The Neutron Scattering Cross Section and Angular Distribution Measurement Program at LANL

. Neutron scattering cross sections and angular distributions are leading terms in descriptions of neutron transport through any system. Despite the fundamental importance of nuclear data on these quantities, significant gaps in understanding and lack of experimental data persist in heavier elements and down to lighter structural materials, such as iron and aluminum. Recent measurements on carbon have also shown definitive proof that the neutron angular distribution can change with respect to the emission angle of γ -rays from in-elastic scattering, thereby complicating γ -tagged measurements of inelastic neutron scattering. In this work, we describe the emerging program at Los Alamos National Laboratory for measurements of neutron scattering cross sections and neutron, γ -ray, and correlated n - γ angular distributions utilizing liquid scintillator detectors and the Correlated Gamma-Neutron Array for Scattering (CoGNAC) of CLYC scintillators. Currently, these detectors are operated simultaneously with the in-progress array of CLYC detectors in an inverted position, and data analysis techniques are being developed to span scattering measurements from light nuclei up through actinides. Preliminary results for measurements on 12 C, 27 Al, and 56 Fe are presented here with a description of the analysis methods applied and anticipated capabilities of the full-scale detection system.


Introduction
Above ≈10-100 keV, neutron scattering is the most likely reaction to occur for neutrons interacting with effectively any nucleus [1,2]. As such, a precise understanding of neutron scattering nuclear data is essential for understanding neutron transport through any medium. However, glaring gaps in our understanding of neutron scattering reactions on elements across the chart of nuclides exist, and produce significant uncertainties in neutron transport simulations. The structural materials aluminum and iron are of particular importance because they are so commonly used in both in experimental environments and application scenarios, and carbon is a nearly unavoidable component of any organic material. Despite the common occurrence and the relative simplicity of experimental neutron scattering measurements of these elements compared with other nuclei, there are significant discrepancies between evaluations and literature data, and sometimes a complete lack of data altogether.
We present here preliminary results for inelastic neutron scattering measurements on natural C, Al, and Fe targets. These data were collected at the Weapons Neutron Research (WNR) facility at the Los Alamos Neutron Science Center (LANSCE), located at Los Alamos National Laboratory (LANL). The data shown in this work were collected with a 54-detector liquid scintillator array, capable of measuring both neutrons and γ rays. The facility and experimental configuration are described in Secs. 2.1 and 2.2, respectively. Data analysis procedures including * e-mail: kkelly@lanl.gov signal processing, background subtraction, data unfolding and neutron environmental response, and γ-ray detection treatment are discussed in Sec. 3. Preliminary results for inelastic scattering cross sections on 12 C, 27 Al, and 56 Fe are shown in Sec. 4. The experiment and analysis procedures described in this work are part of a developing campaign to measure neutron scattering cross section and angular distributions, to eventually focus on data collected with the Correlated Gamma Neutron Array for Scattering (CoGNAC) CLYC scintillator detection system. The design and development progress of this array are described in Sec. 5, with concluding remarks given in Sec. 6.

The WNR Facility
The WNR facility at LANSCE produces neutrons using an 800 MeV pulsed incident proton beam incident on an unmoderated tungsten spallation target. The proton beam is divided into small bursts called "micropulses" with a ≈150 ps spread in time. Groups of ≈347 micropulses are grouped together into macropulses, with each micropulse separated from neighboring micropulses by 1.7889 µs. Each macropulse is ≈625 µs long, and is nominally separated from neighboring macropulses by 8.3 ms. Data for the experiments described in this work were collected at flight 15L (FP15L) located 15 o to the left of the incident proton beam direction. A signal, referred to as the t 0 signal, was recorded just prior to each significant proton spallation reaction, and the incident neutron flux spectrum was   Figure 1: Data collected using a carbon filter for the incident neutron beam collected with a 235 U fission chamber are shown in red as a function time relative to the γ transit time from the tungsten spallation target. The 12 C total cross section converted to time relative to γ transit time is shown in black. This agreement yielded a distance of 19.145(15) m of the 235 U flux monitor from the spallation target. recorded with both 235 U and 238 U fission chambers. Distances of these monitors from the spallation target were determined using carbon transmission, an example of which is shown in Fig. 1 demonstrating the measured distance of 19.145(15) m for the 235 U flux monitor.

