Spectral averaged cross sections as a probe to a high energy tail of 235 U PFNS

. The systematic evaluations of spectrum averaged cross sections of dosimetric reactions over a broad range of energies were performed in 252 Cf (spontaneous fission) and 235 U(n th ,f) neutron fields. The neutron sources used in this study were LR-0, VR-1 zero power research light water reactors, LVR-15 10 MW research light water reactor, and 252 Cf neutron source with emission specified precisely by the manganese sulphate bath. All spectral averaged cross sections were inferred from measured reaction rates which were derived from gamma spectrometry. These gamma spectrometry measurements were performed using a single detector in all cases. The ratios of 252 Cf and 235 U spectral averaged cross sections can be used to specify the high energy tail of the 235 U prompt fission neutron spectrum as the 252 Cf spontaneous fission spectrum is considered as a standard. Furthermore, ratios are independent of cross section uncertainties since uncertainties in the cross sections are eliminated. Theoretical models of fission can be tested based on our measurements. The calculations were performed in MCNP6.2 transport code using different prompt fission neutron spectra and IRDFF-II cross sections for threshold reactions. The ratios are in good agreement using only ENDF/B-VIII.0 235 U prompt fission neutron spectrum suggesting it to be harder than in other evaluations.


Introduction
The 235 U prompt fission neutron spectrum (PFNS) is discrepant above 10 MeV since the existing differential experimental data above 10 MeV are contradictory [1]. State of the art ENDF/B-VIII.0 [2] and JEFF-3.3 [3] nuclear data libraries significantly differ in 235 U PFNS above 10 MeV, see Figure 1. On the contrary, 252 Cf(sf) is the only neutron standard. This source was used for the validation of dosimetric cross sections included in the IRDFF-II library [4]. Reliable estimation of 235 U PFNS is very important as it is used for the safety and regulatory applications in commercial fission reactors, reactor dosimetry, and also from the theoretical point of view. The suitable quantity for assessing the high energy tail are spectral averaged cross sections (SACS) for dosimetric reactions since they are loaded with lower uncertainties than differential data. As the 252 Cf(sf) is the neutron standard, the SACS in its spectrum can be assumed as precisely determined. The ratios of 235 U and 252 Cf SACS can then help for a better estimation of the 235 U PFNS shape. Furthermore, ratios are independent of cross section uncertainties since uncertainties in the cross sections are eliminated.
The systematic evaluations of spectrum averaged cross sections of dosimetric reactions over a broad range of energies were performed in 252 Cf (spontaneous fission) and 235 U(nth,f) neutron fields. All spectral averaged cross sections were inferred from measured reaction rates which were derived from gamma spectrometry.
These gamma spectrometry measurements were performed using a single detector in all cases.

Neutron sources description
The neutron sources used for SACS estimations in experiments were: LR-0, VR-1 and LVR-15 light water reactors, and 252 Cf isotopic source.

U PFNS Comparison
The LR-0 research reactor is a zero-power light water pool type reactor. The specially designed reference core [5] consists of six uranium fuel assemblies with nearly 3.3% 235 U enrichment surrounding a dry assembly with activation foils to be irradiated. Used fuel assemblies are the same as the VVER-1000 type in the radial direction but in the axial direction, they are shortened to 125 cm. Reactor criticality is achieved by variation of a light water level only. Characterization of the special core was performed by the experiments dealing with reactivity characterization [6], fission rates distribution [7], and also neutron spectra measurement using a stilbene scintillation detector [8]. Details about SACS measurements in LR-0 can be found in [9], [10], [11].
The VR-1 research reactor is also a light-water, zero-power pool-type reactor located in Prague. The core consists of tubular fuel assemblies of IRT-4M type enriched to 19.75 wt. % of 235 U, and contains several dry vertical channels with different diameters up to 90 mm and one radial channel with a diameter of 250 mm. The activation targets were placed in the center of a 25 mm channel located in the center of the fuel assembly positioned close to the radial channel of the reactor. The criticality of the reactor during irradiation was managed by the moving of the control rods. The details of the experiments and SACS measurements can be found in [12].
Unlike above mentioned zero power reactors, LVR-15 is a 10 MWt reactor with forced cooling. As well as the VR-1 reactor, LVR-15 employs IRT-4M fuel with an enrichment of 19.7% of 235 U. The fuel has a burn-up due to the high operating power. Fuel composition is calculated using an onsite developed code NODER [13]. The measurement of SACS was performed near the fuel, where a high flux of high energy neutrons is achieved [14].
The 252 Cf isotopic source involved in 252 Cf experiments had initial emission of (9.53±0.11)•10 8 n/s. The emission was measured in the National Physical Laboratory, UK by means of a manganese sulphate bath. The experiments were performed during source emission between 2.9E8 n/s and 8.0E8 n/s. The experimental uncertainties and irradiation geometry of low and high volume sources were extensively described in [15]. The performed set of experiments involving 252 Cf was described in [16][17][18][19].

