Method to Compare Fission-to-Scattering Ratios using Uranium-238

. A novel method was developed to separate the 238 U ﬁssion contribution measured in quasi-di ↵ erential time-of-ﬂight scattering experiments in order to isolate the elastic and inelastic events. Pulse height distributions from in-beam measurements were used to generate response functions, which were used to reconstruct the 238 U prompt ﬁssion neutron spectra. This method was validated by reconstructing the measured 252 Cf spontaneous ﬁssion pulse height distribution. Monte Carlo calculations were used to model the experiment. Good agreement was observed between the measured and calculated 238 U ﬁssion contribution.


Introduction
The Rensselaer Polytechnic Institute (RPI) high-energy quasi-di↵erential neutron scattering (HES) system collects data generated by the deposition of energy from neutrons and gamma-rays emanating from a sample-ofinterest placed in a pulsed neutron beam. The system was configured to measure neutrons with energies between ⇡0.5 and 20 MeV. Data from these measurements were compared to evaluated nuclear data libraries using Monte Carlo simulations. Observed di↵erences between measured data and Monte Carlo calculations have been used by evaluators to constrain their models [1]. Past measurements using the HES system included graphite (carbon) [2], beryllium [3], molybdenum [3], zirconium [4], 238 U [5], iron [6], lead [7], and copper [8].
This study revisits previously measured 238 U data to describe a novel approach that separates the fission contribution from other reaction channels. This method relies on in-beam response functions and builds on previously described techniques used to quantify the elastic-only contribution [6,9]. Results are compared with MCNP [10] simulations to demonstrate proof-of-principle.

RPI LINAC
Experiments were conducted at the Gaerttner Linear Accelerator (LINAC) Center at RPI. The LINAC generated a pulsed electron beam that struck a neutron-producing tantalum target, and through Bremsstrahlung generation and subsequent photoneutron reactions generated a pulsed neutron beam. Neutrons that escaped the tantalum target in the HES system's direction traversed a series of evacuated ⇤ e-mail: Adam.Daskalakis@unnpp.gov and collimated flight tubes that ensured the beam diameter was ⇡7.62 cm at the scattering sample location.
Beam monitors were used to correct for fluctuations in the neutron beam's intensity. They were positioned on an independent flight path at ⇡9 m from the tantalum target and collected data throughout the measurement.

HES System
The HES system is comprised of eight detectors positioned around a scattering sample at angles based on observed discrepancies between evaluated nuclear data libraries [2]. Each detector featured a 12.7 cm diameter by 7.62 cm thick ELJEN Technologies EJ-301 liquid scintillator directly coupled to a 12.7 cm diameter Photonis model XP4572/B photomultiplier. Negative high voltage was supplied by a CAEN power supply, model 1733N. Analog signals generated by scintillation light were sent to an Agilent-Acqiris AP240 8-bit data acquisition (DAQ) board via RG-58 coaxial cables [11]. The DAQ maximum sampling rate was 1 GHz which allowed for 1 ns data collection intervals, and each digitized waveform captured a sequence of 120 1-ns samples per event.

Data Analysis
A series of calculations were performed on each event to classify it as either a neutron or gamma-ray. The event's pulse height, which represents the area under a pulse after baseline subtraction, was also extracted during those calculations. Neutron pulse height distributions are the basis for response functions and the analysis explained in the subsequent sections. Gamma-ray pulse heights were used with a gamma-ray misclassification correction, GMC, which corrected the neutron data for gamma-ray events erroneously classified as neutrons. The GMC is proportional to pulse height, j, with largest correction occurring at low pulse heights [9].
The neutron time-of-flight (TOF) method was used to convert a neutron's recorded time-bin, i, to energy, E i . This relationship is shown in Equation 1.
where, m n c 2 = Neutron rest mass.

Response Functions
Detector in-beam measurements collected data from a single detector placed in the neutron beam path at ⇡30 m from the tantalum target without the presence of a scattering sample. To approximate a mono-energetic neutron beam only data in a narrow energy bin, E i ± dE i , were analyzed. Vectors, or histograms, of pulse heights were generated from that data. These distributions are referred to as energy-dependent response functions, or R E i . Each response function has a unique distribution based on the incident neutron energy. All response functions set dE i to 2.5% of E i , i.e., 1 ± 0.025 MeV. The limited energy range also allows for the approximation that neutron flux does not vary much, and was considered constant throughout this energy bin. Figure 1 displays three response functions for incident neutron energies of 1.0 ± 0.025, 1.5 ± 0.038, and 2.0 ± 0.05 MeV. All data were measured by a single detector.  Figure 1 also shows that the maximum pulse height that contributes to the response function increases with incident neutron energy. This location is referred to as the response function end-point, and its position was determined by traversing the pulse height distribution until ⇡99.5% of all pulses contributing to the histogram were summed. A third-order polynomial was fit to each response function's end-point, which is displayed in Figure 2. For a given incident neutron energy, only neutrons from fission events have energies in excess of elastic scattering. Therefore, to isolate the fission contribution at E i an end-point corresponding to an elastically scattered neutron with energy 5 E i was calculated using the aforementioned polynomial. The fission shape was then normalized to the region above the end-point bin, discussed in 4.2, to ascertain the fission neutron contribution.

