Energy dependence of the prompt $\gamma$-ray emission from the $(d,p)$-induced fission of ${}^{234}\mathrm{U}^{*}$ and ${}^{240}\mathrm{Pu}^{*}$

Prompt-fission $\gamma$ rays are responsible for approximately 5% of the total energy released in fission, and therefore important to understand when modeling nuclear reactors. In this work we present prompt $\gamma$-ray emission characteristics in fission as a function of the nuclear excitation energy of the fissioning system. Emitted $\gamma$-ray spectra were measured, and $\gamma$-ray multiplicities and average and total $\gamma$ energies per fission were determined for the ${}^{233}\text{U}(d,pf)$ reaction for excitation energies between 4.8 and 10 MeV, and for the ${}^{239}\text{Pu}(d,pf)$ reaction between 4.5 and 9 MeV. The spectral characteristics show no significant change as a function of excitation energy above the fission barrier, despite the fact that an extra $\sim 5$ MeV of energy is potentially available in the excited fragments for $\gamma$ decay. The measured results are compared with model calculations made for prompt $\gamma$-ray emission with the fission model code gef. Further comparison with previously obtained results from thermal neutron induced fission is made to characterize possible differences arising from using the surrogate ($d,p$) reaction.

Figure 1

Schematic view of the experimental setup for experiment (A), showing the SiRi ($\mathrm{\Delta }E+E$) telescope, and the NIFF (PPAC) detectors, inside the reaction chamber, surrounded by the CACTUS NaI array. SiRi measures the energy of the outgoing charged particles; NIFF detects fission fragments (FF), and CACTUS detects $\gamma$ rays all in coincidence, within a time interval of 20 ns. The ${}^{233}\mathrm{U}$ target (0.2 mg/${\mathrm{cm}}^2$, green), on the ${}^9\mathrm{Be}$ backing (2.3 mg/${\mathrm{cm}}^2$, orange) was facing NIFF, and SiRi was in the backward direction relative to the beam direction (dotted, purple arrow). The setup for the ${}^{239}\mathrm{Pu}$ experiment was identical, except for CACTUS having 26 crystals instead of 25.

Figure 2

The total (summed over all $E_{\mathrm{x}}$) raw PFGS detected in the ${}^{233}\text{U}(d,pf)$ reaction (black) and the calculated spectral contribution due to interactions of prompt-fission neutrons in the NaI detector (green). The corrected $\gamma$ spectrum is also shown (pink).

Figure 3

Matrix of the fission and proton-gated raw $\gamma$ data from the ${}^{233}\text{U}(d,pf)$ reaction (after subtraction of the contribution from neutrons). The $x$ axis gives the deduced compound nucleus excitation energy $E_x$. The $y$ axis gives the detected $\gamma$-ray energy, and the $z$ axis gives the number of counts recorded during the experiment (not efficiency corrected). The bin width is 64 keV for $E_{\mathrm{x}}$ and $E_{\gamma }$.

Figure 4

The total number of ${}^{233}\text{U}(d,pf)$ and ${}^{233}\mathrm{U}(\mathrm{d},\mathrm{pf}\gamma )$ events recorded during the experiment histogrammed as a function of the deduced compound-nuclear excitation energy of ${}^{234}\mathrm{U}^{*}$ for each event. The inner and outer fission barriers $B_{\mathrm{F},\mathrm{a}}$ at 4.80 MeV and $B_{\mathrm{F},\mathrm{b}}$ at 5.50 MeV, respectively, and the neutron separation energy ${\mathrm{S}}_n$ at 6.85 MeV are shown. The dotted lines indicate the minimum and maximum $E_{\mathrm{x}}$ of the analyzed area. The lower limit on $E_{\mathrm{x}}$ is the inner fission barrier.

Figure 5

Overlay of the eight ${}^{233}\text{U}(d,pf)$ PFGS for different excitation-energy bins in compound-nucleus excitation energy $E_{\mathrm{x}}$. The spectra are normalized to the number of photons per fission and per MeV to provide a comparison of the spectral shapes. The extrapolation from the detector threshold at 450 keV towards zero energy is explained in the text.

Figure 6

Energy dependence of the ${}^{233}\text{U}(d,pf)$ average PFG spectral quantities compared with calculations from the gef code for different $J_{\mathrm{rms}}$ of the ${}^{234}\mathrm{U}^{*}$ nucleus. In addition, results from Pleasonton [17] are shown. Multiplicity, average $\gamma$-ray energy, and total $\gamma$-ray energy as function of excitation energy of ${}^{234}\mathrm{U}^{*}$ are shown. The error bars represent the statistical uncertainty of the measurement. The dash-dotted lines represent the total uncertainty, which is the sum of the systematic uncertainty on the absolute values due to the detector threshold, and the extrapolation towards zero energy plus the statistical uncertainty. Vertical lines mark the inner and outer fission barriers ($E_{\mathrm{x}}=4.8$ MeV and $E_{\mathrm{x}}=5.40$ MeV) and the neutron separation energy ($E_{\mathrm{x}}=6.85$ MeV), respectively.

Figure 7

The total number of ${}^{239}\text{Pu}(d,pf)$ and ${}^{239}\text{Pu}(d,pf\gamma )$ events recorded during the experiment histogrammed as a function of the ${}^{240}\mathrm{Pu}^{*}$ deduced excitation energy event by event. The inner and outer fission barriers $B_{\mathrm{F},\mathrm{a}}$ at 6.05 MeV and $B_{\mathrm{F},\mathrm{b}}$ at 5.15 MeV, respectively, and the neutron separation energy $S_n$ at 6.53 MeV are shown. The dotted lines indicate the minimum and maximum $E_{\mathrm{x}}$ of the analyzed area. The lower limit of $E_{\mathrm{x}}$ is at 4.8 MeV, which is more than 1 MeV below the fission barrier due to subbarrier fission.

Figure 8

Overlay of the six ${}^{239}\text{Pu}(d,pf)$ unfolded PFG gamma spectra for different excitation-energy bins in compound-nucleus excitation energy $E_x$. The spectra are normalized to the number of photons per fission and per MeV to provide a comparison of the spectral shapes. The extrapolation between 140 keV energy and the detector threshold at 450 keV is explained in the text.

Figure 9

Energy dependence of the ${}^{239}\text{Pu}(d,pf)$ PFG average spectral quantities from the gef code for different $J_{\mathrm{rms}}$ of the ${}^{240}\mathrm{Pu}^{*}$ nucleus. The thermal neutron data of Pleasonton (1973) [17] and Verbinski et al. (1973) [15] are shifted slightly around $S_n$ for better visibility. Multiplicity, average $\gamma$-ray energy, and total $\gamma$-ray energy, as function of excitation energy of ${}^{240}\mathrm{Pu}^{*}$ are shown. The error bars represent the statistical uncertainty of the measurement. The dash-dotted lines represent the systematic uncertainty on the absolute values due to the detector threshold and the necessary extrapolation to zero energy. Vertical lines mark the inner and outer fission barriers ($E_{\mathrm{x}}=6.05$ MeV and $E_{\mathrm{x}}=5.15$ MeV) and the neutron separation energy ($E_{\mathrm{x}}=6.5$ MeV), respectively.

Figure 10

A comparison of the ${}^{239}\text{Pu}(d,pf)$ PFGS measured at $E_x\sim S_n$ (red), the PFGS for thermal-neutron-induced fission ${}^{239}\text{Pu}(n_{\text{th}},f)$ from Verbinski et al. [15] (black points), and the calculations by gef for $J_{\mathrm{rms}}=8$ and $E_{\mathrm{x}}=6.35$ (blue).