Calculation methods
All irradiated samples were measured using a single high purity germanium (HPGe) detector in a vertical configuration (ORTEC GEM35P4). The experimental reaction rates were derived from the Net Peak Areas (NPA) measured using the HPGe detector. These reaction rates q were used to derive the SACS by means of the following equation: where: q is the experimental reaction rate per atom per second, N is the number of target isotope nuclei, ε is the detector efficiency, η is gamma branching ratio, λ is the decay constant, k characterizes the abundance of isotope of interest in the target and its purity, ΔT is the time between the end of irradiation and start of measurement, C(Tm) is the measured number of counts, Tm is the real time of measurement by HPGe, Tl is the live time of measurement by HPGe (it is time of measurement corrected to the dead time of the detector), and Tirr is the time of irradiation. The coincidence summing was estimated for each sample separately. The method of efficiency calculation is described in [9].
The SACS is derived from reaction rate q by correction factor C which considers the spectral shift effect, flux loss, and self-shielding together. The correction is computed by means of MCNP6.2 [20] as a ratio between the SACS in the real set-up and the SACS in the same set-up consisting of void cells. The SACS are derived via Equation 2: where C denotes the correction factor, (E) is the calculated neutron spectrum, ( ) is the cross section and denotes SACS. Table 1 shows differences between measured 235 U SACS and calculation using JEFF-3.3 235 U PFNS. Disagreement with experiment was found for 89 Y(n,2n) 88 Y, 19 F(n,2n) 18 F, 58 Ni(n,2n) 57 Ni, and 23 Na(n,2n) 22 Na reactions. These reactions have high mean response energy (E50%). E50% is the energy where integration of the product of spectra and cross section reaches 50%. Table 2 shows differences between measured 235 U SACS and calculation using ENDF/B-VIII.0 235 U PFNS. Agreement within uncertainties is achieved for all reactions. Figure 2 shows 252 Cf over 235 U SACS ratios in dependence on mean response energy. The plotted experimental data are listed in Table  3. The experimental results agree very well with calculated data using 235 U ENDF/B-VIII.0 PFNS unlike JEFF-3.3 which has a much softer neutron spectrum. The difference is clearly visible in E50% above 14 MeV. The difference between these two evaluations is approximately 20 % for reaction 23 Na(n,2n) 22 Na (E50%=15.37 MeV). Figure 3 displays comparison of ENDF/B-VIII.0 235 U SACS with differential data by Staples [21]. The agreement is very good up to 12 MeV, then the agreement worsens with higher energies. The experimental data are up to 10 times higher for 16 MeV.

Conclusions
The work presented the set of SACS ratios over the broad range of mean response energies. The results show that using ENDF/B-VIII.0 235 U PFNS gives good agreement with experimental data including very high mean response energies unlike JEFF-3.3 235 U PFNS. ENDF/B-VIII.0 235 U PFNS has harder neutron spectrum than theoretically expected. These data can be used as a challenge for various theoretical fission models.  Fig. 3. Comparison of 235 U ENDF/B-VIII.0 PFNS with existing differential data measured by Staples.