as done in the improved version of $\mathtt{FREYA}$.

Figure 6

The mean total photon energy $E_{\gamma }$ (a) and the mean photon multiplicity $N_{\gamma }$ (b) as functions of the fragment mass number $A$ calculated for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ for four different values of the parameter $c_S$ which sets the magnitude of the fragment spins. Results are shown for $c_S=0.2$, 0.8, 1.4, and 2.0.

Figure 7

The energy per photon $E_{\gamma }/N_{\gamma }$ as a function of the fragment mass number $A$ calculated for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ for four different values of the parameter $c_S$ which sets the magnitude of the fragment spins. Results are shown for $c_S=0.2$, 0.8, 1.4, and 2.0.

Figure 8

The average fragment angular momentum $S_{\mathrm{f}}$ as a function of the fragment mass $A$ for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ calculated for four different values of the parameter $c_S$ (which controls the magnitude of the fragment spins). Results are shown for $c_S=0.2$, 0.8, 1.4, and 2.0.

Figure 9

The total photon energy $E_{\gamma }$ (a) and the photon multiplicity $N_{\gamma }$ (b) as functions of total fragment kinetic energy TKE for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ calculated for four different values of the parameter $c_S$ (which controls the magnitude of the fragment spins; see Fig. 8). Results are shown for $c_S=0.2$, 0.8, 1.4, and 2.0.

Figure 10

The photon multiplicity distribution $P_{\gamma }\left(N\right)$ for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ calculated for four different values of the parameter $c_S$ (which sets the magnitude of the fragment spins). Results are shown for $c_S=0.2$, 0.8, 1.4, and 2.0 using $g_{\min }=0.1\mathrm{MeV}$ and $t_{\max }=10$ ns. The mean multiplicity for each value of $c_S$ is indicated.

Figure 11

The photon multiplicity $N_{\gamma }$ (a) and the energy per photon $E_{\gamma }/N_{\gamma }$ (b) as functions of fragment mass number $A$ for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ calculated for four different values of $g_{\min }$, the minimum photon energy detected. Results are shown for $g_{\min }=0.05$, 0.10, 0.15, and 0.20 MeV.

Figure 12

The average photon multiplicity $N_{\gamma }$ as a function of total fragment kinetic energy TKE calculated for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ for four different values of the parameter $g_{\min }$, the minimum photon energy detected. Results are shown for $g_{\min }=0.05$, 0.10, 0.15, and 0.20 MeV.

Figure 13

The total photon energy $E_{\gamma }$ (a) and the photon multiplicity $N_{\gamma }$ (b) calculated for ${}^{235}\mathrm{U}$($n_{\mathrm{th}},\mathrm{f}$), ${}^{230}\mathrm{Pu}$($n_{\mathrm{th}},\mathrm{f}$), and ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ as a function of the photon energy cutoff $g_{\min }$. The value of $t_{\max }$ was 10 ns for all cases.

Figure 14

The total photon energy $E_{\gamma }$ (a) and the photon multiplicity $N_{\gamma }$ (b) calculated for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ as a function of photon energy cutoff $g_{\min }$ for three values of $c_S$: $c_S=0.2$, 0.87, and 2.0. The value of $t_{\max }$ was 10 ns.

Figure 15

The energy per photon $E_{\gamma }/N_{\gamma }$ calculated for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ as a function of the photon energy cutoff $g_{\min }$ for three values of $c_S$: $c_S=0.2$, 0.87, and 2.0. The value of $t_{\max }$ was 10 ns taken as for all cases.

Figure 16

The total photon energy (a) and the photon multiplicity (b) as functions of the maximum level half life $t_{\max }$, relative to the results for $t_{\max }\to \infty$ (effectively $t_{\max }=5\mu \mathrm{s}$), for ${}^{235}\mathrm{U}$($n_{\mathrm{th}},\mathrm{f}$), ${}^{230}\mathrm{Pu}$($n_{\mathrm{th}},\mathrm{f}$), and ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$.

