Monte Carlo approach to sequential neutron emission from fission fragments

We have implemented a Monte Carlo simulation of fission fragment statistical decay by sequential neutron emission. Within this approach, we calculate the center-of-mass and laboratory prompt neutron energy spectra as a function of the mass of fission fragments and integrated over the whole mass distribution. We also assess the prompt neutron multiplicity distribution $P(\nu )$, both the average number of emitted neutrons and the average neutron energy as a function of the mass of the fission fragments [respectively $\overline{\nu }(A)$ and $\langle \varepsilon \rangle (A)$]. We investigate the average total energy available for prompt γ-ray emission as a function of the mass of the fission fragments ${\overline{E}}_{\gamma }(A)$. We also calculate neutron-neutron correlations such as the full matrix $\overline{\nu }(A,\mathrm{TKE})$ as well as correlations between neutron energies. Two assumptions for partitioning the total available excitation energy among the light and heavy fragments are considered. Results are reported for the neutron-induced fission of ${}^{235}\mathrm{U}$ (at neutron energy of 0.53 MeV) and for the spontaneous fission of ${}^{252}\mathrm{Cf}$.

Figure 1

(Color) Experimental yields used in our calculations plotted as a function of the mass number of the FF and TKE for ${}^{252}\mathrm{Cf}$(sf) on the right and n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction on the left.

Figure 2

Neutron multiplicity distribution for n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction. Full square symbols $(\blacksquare )$ are from our Monte Carlo calculation assuming partitioning of FF total excitation energy as a function of ${\overline{\nu }}_{\exp }(A)$ (H2 hypothesis), triangles $(▴)$ are the result obtained under the assumption of an equal temperature of complementary FF (H1 hypothesis). The points are experimental data from Diven et al. [15] at 80-keV incident neutron energy.

Figure 3

Neutron multiplicity distribution for ${}^{252}\mathrm{Cf}$(sf). The points are experimental data from Refs. 15, 17, 18.

Figure 4

Neutron energy spectrum in the FF center-of-mass system for n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction. The thick line is our Monte Carlo calculation assuming partitioning of FF total excitation energy as a function of ${\overline{\nu }}_{\exp }(A)$ (H2 hypothesis) and the thin line is the result obtained under the assumption of an equal temperature of complementary FF (H1 hypothesis). The dashed line is result of the Los Alamos model calculation using the optical model potential of Becchetti and Greenlees for the inverse process of compound nucleus formation.

Figure 5

Neutron energy spectrum for n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction in the laboratory frame. The experimental points are from Johansson and Holmqvist [20] at 0.53-MeV neutron energy.

Figure 6

Neutron energy spectrum in the FF center-of-mass system for ${}^{252}\mathrm{Cf}$(sf).

Figure 7

Neutron energy spectrum for ${}^{252}\mathrm{Cf}$(sf) in the laboratory frame. The experimental points are from Poenitz and T. Tamura [22].

Figure 8

Average neutron emission energy, $\langle \varepsilon \rangle$, in the center-of-mass frame as a function of FF mass for ${}^{252}\mathrm{Cf}$(sf). The points are experimental data from Ref. 12.

Figure 9

Average initial fragment excitation energy as a function of FF mass number under both assumptions (H1) and (H2) for ${}^{252}\mathrm{Cf}$(sf).

Figure 10

Average center-of-mass neutron energies as a function of neutron multiplicity for the n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction.

Figure 11

Average neutron multiplicity $\overline{\nu }$ as a function of the mass number of the FF for n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction. The points are experimental data from Ref. 13 at thermal incident neutron energy.

Figure 12

Average neutron multiplicity $\overline{\nu }$ as a function of the mass number of the FF for ${}^{252}\mathrm{Cf}$(sf). The points are experimental data from Ref. 12.

Figure 13

Average energy released in fission as a function of the heavy fragment mass for the n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction, obtained from the difference between the compound nucleus and the FF masses given by the data table by Audi, Wapstra, and Thibault [8].

Figure 14

Sum of the neutron multiplicities from both FF plotted as a function of TKE for ${}^{252}\mathrm{Cf}$(sf). The points are experimental data from Ref. 12.

Figure 15

Sum of the neutron multiplicities from both FF plotted as a function of TKE for n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction. The points are experimental data from Ref. 13 measured at thermal incident neutron energy.

Figure 16

Average neutron multiplicity versus FF mass for specific 5-MeV TKE bins for the n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction. The points are experimental data from Ref. 13 measured at thermal incident neutron energy. The dash and full lines are the results obtained under (H1) and (H2) hypotheses respectively.

Figure 17

Average neutron multiplicity plotted versus TKE for specified mass bins of width of 2 u for the n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction. The points are experimental data from Ref. 13 measured at thermal incident neutron energy. The dash and full lines are the results obtained under (H1) and (H2) hypotheses respectively.

Figure 18

(Color) Average center-of-mass neutron energy as a function of the mass number of the FF and TKE for ${}^{252}\mathrm{Cf}$(sf).

Figure 19

(Color) Three-dimensional representation of the average neutron multiplicity $\overline{\nu }$ as a function of the mass number of the FF and TKE for ${}^{252}\mathrm{Cf}$(sf).

Figure 20

Average total energy, ${\overline{E}}_{\gamma }$, of γ-rays emitted as a function of FF mass for n(0.53 MeV)+${}^{235}\mathrm{U}$ reaction. The points are from F. Pleasonton et al. [14] for thermal-neutron induced fission of ${}^{235}\mathrm{U}$.