Impact of prompt-neutron corrections on final fission-fragment distributions

Background: One important quantity in nuclear fission is the average number of prompt neutrons emitted from the fission fragments, the prompt neutron multiplicity, $\overline{\nu }$. The total number of prompt fission neutrons, ${\overline{\nu }}_{\text{tot}}$, increases with increasing incident neutron energy. The prompt-neutron multiplicity is also a function of the fragment mass and the total kinetic energy of the fragmentation. Those data are only known in sufficient detail for a few thermal-neutron-induced fission reactions on, for example, ${}^{233,235}$U and ${}^{239}$Pu. The enthralling question has always been asked how the additional excitation energy is shared between the fission fragments. The answer to this question is important in the analysis of fission-fragment data taken with the double-energy technique. Although in the traditional approach the excess neutrons are distributed equally across the mass distribution, a few experiments showed that those neutrons are predominantly emitted by the heavy fragments.

Purpose: We investigated the consequences of the $\nu (A,\mathrm{TKE},E_{\mathrm{n}})$ distribution on the fission fragment observables.

Methods: Experimental data obtained for the ${}^{234}$U($n,f$) reaction with a Twin Frisch Grid Ionization Chamber, were analyzed assuming two different methods for the neutron evaporation correction. The effect of the two different methods on the resulting fragment mass and energy distributions is studied.

Results: We found that the preneutron mass distributions obtained via the double-energy technique become slightly more symmetric, and that the impact is larger for postneutron fission-fragment distributions. In the most severe cases, a relative yield change up to 20–30$\%$ was observed.

Conclusions: We conclude that the choice of the prompt-neutron correction method has strong implications on the understanding and modeling of the fission process and encourages new experiments to measure fission fragments in coincidence with prompt fission neutrons. Even more, the correct determination of postneutron fragment yields has an impact on the reliable assessment of the nuclear waste inventory, as well as on the correct prediction of delayed neutron precursor yields.

Figure 1

(a) Neutron-multiplicity distributions for the uranium isotopes together with the mass distribution for ${}^{234}$U($n,f$) (see text for details). The data for ${}^{233,235}$U and ${}^{239}$Pu are from Ref. [7]. (b) The total average neutron multiplicity ${\overline{\nu }}_{\mathrm{tot}}$ as a function of incident neutron energy. For ${}^{234}$U a linear fit was used, based on Ref. [8].

Figure 2

The full neutron multiplicity distribution from Eq. (2) as a function of fragment mass for the (AV) method. The spread of $\nu$($A$, TKE) is attributable to the TKE dependence.

Figure 3

The prompt neutron multiplicity distribution, $\overline{\nu }$($A$), for the three cases discussed in this work: $\overline{\nu }$($A$) taken at thermal incident-neutron energy (black circles), $\overline{\nu }$($A$) distributing the excess neutrons amongst all fission fragments (AV method, red squares), assuming the excess neutrons coming only from the heavy fragments with mass larger than 120 (HE method, blue triangles) increases $\overline{\nu }$ and introduces an artificial step at $A=120$.

Figure 4

(a) The difference in neutron multiplicity, as a function of mass, between the AV and HE methods. (b) The difference in $\langle$TKE ($A$)$\rangle$ for the AV and HE methods, as a function of fragment mass, $A$.

Figure 5

(a) Post-neutron-emission kinetic energy as a function of post-neutron-emission mass for $E_{\mathrm{n}}=5$ MeV. (b) The difference in $\langle E_{\mathrm{kin}}\rangle$ between the AV and the HE methods. A relative change of 0.75 MeV is observed for the heavy fragments.

Figure 6

The mass distributions for the 5 MeV case for heavy and light fragments, respectively. The pre-neutron-emission yields are to the left and the post-neutron-emission yields are shown to the right.

Figure 7

(a) The absolute mass difference of the AV and HE methods, shown for the pre-neutron-emission mass distribution. (b) The corresponding difference in post-neutron-emission mass distribution. Both distributions become more symmetric using the HE method and the differences are larger in the post-neutron-emission case. Note that these are absolute yield differences and that the maximum mass yield is typically 6–7$\%$.

Figure 8

The relative change between the two correction methods, as a function of post-neutron-emission mass. The yield change introduced by the wrong correction method is around 15$\%$ for $A=90$, 102, 132, and 145 and may reach 20–30$\%$ for very symmetric or asymmetric masses.

Figure 9

(a) The TKE and mean pre-neutron-emission mass as a function of the total neutron emission for the AV method. The original parametrization from Eq. (1) was scaled to the different $\overline{\nu }$ values. The change in $\langle$TKE$\rangle$ (b) and pre-neutron-emission mass, $\langle A_{\mathrm{H}}\rangle$ (c), for the two approaches, fitted linearly.