Fast-neutron-induced fission of 242 Pu at n ELBE

The fast neutron-induced fission cross section of 242Pu was determined in the range of 0.5 MeV to 10 MeV relative to 235U(n,f) at the neutron time-of-flight facility nELBE. The number of target nuclei was calculated by means of measuring the spontaneous fission rate of 242Pu. Neutron transport simulations with Geant4 and MCNP6 are used to correct the relative cross section for neutron scattering. The determined results are in good agreement with current experimental and evaluated data sets.


Introduction
Neutron-induced fission cross sections of actinides such as the Pu-isotopes are of relevance for the development of nuclear transmutation technologies.Apart from 244 Pu, whose abundance in spent nuclear fuel could be neglected [1], 242 Pu is the plutonium isotope with the longest halflife (T 1/2 = 373300 a).Thus, there is a special interest to investigate the fission of this particular isotope using fast neutrons.
The fast neutron-induced fission cross section of 242 Pu was studied first by Butler in 1960 [2].A brief summary of the available experimental data acquired since then is given in Ref. [3].Results of measurements at the Los Alamos National Laboratory by Tovesson et al. [4] and at the Joint Research Center Geel by Salvador-Castiñeira et al. [3] were published recently and tend to be lower than present evaluated nuclear data [5].
For 242 Pu(n,f) current uncertainties are of about 21% in an energy range of 0.5-2.23 MeV.Sensitivity studies [6,7] show that the total uncertainty has to be reduced to below 5% to allow for reliable neutron physics simulations of plutonium using reactor concepts.
This challenging task was performed at the neutron time-of-flight facility nELBE of the Center for High-Power Radiation Sources ELBE at Helmholtz-Zentrum Dresden -Rossendorf.Improved experimental conditions (low scattering environment) and beam power, paired with the right spectral shape of the neutron source provide excellent conditions to achieve this aim.
The present work reports an experiment at nELBE studying the neutron-induced fission cross section of 242 Pu relative to 235 U(n,f).a e-mail: t.koegler@hzdr.deb e-mail: a.junghans@hzdr.de

Fast neutrons at ELBE
At nELBE fast neutrons between 10 keV and 20 MeV are generated by a photo-neutron source.Impinging electrons of the ELBE beam produce bremsstrahlung while getting decelerated in a liquid lead target [8].Neutrons are further produced via (γ, n) reactions on the lead nuclei.The compactness of the neutron producing target together with the excellent timing of the ELBE electron beam enables high resolution neutron time-of-flight experiments even at short flight paths of around 6 m.Further details of nELBE can be found in Ref. [9].For this experiment a repetition rate of 406.25 kHz was chosen as a compromise between avoiding pulse overlap and maximum beam intensity.The electron beam energy was 30 MeV and the average bunch charge 73 pC.

Fission chambers
Within the TRAKULA project [10], large and homogeneous deposits of 235 U and 242 Pu have been produced successfully [11].Two fission ionization chambers, one assembled with uranium (UFC) and one with plutonium (PuFC), have been constructed and built at HZDR [12,13].In the reported experiment only the PuFC was used.The incident neutron flux was determined with the well characterized transfer device H19 of the PTB Braunschweig [14,15], which is also an 235 U fission chamber.Both fission chambers were operated in the forward biasing mode, which means that the five doublesided fission samples of the H19 and the eight sin-gle-sided samples of the PuFC are cathodes on positive potential.The induced charge on the anode was read out by a nanosecond preamplifier developed in-house.

Data acquisition
The short signal length of the ns-preamplifier reduces the α-pile-up probability by nearly a factor of 5 compared to conventional µs-shaping time preamplifiers.In addition it enables the use of a charge-to-digital converter (QDC) instead of the combination of a spectroscopic amplifier and an analog-to-digital converter (ADC).A scheme of the VME-based data acquisition electronics is shown in Fig. 1.Further details of the used experimental setup and electronics can be taken from Ref. [16].

Data analysis
The recorded list-mode data were analyzed using the Qt/ROOT-based software framework Go4 [17].The produced time-of-flight spectra (cf.Fig. 2) were calibrated with respect to the bremsstrahlung peak.A gate on the QDC values was applied to filter out the α-particle background coming from the radioactive decay of the target nuclei.Time-independent fission events caused by room-return background and spontaneous fission were approximated by a constant in front of the bremsstrahlung peak, between this peak and the begin of the neutroninduced fission events and at the end of the spectrum.
Both, time-of-flight spectrum and background were translated into kinetic energy by using Eq. ( 1).
where m n c 2 stands for the neutron rest energy, L for the flight path and t for the time-of-flight of the neutron to a certain actinide target.After background subtraction the relative fission cross section can be calculated by:

/ ns t
Here Ṅ(n,f) = Ṅ(n,f) (E n (t)) is the detected neutron-induced fission rate at a certain time-of-flight t in the i-th actinide target of the PuFC or the H19.This count rate has to be corrected for the fission fragment detection efficiency ε and for neutron scattering C, which will be discussed in Sect.2.5.
The normalization factor K is the ratio of the total areal densities n A of the two fission chambers and depends only on constants.
Because 242 Pu has a high spontaneous fission (SF) rate λγ , which is in addition known better than 2% (see Ref. [18,19]), n PuFC A can be determined by measuring the spontaneous fission rate Ṅ(SF) .As the target area F PuFC i is equal for all eight deposits this simplifies to a sum over the effective areal density of each actinide target: Here α accounts for the small dead time correction of the DAQ during this measurement.With Eq. ( 3) the normalization factor can be written as follows: Using this expression in Eq. ( 2), the relative cross section gets independent from the fission fragment detection efficiency of the PuFC, which is usually difficult to determine [20].Of course one has to correct for the linear and angular momentum introduced by the incident neutrons.Subsequently to this momentum transfer an anisotropy in the emission of the fission fragments arise, which lowers the detection efficiency [21].Due to the lack of experimental data for this anisotropy, this inefficiency was not corrected for.An estimation of this measure was done using unpublished data of Salvador-Castiñeira et al. and included to the systematic uncertainties.

Neutron scattering corrections
To correct for the influence of neutron scattering one has to consider two different aspects.The first is the attenuation of the neutron beam by passing any material along its track.The second is the loss of the energy to time-of-flight correlation of scattered neutrons.Especially for inelastic scattered neutrons this is an important issue, because they are losing a large amount of their total kinetic energy in one interaction.Measuring their time-of-flight afterwards will lead to a much higher kinetic energy, if the scattering was close to the fission targets.As a result of that, the cross section at high energy would be overestimated.Both effects have been corrected for using an MCNP 6.1.1 and a Geant 4.10.1 simulation.The results of both neutron transport codes were in a very good agreement to each other.The outcome of the simulation is a correlation matrix of the true kinetic energy E n and the kinetic energy E n (t) one would calculate from their time-of-flight and the assumed undisturbed flight path.For the Geant 4 simulation such a correlation matrix for an arbitrary actinide target is shown in Fig. 3.
The attenuation of the neutron beam was corrected by the ratio of all impinging neutrons N i in the i-th actinide target, which have not been scattered on their way to the target (on the left of Fig. 3), to the total number of started neutrons N 0 .Hence one could define a transmission correction factor T up to the target i as: The loss of the energy to time-of-flight correlation could be expressed in a similar way.Here the correction factor k i is the ratio of the detected fission rate of unscattered neutrons to the total detected fission rate.Because the fission rate depends on the cross section, the results of the simulations were multiplied by the JEFF 3.2 evaluated fission cross section of 242 Pu: The delta-distribution δ(E n − E n (t)) in the numerator ensures that only unscattered neutrons are taken into account.With Eq. ( 5) and Eq. ( 6) the neutron scattering correction factor C i is defined in the following way: As only the sum of all H19 fission targets is available, the arithmetic mean C H19 was calculated to take care of the neutron scattering within this chamber.Then, the average total correction factor is in the order of 9%.

Results
Including the neutron scattering corrections into Eq.( 2) one can finally calculate the relative neutron-induced fission cross section of 242 Pu.The result of this calculation is shown in Fig. 4.
The nELBE data are in good agreement in shape and absolute scale to present nuclear data.Compared to the data of Staples et al. [22], the accordance in absolute scale is above 99%.The discrepancy to the Tovesson [4] data set is around 2% in the considered energy range.Larger deviations to the Weigmann data [20] in the order of 5.4% are present especially in the plateau region between 1.2 MeV and 5 MeV.The recently published data of Salvador-Castiñeira et al. [3] are also below this cross section ratio.This is of special interest, because the current European evaluation JEFF 3.2 (see Ref. [23]) is mainly based on the Weigmann data.

Figure 1 .
Figure 1.Scheme of the electronic setup and the data acquisition system.The output signals of the charge-sensitive (ns-) preamplifiers are split to determine the timing and the collected charge.The pulse heights of the H19 signals are acquired with an ADC after getting shaped by a spectroscopic amplifier, whereas the charge of the eight PuFC channels (only one is shown here) is determined by a QDC.The second output signal is converted to a logical signal by an in-house developed constant fraction discriminator (CFD).The production of a fast trigger makes the use of a timing-filter-amplifier in the fast branch of the H19 necessary.The logical signals are used to determine the timing in a time-to-digital converter (TDC) and to produce a trigger for the data acquisition in an FPGA.

Figure 2 .
Figure 2. Left: neutron time-of-flight spectrum acquired by one channel of the plutonium fission chamber before (in black) and after (in blue) background subtraction.The red line indicates a constant extrapolation of the background induced by room-returned neutrons and spontaneous fission events.Right: background subtracted energy spectrum calculated using the time-of-flight spectrum shown on the left side.

Figure 3 .
Figure 3. Simulated energy to time-of-flight-correlation calculated using Geant4.Shown are from left to right: unscattered neutrons, scattered neutrons and the sum of both.Here the bin content was multiplied columnwise with the 242 Pu fission cross section.

ND2016Figure 4 .
Figure 4. Neutron-induced-fission cross section of 242 Pu relative to 235 U.The nELBE data are shown in blue together with selected EXFOR-data of Tovesson et al. [4], Staples et al. [22] and Weigmann et al. [20].Within their uncertainties there is a good agreement of the presented data set with the data of Staples and Tovesson.Small deviations from the re-normalized (ENDF/B-V→ ENDF/B-VII.1)Weigmann data are clearly visible.