Targets and n-γ Detection System
Data for each target described in this work were collected using a 3-arm sample changing system, where the target was frequently swapped in and out of the beam every ≈10 min to minimize variation in incident neutron beam characteristics between target-in and target-out measurements. Carbon, aluminum, and iron data were collected with a 2 cm beamspot using targets of 2.5, 0.2, and 0.1 cm thick targets, respectively. All targets had a radius greater than 3 cm, thus the neutron beam was safely within the dimensions of the target, and all targets were of natural isotopic composition.
Neutrons and γ rays from scattering were detected in an array of 54 EJ-309 [3] liquid scintillator detectors, each with an R4144 Hamamatsu PMT attached [4]. Detectors cover laboratory detection angles from 30-150 o at 15 o increments, and with ±5 o angular resolution based on detector size. This detector array is shown in Fig. 2. High voltages for these detectors were maintained using a CAEN SY4527 HV supply [5], and data were collected asynchronously using a series of CAEN 1730B waveform digitizers [6] and recorded using the MIDAS data acquisition framework [7].

Signal Processing
Signals collected in each liquid scintillator detector were recorded in terms of integrals of the early (head), late (tail), and total (head-tail sum) portions of the signal. A pulse shape discrimination (PSD) spectrum was calculated for each detector using the tail-to-total signal integral ratio, and neutrons and γ rays were separated based on this spectrum. An example PSD spectrum for Al scattering data is shown in Fig. 3, with n and γ gates shown on the figure. Each liquid scintillator was processed as both a neutron and a γ-ray detector, and coincidences between n-gated and γ-gated detectors were formed in postprocessing analysis. The γ-ray detection time, t γ , was used to define the incident neutron beam energy from the t γ -t 0 time difference, and the outgoing neutron energy was determined from the t n -t γ time difference, where t n is the neutron detection time in a liquid scintillator detector. After correction for the γ transit time, these energies were then formed into a 2D spectrum of outgoing versus incident neutron energy, as shown for Fe data in Figs. 4a. Kinematic bands corresponding to inelastic nuclear excitations in the target material are seen as the lines of counts displaying increasing outgoing neutron energy with increasing incident neutron energy.

Random-Coincidence Backgrounds
The raw n-γ coincidence data contain a substantial contribution from random coincidences between neutrons and γ rays that are not truly in coincidence with each other. Typically, elastic neutron scattering is the dominant contributor to γ-anticoincident neutron background, and these elastically-scattered neutrons are accidentally measured to be in coincidence with γ rays from inelastic neutron scattering or from environmental backgrounds [8]. This background can be seen in Fig. 4a as a pervasive region of counts with kinematic bands that show a decreasing slope with increasing incident neutron energy. See Ref. [8] for more details on reasons for this behavior of the background. These complicated backgrounds were accounted for using the same raw data as was used to create the spectrum in Fig. 4a using the method described in Refs. [9,10]. Briefly, the pre-coincidence (singles) data as a function of time relative to the t 0 incident neutron creation time can be used to determine the Poisson probabilities for (a) detecting a γ ray at the time t γ , (b) not detecting a neutron for a time t n -t γ , and (c) detecting a neutron at a time t n . Under most constant experimental conditions, these probabilities can be used to form a simple expression for the random-coincidence background as described in Refs. [9][10][11][12], which can then be subtracted from the n-γ coincidence data, leaving only data describing the true coincidences in the data. To demonstrate the effect of this analysis, the Fe data shown in Fig. 4a before background subtraction are also shown in Fig. 4b after subtraction.

