Neutron induced fission cross section measurements of 240Pu and 242Pu

Accurate neutron induced fission cross section of 240Pu and 242Pu are required in view of making nuclear technology safer and more efficient to meet the upcoming needs for the future generation of nuclear power plants (GEN-IV). The probability for a neutron to induce such reactions figures in the NEA Nuclear Data High Priority Request List [1]. A measurement campaign to determine neutron induced fission cross sections of 240Pu and 242Pu at 2.51 MeV and 14.83 MeV has been carried out at the 3.7 MV Van De Graaff linear accelerator at PhysikalischTechnische Bundesanstalt (PTB) in Braunschweig. Two identical Frisch Grid fission chambers, housing back to back a 238U and a APu target (A = 240 or A = 242), were employed to detect the total fission yield. The targets were molecular plated on 0.25 mm aluminium foils kept at ground potential and the employed gas was P10. The neutron fluence was measured with the proton recoil telescope (T1), which is the German primary standard for neutron fluence measurements. The two measurements were related using a De Pangher long counter and the charge as monitors. The experimental results have an average uncertainty of 3–4% at 2.51 MeV and for 6–8% at 14.81 MeV and have been compared to the data available in literature.


Introduction
Three out of the six nuclear energy systems chosen by the Generation IV International Forum are fast neutron reactors.Plutonium will represent up to 20% in weight of the first load fuel composition of Gas Cooled Fast Reactors [2], and will exceed 26% in the MYRRHA accelerator driven system demonstrator [3].High accuracy neutron induced cross section data on the even-even isotopes of plutonium, among others, are therefore needed.An uncertainty reduction of up to 10% is required on 242 Pu σ (n, f ) in the neutron kinetic energy region between 2.23 MeV and 6.07 MeV and of up to 24% between 6.07 MeV and 19.6 MeV.The accuracy on 240 Pu σ (n, f ) needs to be improved from the present 5% to the demanded 3% in the neutron kinetic energy region between 2.23 MeV and 6.07 MeV [4].

Experimental set-up
The 3.7 MV Van De Graaff linear accelerator at the Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig was used to produce monoenergetic neutron beams of 2.51 MeV and 14.83 MeV kinetic energy through p+ 3 H and d+ 3 H reactions respectively.Two identical Frisch Grid fission chambers were manifactured in JRC-Geel.One was loaded with 0.808 (16) mg of 238 U in a U(OH) 4 target (assuming the layer is a hydroxide) back to back with a 0.0971 (4) mg of 240 Pu in a Pu(OH) 4 deposit (always assuming the layer is a hydroxide, here as in the a e-mail: francesca.belloni@cea.frrest of the text), and the other with 0.861 (16) mg of 238 U (in U(OH) 4 ) back to back with a 0.625 (5) mg of 242 Pu (in Pu(OH) 4 ).The target references are respectively TP2011-008-07, TP2011-011-06, TP-2011-008-03x and TP2010-012-03 [5].All targets were molecular plated on 0.25 mm aluminium foils kept at ground potential.On the uranium side, the charges produced through ionization in P10 were collected by an anode positioned at 6 mm from the deposit.The gas volume on the plutonium side was instead larger.A grid was located at 3 cm from the target, followed by an anode at an additional distance of 6 mm.The 238 U, 240 Pu and 242 Pu distances to the neutron converter and the resulting beam energy spreads are summarized in Table 1.

Neutron flux measurement
The neutron fluence was measured with the proton recoil telescope (PRT) T1, which is the German primary standard for neutron fluence measurements between 1.2 MeV and 20 MeV and with a De Pangher long counter (PLC) [6].During dedicated runs, the fission chambers were moved away from the beam at backward angles, the PRT was positioned at 0 degrees with respect to the ion beam line, at a distance from the neutron producing target varying between 20 cm and 35 cm, and the fluence was extracted from the T1 with reference to the (n,p) elastic cross sections (ENDF/B-V).In the same time, the counts detected by the PLC were registered.The neutron fluence during the neutron induced fission measurements was extracted from the De Pangher long counter [6] calibrated on the PRT as described above.The De Pangher long counter was positioned at 98 • relative to the direction of the ion beam.Alternatively the fluence for the fission measurements could be determined using the charge collected on the neutron production target and the fluence/charge factor obtained with the PRT.For comparison the neutron fluence was measured also using the Frisch Grid fission chambers and the standard neutron induced fission cross sections of 238 U [7].

