Measurement of the $\alpha$ ratio and $(n,\gamma )$ cross section of ${}^{235}\mathrm{U}$ from 0.2 to 200 eV at n_TOF

We measured the neutron capture-to-fission cross-section ratio ($\alpha$ ratio) and the capture cross section of ${}^{235}\mathrm{U}$ between 0.2 and 200 eV at the n_TOF facility at CERN. The simultaneous measurement of neutron-induced capture and fission rates was performed by means of the n_TOF ${\mathrm{BaF}}_2$ Total Absorption Calorimeter (TAC), used for detection of $\gamma$ rays, in combination with a set of micromegas detectors used as fission tagging detectors. The energy dependence of the capture cross section was obtained with help of the ${}^6\mathrm{Li}(n,t)$ standard reaction determining the n_TOF neutron fluence; the well-known integral of the ${}^{235}\mathrm{U}(n,f)$ cross section between 7.8 and 11 eV was then used for its absolute normalization. The $\alpha$ ratio, obtained with slightly higher statistical fluctuations, was determined directly, without need for any reference cross section. To perform the analysis of this measurement we developed a new methodology to correct the experimentally observed effect that the probabilities of detecting a fission reaction in the TAC and the micromegas detectors are not independent. The results of this work have been used in a new evaluation of ${}^{235}\mathrm{U}$ performed within the scope of the Collaborative International Evaluated Library Organisation (CIELO) Project, and are consistent with the ENDF/B-VIII.0 and JEFF-3.3 capture cross sections below 4 eV and above 100 eV. However, the measured capture cross section is on average 10% larger between 4 and 100 eV.

Figure 1

Schematic view of part of the n_TOF TAC, together with beam pipes and half of a neutron absorber inside (not the one used in this measurement). Some of the ${\mathrm{BaF}}_2$ modules are not shown, to make it possible to see the center. ${\mathrm{BaF}}_2$ crystals with pentagonal and hexagonal shapes appear, respectively, in red and blue.

Figure 2

Picture of the FTMG detectors used during the ${}^{235}\mathrm{U}(n,\gamma$) campaign.

Figure 3

Picture of the fission chamber placed in the center of the TAC. In white, half of the borated polyethylene neutron absorber shell.

Figure 4

Fission cross section obtained with the FTMG detectors (this work) compared with JEFF-3.3, in two different neutron energy ranges. The residuals correspond to the difference between the measured and the evaluated cross sections divided by the uncertainty due to counting statistics.

Figure 5

Total deposited energy registered by the TAC, in anticoincidence with the FTMG detectors, during the ${}^{235}\mathrm{U}(n,\gamma$) measurement (Total), together with different contributions to the total spectrum (see the text for details). The data correspond to neutron energies between 1 and 20 eV and $m_{cr}>2$. The full capture $Q$ peak is broadened due to the presence of the neutron absorber and a long-lived isomeric state of ${}^{236}\mathrm{U}$.

Figure 6

Number of events detected in the TAC in anticoincidence with the FTMG detectors in the ${}^{235}\mathrm{U}(n,\gamma$) measurement (Total) per pulse and per unit lethargy ($\mathrm{\Delta }ln\mathrm{E}$, which means that the bin contents have been divided by the natural logarithm of the ratio between the upper and lower bin limits) as a function of neutron energy, together with different background components. Only events with $2<m_{cr}<6$ and $2.5<E_{\mathrm{sum}}<7$ MeV are considered.

Figure 7

Number of events detected in the TAC in anticoincidence with the FTMG detectors in the ${}^{235}\mathrm{U}(n,\gamma$) measurement (Total) per pulse and per unit lethargy as a function of neutron energy (same as in Fig. 6), together with the total background (Background) and the counts due to ${}^{235}\mathrm{U}(n,\gamma$) reactions (Capture).

Figure 8

Time difference distribution between events from the TAC and the FTMG detectors, for times of flight corresponding to neutron energies between 0.2 and 1.2 eV. Three different cuts in the TAC events were considered: no cuts (Cond01); $E_{\mathrm{sum}}<2.5$ MeV and $m_{cr}\le 4$ (Cond02); and $E_{\mathrm{sum}}>2.5$ MeV and $m_{cr}>4$ (Cond03). The dotted line is the estimate of random coincidences.

Figure 9

Total deposited energy spectra in the TAC in coincidence with the FTMG detectors. Each spectrum was constructed by setting different conditions in the FTMG amplitude “Amp,” which ranges from 30 to 170 ADC channels. The spectra are normalized to (a) the total area and (b) the $E_{\mathrm{sum}}>10$ MeV region.