Iterative Data Unfolding
Following the extraction of the true n-γ coincidence data as described above, corrections for environmental neutron response and intrinsic neutron detector efficiencies were applied via the iterative unfolding technique originally derived in Ref. [13] and recently applied in Ref. [14]. A requirement for this method is knowledge of the detector response matrix [14,15] describing interactions of neutrons emitted from the target with the experimental environment, including the detectors, in terms of a 2D efficiency function of emitted neutron energy from target versus detected neutron energy as calculated from the t nt γ time difference. This response matrix is denoted as R(E, E i ) here, where E is the outgoing energy measured using time of flight, and E i is the neutron energy initially emitted from the target (before any environmental interactions). The matrix used for the preliminary results shown here was calculated using MCNP ® [16], building off of the highly-detailed and well-tested MCNP simulation used for analysis of data from the Chi-Nu experiment [11,12,17].
The iterative unfolding method applied here can be expressed as where n is the iteration number of the unfolding procedure, N is the total number of initial neutron energies considered in R(E, E i ), c(E) is the counts measured at timeof-flight energy E, and m (n) (E) is the unfolding measurement result at iteration n. The 0 th -order guess, m (0) (E), is obtained by simply dividing c(E) by the y-axis (E i ) projection of the response matrix, to represent division of c(E) by a 1D neutron-detection efficiency curve. The sum in the denominator represents the sum of contributions to the the counts observed at E based on R(E, E i ) scaled by m n (E i ). If the result at iteration n is correct, then the ratio in square brackets will be unity. If m (n) (E) is not correct, then the ratio in square brackets represents a correction applied to m (n) (E) to obtain m (n+1) (E). This unfolding approach quickly reaches an accurate answer in 1-2 iterations [14]. A significant advantage of this unfolding method over Monte Carlo-style unfolding methods is that it is entirely analytical, and so covariances can be directly propagated through each iteration of the unfolding procedure as opposed to generating posterior distributions or other quantities to estimate the uncertainty of the unfolded result. An example of the improvements observed from application of this method to Fe data analyzed for the results shown in this work is shown in Fig. 5. The improvement in resolution and separation of the lower excitations of 56 Fe over this incident energy range is clear. Following unfolding of outgoing versus incident neutron energy spectra like that shown in Fig. 4b for each data set, each excitation trend was defined with the observed energy resolution and neutron angular distributions, summed over all γ-detection angles, were extracted for each observed excitation. These distributions were integrated with l max = 2, 3, and 4 Legendre polynomial distributions, with the optimal Legendre fit chosen according to a statistical F-test calculated for each increasing l max [18,19]. These fit distributions were then integrated to form the shape of the cross section results shown in Sec. 4.

Relative γ-Ray Detection Probabilities
Rather than define an absolute normalization for each cross section shape extracted from the data described in this work, a single data point in a single cross section shape was chosen for normalization of the entire data set based on agreement of literature data of multiple types, if available, and nuclear data evaluations. The relative scaling of each cross section shape was then defined according to the relative probabilities for detecting a neutron-coincident γ ray from inelastic scattering for each excitation channel γ Normalized Figure 6: The γ-ray detection efficiency curve for the liquid scintillator array used in this work, as calculated using MCNP. The uncertainty band reflects variations in the efficiency shape from variations of γ-ray energy thresholds and pulse-integral resolution for this experiment.
observed. The calculation of this total detection probability consists of (a) extraction of the relative branching ratios for γ rays from each possible decay, (b) combining the set of branching ratios for each level to obtain the total probability for detecting any single γ ray from a decay cascade, (c) calculation of a γ-ray detection efficiency curve using MCNP, and (d) convolution of the γ-ray detection efficiency curve into a calculation of the total probability for detecting any number of any γ ray(s) from the decay of each excited state. These steps are detailed further in the remainder of this subsection. For nuclei like 27 Al and 56 Fe, the branching ratios for γ decays of each excited state are relatively well known and can be extracted directly from the latest ENSDF evaluation [20,21]. The total probability for populating a level j from an excitation of level i via inelastic scattering can be written as where B k j is the branching ratio for transitioning to level j from any higher-energy level, k. If this formula is applied starting from the highest excited state in a cascade, then each p ik term is known and can be applied to the lower-energy levels. The probability for emitting each γ ray from a given excited state j following inelastic excitation of level i is then simply with f being the final state from the decay. The MCNPcalculated γ-ray detection efficiency curve for the sum of all liquid scintillator detectors is shown in Fig. 6, with an uncertainty band derived from variations of the γ-ray energy threshold and pulse-integral resolution within uncertainties of 30% and 5%, respectively. Finally, the total probability for detecting any number of any γ ray(s) emitted from the de-excitation cascade can be calculated. If the γ-ray detection efficiency, ε, was constant, then this would amount to a sum of binomial distributions for each possible number of γ-ray detections (success, s) given a total number of possible emitted γ rays, N γ . In the constant ε case, each binomial distribution, β ε (s|N γ ), could be written as Given that ε is not constant for all γ-ray energies, each contributing term to the binomial-like probability of detecting any number of any γ ray(s) must be calculated individually, which is not easily shown analytically. The summation of all coincident γ-ray detection possibilities yields Γ(E x ), the total probability for detecting a coincident γ with a neutron emitted from inelastic excitation of the state at energy E x . Using Γ(E x ) for each excited state, a single normalization point can be defined in the cross shape for the chosen excited state, E * x , and the relative scaling scaling of each other cross section shape is Γ(E * x )/Γ(E x ).

