Examination of how properties of a fissioning system impact isomeric yield ratios of the fragments

The population of isomeric states in the prompt decay of fission fragments—so-called isomeric yield ratios (IYRs)—is known to be sensitive to the angular momentum $J$ that the fragment emerged with, and may therefore contain valuable information on the mechanism behind the fission process. In this work, we investigate how changes in the fissioning system impact the measured IYRs of fission fragments to learn more about what parameters affect angular momentum generation. To enable this, a new technique for measuring IYRs is first demonstrated. It is based on the time of arrival of discrete $\gamma$ rays, and has the advantage that it enables the study of the IYR as a function of properties of the partner nucleus. This technique is used to extract the IYR of ${}^{134}\mathrm{Te}$, strongly populated in actinide fission, from the three different fissioning systems: ${}^{232}\mathrm{Th}(n,\mathrm{f}), {}^{238}\mathrm{U}(n,\mathrm{f})$, at two different neutron energies, as well as ${}^{252}\mathrm{Cf}$(sf). The impacts of changing the fissioning system, the compound nuclear excitation energy, the minimum $J$ of the binary partner, and the number of neutrons emitted on the IYR of ${}^{134}\mathrm{Te}$ are determined. The decay code talys is used in combination with the fission simulation code freya to calculate the primary fragment angular momentum from the IYR. We find that the IYR of ${}^{134}\mathrm{Te}$ has a slope of $0.004\pm 0.002$ with increase in compound nucleus (CN) mass. When investigating the impact on the IYR of increased CN excitation energy, we find no change with an energy increase similar to the difference between thermal and fast fission. By varying the mass of the partner fragment emerging with ${}^{134}\mathrm{Te}$, it is revealed that the IYR of ${}^{134}\mathrm{Te}$ is independent of the total amount of prompt neutrons emitted from the fragment pair. This indicates that neutrons carry minimal angular momentum away from the fission fragments. Comparisons with the freya$+$talys simulations reveal that the average angular momentum in ${}^{134}\mathrm{Te}$ following ${}^{238}\mathrm{U}(n,\mathrm{f})$ is $6.0\hslash$. This is not consistent with the value deduced from recent cgmf calculations. Finally, the IYR sensitivity to the angular momentum of the primary fragment is discussed. These results are not only important to help understanding the underlying mechanism in nuclear fission, but can also be used to constrain and benchmark fission models, and are relevant to the $\gamma$-ray heating problem of reactors.

Figure 1

The experimental $E_{\gamma }$ spectrum for the reactions (a) ${}^{238}\mathrm{U}(n,\mathrm{f})$ and (b) ${}^{232}\mathrm{Th}(n,\mathrm{f})$ at ${\overline{E}}_n=$ 1.9 and 2.0 MeV respectively; (c) ${}^{252}\mathrm{Cf}$(sf); as well as (d) the multiplicity distribution $M$ for fission events. The 1279 keV $\gamma$ ray from ${}^{134}\mathrm{Te}$ is indicated in (a)–(c). In (d), the shape of the ${}^{238}\mathrm{U}/{}^{232}\mathrm{Th}$ multiplicity distributions are slightly different from ${}^{252}\mathrm{Cf}$ due to the exclusion of $M<2$ events, as described in the text. The distributions are therefore normalized in the range $M=[2,15]$.

Figure 2

The experimental $E_{\gamma }-E_{\gamma }$ coincidence spectrum following ${}^{238}\mathrm{U}(n,\mathrm{f})$ at ${\overline{E}}_n=$ 1.9 MeV. The circle in the inset shows coincidences between the 1279 and 297 keV $\gamma$ rays following the decay of ${}^{134}\mathrm{Te}$.

Figure 3

Illustration of the lowest-lying levels of ${}^{134}\mathrm{Te}$, constructed using energies and feeding values found in Ref. [20]. There are no additional transitions between the levels, i.e., the $6^{+}$ state decays only to the $4^{+}$ state, etc. The side-feeding branches, where the decay bypasses, e.g., the $4^{+}$ and goes directly to the $2^{+}$, are also indicated. The shaded area represents the double gate on discrete $\gamma$ rays used in this work.

Figure 4

Background-subtracted spectrum showing the time of arrival of a pair of 297 and 1279 keV $\gamma$ rays, created using gates on the $4^{+}\to 2^{+}$ and $2^{+}\to 0^{+}$ transitions in ${}^{134}\mathrm{Te}$. The components of the fitted spectrum are also shown, along with the fit range.

Figure 5

Illustration of partner gating following ${}^{238}\mathrm{U}(n,\mathrm{f})$, where one $\gamma$ gate is placed in ${}^{134}\mathrm{Te}$ and the other in ${}^{102}\mathrm{Zr}$.

Figure 6

Isomeric yield ratios of ${}^{134}\mathrm{Te}$ as a function of the compound nucleus mass number, using gates on $2^{+}\left[{}^{134}\mathrm{Te}\right]$&$4^{+}\left[{}^{134}\mathrm{Te}\right]$. The linear uncertainty-weighted fit to the data points is also shown.

Figure 7

Isomeric yield ratios of ${}^{134}\mathrm{Te}$ from the reactions ${}^{238}\mathrm{U}(n,\mathrm{f})$ and ${}^{232}\mathrm{Th}(n,\mathrm{f})$ when a gate is placed on $2^{+}\left[{}^{134}\mathrm{Te}\right]$ and a specified transition in the partner.

Figure 8

Isomeric yield ratios of ${}^{134}\mathrm{Te}$ from the reactions ${}^{238}\mathrm{U}(n,\mathrm{f})$ and ${}^{232}\mathrm{Th}(n,\mathrm{f})$ when a gate is placed on $2^{+}\left[{}^{134}\mathrm{Te}\right]$ and the gate on the partner is changed.

Figure 9

The IYR of ${}^{134}\mathrm{Te}$ as a function of the average initial angular momentum $J_{\text{i}}$ of the primary fission fragment from the reaction ${}^{238}\mathrm{U}(n,\mathrm{f})$ at $E_n=1.9$ MeV. In (a), the IYR are only shown for the different neutron channels, and (b) shows the summed contribution for the $n>0$ channels. In (b), the value of the measured IYR is marked along with ${\overline{J}}_{\text{i}}$ to which it corresponds.