High accuracy 234 U ( n , f ) cross section in the resonance energy region

New results are presented of the 234U neutron-induced fission cross section, obtained with high accuracy in the resonance region by means of two methods using the 235U(n,f) as reference. The recent evaluation of the 235U(n,f) obtained with SAMMY by L. C. Leal et al. (these Proceedings), based on previous n TOF data [1], has been used to calculate the 234U(n,f) cross section through the 234U/235U ratio, being here compared with the results obtained by using the n TOF neutron flux.


Introduction
The 234 U isotope is present in the uranium-enriched fuel of current reactors and is also produced during the thorium-fuel cycle.Because of its relatively low (n,f) cross section, data found in current nuclear databases could be sufficient for a first evaluation of critical reactors as well as for Accelerator Driven Systems.Nevertheless, a detailed assessment of relevant integral reactor quantities requires a more precise and complete set of basic nuclear data for this important isotope.Experimental datasets available in EXFOR as well as data in the evaluated libraries [2] show discrepancies.The ENDF/B-VII.1 and JENDL-4.0 evaluations are shifted in energy and some resonances are missing in one of the two databases.In the Resolved Resonance Region (RRR), both evaluations are based on the experimental data of James et al. [3], but JENDL-4.0 includes also the resonance parameters provided by Dridi et al. [4] for the capture reaction and the fission cross section of Heyse et al. [5] for the 5.17 eV resonance.Above

The experimental setup
The 234 U(n,f) cross section was measured in 2012 during the so-called Phase-II at the CERN-n TOF facility [6] using ten PPACs consisting of one central anode with a very fast signal (time resolution ∼500 ps) and two segmented cathodes, used to measure the two coordinates of the fission fragment (FF) hit [7].The targets, which consisted of thin radioactive layers electrodeposited on an aluminium foil, were interleaved with ten PPAC detectors.The data here presented correspond to three 234 U and two 235 U targets.The thickness of the Al backing was 2.0 µm for the 234 U and one 235 U and 0.7 µm for the second 235 U target.There was a slight isotopic contamination in the 235 U targets of 234 U (0.74%), 236 U (0.27%) and 238 U (6.28%), as well as a 235 U (0.077%) content in the 234 U targets, which has been subtracted during the data analysis.
The n TOF spallation target in previous PPAC experiments, performed during the Phase-I [1,8] used normal water as the neutron moderator, which was changed to borated water in the last campaign of Phase-II when the data presented in this work have been taken.Important differences in the neutron flux are observed below hundreds of eV depending on the type of moderator material [9].
The PPAC configuration was also modified in Phase-II.The detectors and targets were tilted by 45 • with respect to the neutron beam direction in order to reach up to 90 • angular acceptance of the FF detection compared to the 60 • achieved with the perpendicular setup used in Phase-I, see Ref. [7] for details.

Data analysis and results
The fission cross section (σ ) is related to the number of detected fission events (C) per unit of incident neutron energy (E n ) by: where is the neutron fluence, is the detection efficiency and N is the areal density of a target (x) of radius R.

235 U(n,f) cross section
As the neutron fluence received by the targets during the experiment is not accurately known, the 235 U(n,f) has been used as a reference in the 234 U(n,f) cross section calculation.However, the n TOF neutron flux shape was known [10] and was normalised with Eq. (1) using the 235 U(n,f) cross section area of 246.4 ± 1.2 b • eV given by the IAEA in the neutron energy interval from 7.8 to 11 eV as explained in Ref. [1].
The 235 U(n,f) cross section, obtained as the mean value of both 235 U targets, is compared in Fig. 1 with the recent evaluation presented in this conference by L. C. Leal et al., based on the data of Paradela et al. [1], and with the ENDF/B-VII.1 database.The averaged integral cross sections, calculated with the Analysis of Geel Spectrum (AGS) code [11], are provided in Table 1 where the ratios of the n TOF data to those in each column are given in parentheses for different energy regions.

234 U(n,f) cross section
The 234 U(n,f) cross section is calculated in this work by means of two methods, both based on the fact that all targets receive the same neutron flux and assuming that the efficiency of all detectors is the same within the uncertainties we are dealing with.With the first method (n TOF 1 ), the 235 U(n,f) cross section obtained in the previous subsection has been used as a reference.The normalisation factor is inversely proportional to N 5 • so, assuming that the efficiency is the same for all detectors, we can get the 234 U(n,f) cross section via the relation between the areal densities of the samples given by:  The second method (n TOF 2 ) is based on the ratio of the number of fission events obtained for the 234 U and 235 U samples, using the 235 U(n,f) cross section evaluated by L.C. Leal et al., with Eq. ( 1), where the neutron flux and the efficiency cancel.The cross section obtained by the first method is compared in Fig. 2 with the experimental data provided by EXFOR and with the ENDF/B-VII.1 and JENDL-4.0 evaluations.The data presented in this work have better resolution than the others, being closer to the previous n TOF data measured by Paradela et al. [8].A slight energy offset is observed between the ENDF/B-VII.1 and JENDL-4.0 evaluations in addition to differences in the cross sections.This energy shift is also observed between the evaluations and the experimental data, being more pronounced in the case of the JENDL-4.0 database.
Above the RRR some groups of fission resonances are observed in the experimental data, which are not evaluated in the databases, as can be seen in Fig. 3.
The averaged integral cross sections calculated with both methods are given in Table 2 for different energy regions, compared with Paradela et al., ENDF/B-VII.1 and JENDL-4.0.The ratios of the first column data over the values in the other columns are given in parentheses.On average, the differences between n TOF 1 and the other columns in Table 2 are respectively 0.9% (n TOF 2 ), −18% (Paradela), −76% (ENDF/B-VII.1)and −73% (JENDL-4.0).

Conclusions
The 234 U(n,f) cross section data has been obtained by means of two approaches, being in very nice agreement between them.When comparing these data with the    2. experimental data provided by EXFOR, a better resolution is observed in the present data, having a shape very close to the previous n TOF data in [8].Huge discrepancies have been found in the cross sections and energies with the evaluations in the ENDF/B-VII.1 and JENDL-4.0 libraries.
The averaged integral cross section ratios given in parentheses in Table 2 are shown in Fig. 4, differing by factors of 0.5 to 5. It is worth to mention the good agreement between both experimental methods, the difference of −18% with respect to Paradela et al. [8] and the severe disagreement with the evaluated libraries.
1.5 keV, in the Unresolved Resonance Region (URR), the fission data of James et al. and the capture data of Pennington were used in ENDF/B-VII.1 whereas JENDL-4.0 used the experimental data sets mentioned in Ref. [2].The 234 U(n,f) cross section data presented in this work, in the neutron energy range from 3 eV up to 10 MeV, have been measured at the Neutron Time-of-Flight (n TOF) facility at CERN with an improved detection setup based on Parallel Plate Avalanche Counters (PPACs).

1 Figure 1 .
Figure 1. 235U(n,f) cross section data.The dashed vertical lines correspond to the normalisation limits.

Figure 2 .
Figure 2. 234 U(n,f) cross section data in different energies of the RRR.

Figure 4 .
Figure 4. Ratio of the 234 U(n,f) integral cross sections averaged over the energy ranges given in Table2.

f
Figure 3. 234 U(n,f) cross section data in the 7 keV energy region.