252 Cf Measurement and Analysis
To demonstrate that response functions can successfully reconstruct the 238 U prompt fission neutron spectra (PFNS) pulse height distribution from measured HES data, a proof-of-concept calculation was performed using data previously measured from a 252 Cf source to quantify the GMC [9]. A series of response functions were generated to cover the range of fission neutron energies that were measured by the HES detectors. Response function pulse height distributions were generated for energies between 0.55 and 20 MeV in 0. R 252 s. f. was area normalized to the measured 252 Cf pulse height data and is displayed in Figure 3, which shows good agreement between the measured 252 Cf data and R 252 s. f. . The only source of uncertainty presented here comes from counting statistics associated with the 252 Cf and background measurements. Additional sources of uncertainty can be attributed to response functions' pulse height distributions, detector e ciencies, and experimental setup; however, those sources were not characterized.

U
The 238 U measurement and analyses were previously performed with the intent to constrain models used to help generate evaluated nuclear data libraries. Experiment conditions, results, and findings are documented in [1,5,9]. 238 U data from a single detector, along with the corresponding in-beam response functions, were reanalyzed. During the 238 U measurement that detector was positioned at 130 relative to the incident neutron beam. 238 U results using the methods described above are detailed in the subsequent sections.

Generating 238 U Fission Pulse Height Distribution
The 238 U scattering measurement di↵ered from the 252 Cf static measurement in several ways. First, the open beam, or time-dependent background, pulse height contribution was removed. For quasi-di↵erential measurements the time-independent room background was negligible. Second, the 252 Cf sample was considered a point source, and neutron transmission through the low mass fission chamber was neglected. In contrast, both incident and fission neutrons had to traverse part of the 238 U sample. An energy-dependent correction was applied to response functions and is included in Equation 3. This correction calculates the fraction of fission neutrons that did not interact with the 238 U sample. The depth where fission was modeled corresponds to where 50% of interactions occurred in the 238 U sample. This depth varied based on the incident neutron's energy, E i .
where, = The 238 U total cross section at E k .
The 238 U energy bins analyzed were set dE i to 2.5% of E i , mimicking the energy bins used to generate in-beam response functions. Additional e↵ort was made to include the contribution of fission neutrons from times outside the energy bin being analyzed, i.e., high-energy fission neutrons from incident neutron energies < E i and vise versa, which resulted in a minor correction.

Calculating the Fission Contribution
After R 238 E i was generated an end-point corresponding to elastically scattered neutrons at energy E i to the detector at 130 degrees was calculated using the polynomial presented in Figure 2. For incident 1.7 MeV neutrons this corresponded to a pulse height of ⇡2200 and R 238 E i was area normalized to the pulse height data above this location. After normalization, the fission neutron ratio was calculated by taking the ratio of the reconstructed 238 U fission neutron pulse height distribution relative to all measured neutrons in a given energy-bin. Figure 4 shows the measured 238 U pulse height distribution and R 238 1.7 , the reconstructed 238 U fission neutron pulse height distribution for incident 1.7 MeV neutrons. R 238 1.7 was area normalized to the measured 238 U region above the 1.7 MeV elastically scattered end-point. The measured fission neutron ratios were compared with MCNP simulations that modeled the 238 U quasi-di↵erential measurement. ENDF/B-VIII.0 , JEFF-3.3 , and JENDL-4.0 238 U evaluations were compared with the measured data by only varying the evaluation used to model the 238 U reactions. Lastly, at each energy and for each evaluation two separate simulations were performed, with the only di↵erence being the enabling or disabling of the fission contribution from the 238 U sample. The fission ratios from measured data and MCNP simulations have the same general trend. However, the differences observed from 1.4 to 1.8 MeV are large and may warrant additional investigations to determine their origin. Only the 238 U statistical uncertainty is reported, and one source for the discrepancies can be attributed to the limited number of counts associated with both response functions and quasi-di↵erential 238 U data. Other sources of uncertainty, i,e., systematic, are not included.

Conclusion
The method to reconstruct the fission contribution using pulse height information and eliminate it from a 238 U scattering measurement was discussed. A proofof-principle was demonstrated by reconstructing a measured 252 Cf PFNS pulse height distribution with in-beam response functions coupled with ENDF/B-VIII.0 prompt fission neutron spectra. This technique was then applied to 238 U quasi-di↵erential data in order to separate the fission contribution from scattering reactions. The measured fission contributions were compared with MCNP calculations performed with several libraries, which all showed similar trends.
Eliminating the fission contribution can allow further analysis on anisotropic reactions utilizing the methods discussed herein.