Figure 17

The total photon energy (a) and the photon multiplicity (b) as functions of the maximum level half life $t_{\max }$, relative to the results for $t_{\max }\to \infty$, for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ using $g_{\min }=0.05$, 0.10, 0.15, and 0.20 MeV.

Figure 18

The total energy per photon, $E_{\gamma }/N_{\gamma }$, as a function of the maximum level half life $t_{\max }$, relative to the results for $t_{\max }\to \infty$, for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ using $c_S=0.2$, 0.87 (the default value), and 2.0.

Figure 19

For ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$, the calculated total photon energy $E_{\gamma }$ as a function of the primary fragment mass number $A$ (a) and the combined photon energy from both fragments as a function of the mass number of the light fragment $A_L$ (b), compared to data from Nifenecker [26] (b) and from Nardi [27] (a) and (b). The calculation used one million events; the associated sampling errors are shown in (b).

Figure 20

For ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$, the calculated total photon energy as a function of total fragment kinetic energy is compared to data from Nifenecker [26] and Nardi [27].

Figure 21

The photon multiplicity as a function of fragment mass calculated for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ are compared to data from Pleasonton [28] and Johansson [29]. (Note that the method used by Johansson does not allow precise determination of the mass [29]).

Figure 22

The photon energy spectrum calculated for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ compared to data from Billnert et al. [18]. The total photon spectrum is shown in (a) while the spectrum for energies less than 1 MeV are shown in (b). The spectra are normalized to the fission photon multiplicity.

Figure 23

(a) The photon multiplicity distribution $P\left(N_{\gamma }\right)$ calculated for ${}^{252}\mathrm{Cf}\left(\mathrm{sf}\right)$ is compared to data from DANCE [19] as well as data from Oberstedt et al. [35] and the Valentine evaluation [36]. (b) The LiBerACE [30] photon multiplicity distributions resulting from two and four neutrons emitted compared to the $\mathtt{FREYA}$ results for the same quantities.

Figure 24

The total photon energy (a) and the photon multiplicity (b) as a function of fragment mass calculated for ${}^{235}\mathrm{U}$($n_{\mathrm{th}},\mathrm{f}$) are compared to data from Pleasonton [31] (a) and (b), and data from Albinsson [40] (b).

Figure 25

The energy per photon as a function of fragment mass calculated for ${}^{235}\mathrm{U}$($n_{\mathrm{th}},\mathrm{f}$) is compared to data from Pleasonton [31].

Figure 26

The total photon energy as a function of total fragment kinetic energy calculated for ${}^{235}\mathrm{U}$($n_{\mathrm{th}},\mathrm{f}$) is compared to data from Pleasonton [31].

Figure 27

The photon energy spectrum calculated for ${}^{235}\mathrm{U}$($n_{\mathrm{th}},\mathrm{f}$) compared to data from Oberstedt et al. [41]. The total photon spectrum is shown in (a) while the spectrum for energies less than 1 MeV is shown in (b). The spectra are normalized to the fission photon multiplicity.

Figure 28

The total photon energy (a), the photon multiplicity (b), and the energy per photon (c) as functions of fragment mass number calculated for ${}^{233}\mathrm{U}$($n_{\mathrm{th}},\mathrm{f}$) are compared to data from Pleasonton [32].

Figure 29

The total photon energy as a function of total fragment kinetic energy calculated for ${}^{233}\mathrm{U}$($n_{\mathrm{th}},\mathrm{f}$) is compared to data from Pleasonton [32].

Figure 30

The total photon energy (a) and the photon multiplicity (b) as a function of fragment mass calculated for ${}^{239}\mathrm{Pu}$($n_{\mathrm{th}},\mathrm{f}$) are compared to data from Pleasonton [32].

Figure 31

The total photon energy as a function of total fragment kinetic energy calculated for ${}^{239}\mathrm{Pu}$($n_{\mathrm{th}},\mathrm{f}$).