Data analysis
The neutron induced fission cross sections were calculated from the number of nuclei n of the investigated isotopes in the target, the amount N of detected fission fragments (FFs), and the measured neutron fluence (E): The detection efficiency (E) of the ionization chamber for fission fragments (FFs) generated by neutrons of kinetic energy E accounts both for the number of FFs producing a signal below threshold and the amount of FFs trapped inside the target.The factor f (E) = c LT /c(E) ms includes the live time (LT ) and the multiple scattering corrections.The ionization chambers were operated in pulse mode.A threshold was imposed on the pulse height spectra (PHS) in order to discriminate FFs from α particles.The number N was obtained by integrating the spectra from threshold to full-scale in background ("beam off") and foreground ("beam on") measurements and by subtracting the first contribution from the second to discard the spontaneous fission (SF) events.
GEANT4 simulations were carried out to determine the fraction of FFs trapped inside the targets for background and "beam on" conditions.The multiple scattering corrections were calculated with the help of the MCNP code, by comparing the neutron induced fission reaction rate obtained in a target located at the desired position from the neutron source and surrounded by vacuum with the neutron induced fission reaction rate in the same deposit inserted in the fission chamber.
The live time of the electronic chains connected to each electrode was measured with a pulser and calculated by dividing the number of delivered pulses by the number of detected pulses.The same pulser was used to inject signals of decreasing voltage in all electronic chains and the corresponding PHS were recorded, allowing an offset determination.
The amount of FFs producing a signal below threshold was extracted following two different methodologies.

Fitting method
The low energy tail of the PHS in background and "beam on" conditions was fitted with an exponential superimposed to a flat background (y = exp p 0 + p 1 •x + p2).The integral between the offset and the threshold pulse amplitudes of the fit performed on a region delimited by a minimum and maximum channel ([min ch, max ch] ⊆ [offset, threshold]) gives the number of FFs entering the gas, and producing a signal so low that it is discarded by the ADC threshold or is recorded in the α background region.The error bar associated to the number of FFs calculated this way is obtained as the deviation from such number when the lower or the upper limit of the fitting region is varied by one channel.The four fitting region configurations used to calculate the error bar associated to the number of FFs are: [min ch+1, max ch], [min ch-1, max ch], [min ch, max ch +1], [min ch, max ch-1].
This analysis method revealed to be quite subjective since changing by one single channel the fitting region, the calculated cross sections significantly change.For example, the value obtained for 240 Pu σ n, f increases by 1.8% when the fitting region is [min ch-1, max ch], while it decreases by 4.3% if the fit is performed between [min ch+1, max ch].In view of this sensitivity to the choice of threshold this method is not reliable and we had to resort to a second method.

Efficiency method
The procedure is based on the assumption that the PHS of the anode signals in background and beam conditions show no significant difference.This allows to introduce a detection efficiency "R", defined as the ratio of the amount of SF events above threshold in background condition to the total number of expected SF events during a certain interval, calculated from the half life of the considered isotope.The value of R will be the same for a SF spectrum and a neutron induced fission spectrum, provided that the same isotope is considered.Given R and the integral of the neutron induced PHS above threshold, the number of FFs below threshold can be computed.The error bar associated to the counting statistics is calculated by error propagation of the quantities involved in its determination.

Results
The neutron induced fission cross sections of 240 Pu and 242 Pu measured at 2.51 MeV and 14.83 MeV are reported in Table 2.
Our final results are those of the Efficiency method.For completeness we also show the result of the Fitting procedure which are clearly biased.From the Table 2 it is evident that the data at 14.83 MeV have larger uncertainties.This is a combination of the counting statistics and the value of the 238 U σ (n, f ) , which is higher at higher neutron energies and is directly proportional to the flux.The neutron flux extracted from 238 U data is always in agreement with the one provided by PTB within its accuracy (2.9%).
The live times of the electronic chains are similar, and range between 99.83% ± 0.04% and 99.93% ± 0.04%.The percentage of FFs trapped in the targets is higher for the thicker 242 Pu (average 2.29%) than for the thinner  The lower panel of Fig. 2 shows the comparison among the available 242 Pu σ n, f experimental cross sections in the neutron energy ranging from 14.5 MeV to 15.5 MeV.
Tovesson [8] and Manabe [18] agree with all our results.Not much can be said for Gul [19] and Alkhazov [20] , since the energy is not exactly the same and only one data point is available for each of these measurements.Khan [21] and Meadows [22] result to be lower than all other data.

Conclusions
Neutron induced fission cross section measurements of 242 Pu and 240 Pu at 2.51 MeV and 14.83 MeV have been performed at the 3.7 MV Van De Graaff linear accelerator at Physikalisch-Technische Bundesanstalt (PTB) in Braunschweig.Two analysis method have been employed and the results are mainly in agreement with the experimental data collected in the past.The results confirm that the 242 Pu σ n, f measured at 14.8 MeV by Khan [21] and Meadows [22] seem to be too low.To exclude other data, higher accuracy is needed.

Figure 2 .
Figure 2. Experimental neutron induced fission cross sections of 242 Pu in the energy region between 2 MeV and 3 MeV (upper panel) and between 14.5 MeV and 15.5 MeV (lower panel).
Experimental neutron induced fission cross sections of240Pu in the energy region between 2 MeV and 3 MeV (upper panel) and between 14.5 MeV and 15.5 MeV (lower panel).
238Eff.Method -Flux from This work was partly supported by the EMRP ENG08 METROFISSION project of the European Metrology Research Programme which is jointly funded by EURAMET and the European Union.The authors thank the operators of the PTB