Figure 10

Ratio between tagged fission events $c_{tag}$ for ${\{E_{\mathrm{sum}},m_{cr}\}}_a$ and ${\{E_{\mathrm{sum}},m_{cr}\}}_b$ cuts, for different intervals of the amplitude of the FTMG signals (Amp). The first interval, inside the shadowed rectangle, does not correspond to experimental data. It represents the fissions not detected by the FTMG detectors, and its value is the same as the interval just above the amplitude threshold. The horizontal lines represent the average ratio calculated with (dashed) and without (solid) this first interval. Vertical error bars correspond to uncertainties due to counting statistics.

Figure 11

Experimental (solid lines) and simulated (dotted lines) total deposited energy spectra from ${}^{235}\mathrm{U}(n,\gamma$) cascades for different cuts in $m_{cr}$, for the geometry with the neutron absorber.

Figure 12

Experimental (solid lines) and simulated (dotted lines) total deposited energy spectra from ${}^{235}\mathrm{U}(n,\gamma$) cascades for different cuts in $m_{cr}$, for the geometry without the neutron absorber.

Figure 13

Ratio between the number of counts in coincidence between both detection systems ($c_{tag}$) and the number of counts in the FTMG detectors ($c_{tot,f}$), as a function of neutron energy and for two different cuts in the TAC events. The experimental values are shown in histograms, whose error bars are due to the counting statistics. They have been normalized to the content of the first bin. The dotted lines correspond to the predictions of the pile-up model developed for this work.

Figure 14

One minus the fraction of ${}^{235}\mathrm{U}(n,\gamma$) events lost ($f_{\mathrm{losses}}$) due to the pile-up, as a function of neutron energy. Three different cuts have been considered, all of them with $2.5<E_{\mathrm{sum}}<7$ MeV but with different $m_{cr}$ conditions.

Figure 15

Magnitude of the different sources of uncertainty in the capture cross section, as a function of neutron energy. The total uncertainty was calculated as the quadratic sum of the ${\varepsilon }_f$, ${\varepsilon }_{\gamma }$, $\mathrm{\Delta }\text{bkg}$, $\mathrm{\Delta }\text{norm}$, and $\mathrm{\Delta }$pile-up contributions; it corresponds to the total uncertainty due to systematic effects.

Figure 16

(a) $\alpha$ ratio of ${}^{235}\mathrm{U}$ obtained in this work together with those in the JEFF-3.3, ENDF/B-VIII.0, and ENDF/B-VII.1 data libraries, between 4 and 20 eV. The error bars correspond to uncertainties due to counting statistics. The residuals (measured minus evaluated divided by the uncertainty due to counting statistics) in comparison with (b) JEFF-3.3, (c) ENDF/B-VIII.0, and (d) ENDF/B-VII.1 are also shown.

Figure 17

Average ${}^{235}\mathrm{U}$ capture ($x=\gamma$) and fission ($x=f$) cross sections $\langle {\sigma }_x\rangle ={\int }_{E_1}^{E_2}{\sigma }_x\left(E\right)dE/(E_2-E_1)$ obtained in this work together with those in the JEFF-3.3, ENDF/B-VIII.0, and ENDF/B-VII.1 data libraries. In particular, the figures show (a) the capture cross section and the ratios between the evaluated values and those obtained in this work for (b) the capture cross section, (c) the fission cross section, and (d) the ratio between them. The uncertainties shown correspond to the quadratic sum of those from counting statistics and systematic effects (Fig. 15). In (b)–(d) the uncertainties are indicated in $y=1$, and are the same for the three plotted ratios.

Figure 18

Ratio between the capture cross sections reported by other ${}^{235}\mathrm{U}(n,\gamma$) cross-section measurements—Jandel et al. [7], Perez et al. [72], De Saussure et al. [18], and Gwin et al. [73]—and this work.

Figure 19

In the upper panels, capture cross section obtained in this work compared with JEFF-3.3. In the bottom panels, ratio of the evaluated cross-section resonance integrals compared to the experimental data. Uncertainties due to counting statistics are given by the vertical error bars. Uncertainties due to systematic effects associated to the calculation of ${\varepsilon }_f$ and to the subtraction of the background related with the interaction of the neutron beam with materials different than the ${}^{235}\mathrm{U}$ targets ($\mathrm{\Delta }\text{bkg}$) are given by horizontal error bars, which also define the integration ranges. The uncertainties appear only in the ratios with JEFF-3.3, but they are the same in the ratios with ENDF/B-VIII.0 and ENDF/B-VII.1.

Figure 20

The same as in Fig. 19 but for different neutron energy range.