Neutron-induced fission cross sections of ${}^{232}\mathrm{Th}$ and ${}^{233}\mathrm{U}$ up to 1 GeV using parallel plate avalanche counters at the CERN n_TOF facility

The neutron-induced fission cross sections of ${}^{232}\mathrm{Th}$ and ${}^{233}\mathrm{U}$ were measured relative to ${}^{235}\mathrm{U}$ in a wide neutron energy range up to 1 GeV (and from fission threshold in the case of ${}^{232}\mathrm{Th}$, and from 0.7 eV in case of ${}^{233}\mathrm{U}$), using the white-spectrum neutron source at the CERN Neutron Time-of-Flight (n_TOF) facility. Parallel plate avalanche counters (PPACs) were used, installed at the Experimental Area 1 (EAR1), which is located at 185 m from the neutron spallation target. The anisotropic emission of fission fragments were taken into account in the detection efficiency by using, in the case of ${}^{233}\mathrm{U}$, previous results available in EXFOR, whereas in the case of ${}^{232}\mathrm{Th}$ these data were obtained from our measurement, using PPACs and targets tilted ${45}^{\circ }$ with respect to the neutron beam direction. Finally, the obtained results are compared with past measurements and major evaluated nuclear data libraries. Calculations using the high-energy reaction models INCL$++$ and ABLA07 were performed and some of their parameters were modified to reproduce the experimental results. At high energies, where no other neutron data exist, our results are compared with experimental data on proton-induced fission. Moreover, the dependence of the fission cross section at 1 GeV with the fissility parameter of the target nucleus is studied by combining those $(p,f)$ data with our $(n,f)$ data on ${}^{232}\mathrm{Th}$ and ${}^{233}\mathrm{U}$ and on other isotopes studied earlier at n_TOF using the same experimental setup.

Figure 1

Schematic views (not to scale) of the PPAC detectors and the targets used during Phase 1 (a) and Phase 2 (b). The targets studied in this work are indicated by the red rectangles. A photo of the stack of PPACs and targets used in Phase 2 can be seen in (c), where the arrow follows the neutron beam direction, and points to the aluminized electrode of the first PPAC. The active area of each PPAC is $20\times 20{\mathrm{cm}}^2$.

Figure 2

Reference system used to calculate the emission angle $\theta$ of the fission fragments (FFs) in Phase 2, where PPACs and targets are tilted ${45}^{\circ }$ with respect to the neutron beam direction. Fission fragments emitted at every possible value of $\theta$ between $0^{\circ }$ and ${90}^{\circ }$ can be detected. See Ref. [20] for a more detailed description.

Figure 3

Fission yield ratios between each sample of ${}^{232}\mathrm{Th}$ and the average, during Phase 1 (a) and Phase 2 (b). The horizontal lines represent the average standard deviations.

Figure 4

Experimental values of the anisotropy parameter $A=W\left(0^{\circ }\right)/W\left({90}^{\circ }\right)$ for the neutron-induced fission of ${}^{233}\mathrm{U}$ (a) [23, 24, 25, 26, 27, 28, 29, 30, 31] and ${}^{235}\mathrm{U}$ (b) [24, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 38, 39, 40] retrieved from EXFOR, as a function of the neutron energy. The solid lines represent the parametrizations of the anisotropy used in this work.

Figure 5

Experimental values of the anisotropy parameter $A=W\left(0^{\circ }\right)/W\left({90}^{\circ }\right)$ for the neutron-induced fission of ${}^{232}\mathrm{Th}$ as a function of neutron energy. The solid line connects the values deduced from the experimental angular distributions measured in our earlier works [20, 41], and whose fits to Eq. (4) are used in the present work. Below 100 MeV, second- and fourth-order terms were needed to describe the features of the angular distribution [20], whereas above 100 MeV, the second-order term was enough [41]. Other experimental values on the anisotropy parameter, directly retrieved from EXFOR, are shown for comparison [24, 26, 28, 33, 42, 43, 44, 45, 46, 47].

Figure 6

Detection efficiency of the tilted setup (Phase 2) as a function of the emission angles $\theta$ and $\varphi$, according to geant4 simulations. The red lines represent the contour used to calculate the total efficiency. More details about the detection efficiency on this setup can be found in Ref. [20].

Figure 7

Angular contribution to the detection efficiency ratios between the reference isotope ${}^{235}\mathrm{U}$, and the studied samples of ${}^{232}\mathrm{Th}$ and ${}^{233}\mathrm{U}$.

Figure 8

Comparison of different evaluations of the ${}^{235}\mathrm{U}(n,f)$ cross section above 100 MeV: JENDL/HE-2007 [50], the IAEA High-Energy reference [52], and the evaluation by Duran et al. [53].

Figure 9

Fission cross section ratio of ${}^{232}\mathrm{Th}$ relative to ${}^{235}\mathrm{U}$, compared with previous results [54, 55, 56]. Panel (b) shows a detailed view around fission threshold of the full range in (a). The error bars in our data represent statistical uncertainties.

Figure 10

The final cross section of ${}^{232}\mathrm{Th}(n,f)$ obtained in the present work is compared with previous results available in the EXFOR database [54, 56, 57, 58, 59, 60] and with the ENDF/B-VIII.0 evaluation [1]. The full energy range is shown in (a). For clarity, detailed views covering different energy ranges are shown in separate panels: (b) shows the threshold for first-chance fission, while the second-chance fission threshold is displayed in (c); the high energy range can be seen in (d).

Figure 11

Fission cross section ratio of ${}^{233}\mathrm{U}$ relative to ${}^{235}\mathrm{U}$ from 10 keV up to 1 GeV, compared with previous results [54, 56, 63, 64]. The error bars in our data represent statistical uncertainties.

Figure 12

Final cross section of ${}^{233}\mathrm{U}(n,f)$ obtained in the present work. Previous experimental data [54, 63, 64, 65, 66] and evaluations [1, 2] are shown for comparison. The low-energy resonance region can be seen in (a), and the URR in (b) and (c). The high-energy region, between 0.1 MeV and 1 GeV, is plotted in (d). Panel (e) shows a detailed view on the limit at 600 eV of the evaluated RRR. Panel (f) plots the lowest neutron energies available at n_TOF; the region 8.1–14.7 eV is being considered for an integral cross-section standard (see text for details).

Figure 13

Ratios between our data and evaluations from the major libraries [1, 2, 3, 68, 69] for the fission cross section ratios ${\sigma }_f{(}^{232}\text{Th})/{\sigma }_f{(}^{235}\text{U})$ (a) and ${\sigma }_f{(}^{233}\text{U})/{\sigma }_f{(}^{235}\text{U})$ (b).

Figure 14

Ratio between our data and the ENDF/B-VIII.0 evaluation [1] for ${\sigma }_f{(}^{233}\text{U})$ below 10 keV.

Figure 15

Our results on neutron-induced fission cross sections for ${}^{232}\mathrm{Th}$ (a) and ${}^{233}\mathrm{U}$ (b) are shown together with the calculated values from the combination of reaction codes incl$++$ and abla07. Proton-induced data from Ref. [72] are also shown for comparison.

Figure 16

Experimental data on fission cross section for proton- and neutron-induced fission, at 1 GeV nucleon energy, as a function of the fissility parameter of the target nucleus. Proton-induced data are from Kotov et al. [72]. The neutron-induced data include the present work and our earlier data obtained with PPACs at n_TOF [14, 15, 16], updated by using the ${}^{235}\mathrm{U}$ cross section from Ref. [53] as reference, which is also included in the figure. The error bars include both statistical and systematic uncertainties.