Preliminary Results
Preliminary results for inelastic excitation of the 4.4398 MeV first excited state in 12 C is shown in Fig. 7. In all cases, the present results are denoted as "Liq. Scint. nγ" to denote the n-γ coincidence analysis described here. Literature data [22][23][24][25][26] and the ENDF/B-VIII.0 evaluation of this cross section are shown for comparison. For the specific case of 12 C, where the excited states are well separated and there is minimal competition for γ emission, the yield for the 4.4398 MeV γ ray can be extracted independent of the n emission and as a function of incident neutron energy to produce a high-statistics and high-resolution measurement of this same cross section. The agreement between the n-γ and γ-only results from the liquid scintillators is encouraging, and is a good test of the analysis technique. Above 12 MeV, additional γ backgrounds are present from n-induced reactions on 12 C, and so an increase in the γ-only measurement is expected. There appear to be multiple places in the ENDF/B-VIII.0 evaluation of this cross section where the present data disagree substantially with the evaluation, e.g., 8.5-9.5 MeV and in the relative magnitude of the peaks at 9.5 and 10.75 MeV.
Preliminary results for inelastic excitations of 27 Al are shown in Figs. 8a-8d. Figure 8a shows the combined inelastic excitations of the 844 and 1015 keV levels, Figs. 8b and 8c show excitations of the 2212 and 2735 keV levels, respectively, and Fig. 8d shows the combined excitation of the 2982 and 3004 keV states. All data are normalized according to the 4 MeV incident energy data point of Fig. 8b, with the relative scaling of each cross section shape determined according to total γ-ray emission probabilities and detection efficiency. Presently, only statistical uncertainties have been propagated through to the final results shown here. Literature data are shown for comparison [27][28][29][30][31][32][33] along with ENDF/B-VIII.0 results, which are identical to the ENDF/B-VI evaluation from 30 years ago [34]. The preliminary results shown here seem to show significantly more structure than ENDF/B-VIII.0, while broadly agreeing with literature data where there is overlap. The agreement with the Kinney (1972) data [27] in Fig. 8d is particularly encouraging considering that the magnitude of the cross section in this panel is clearly lower than in ENDF/B-VIII.0.
Preliminary results for 56 Fe are shown in Figs. 9a-9d, with data for excitations of the 847, 2085, 2658, and sum of the 2941 and 3004 keV states shown in Figs. 9a, 9b, 9c, and 9d, respectively. All data are again normalized according to the 4 MeV incident energy data point of Fig. 9b, with the relative scaling of each cross section shape determined according to total γ-ray emission probabilities and detection efficiency. The ENDF/B-VIII.0 evaluation results are again shown for comparison, along with two prominent literature data sets [35,36]. The structural agreement of the cross section in Fig. 9a with ENDF/B-VIII.0 and the Negret (2013) data [37] is very good, and extension of these results out to higher energies appear to agree with the data of Ramirez (2017) [36]. The present nγ results appear to be systematically higher than Ramirez data [36] at 7 MeV in both Figs. 9a and 9b, though lowerenergy data appear to be in agreement. Data on higherenergy excitations appear promising, though there are no overlaps between the present data and these literature data sets.

Development of the CoGNAC CLYC Detector Array
While impactful results can be extracted from liquid scintillator detectors as shown in this work, there are significant downsides to these detectors. Primarily, liquid scintillators suffer from poor pulse-integral resolution, a limited range of PSD capability, and a limited neutron dynamic energy range. These features imply that liquid scintillators generally can not produce measurements of elastic scattering or measurements of inelastic scattering from near reaction threshold, except for special cases like 12 C. As such, a new detector array is in development at LANL to improve upon these experimental deficiencies. The Correlated Gamma Neutron Array for Scattering (CoGNAC) design consists of 120 6 Li-enriched Cs 2 LiYCl 6 :Ce (CLYC) detectors [38][39][40] in the geometry shown in Fig. 10. These detectors provide neutron energy measurements from 10s of keV up through 10s of MeV through the combination of the 6 Li(n,t) and 35 Cl(n,p) detection reactions. CLYC scintillators also display near-perfect n-γ PSD separation for all energies of both particles, and yield 4% resolution for γ-ray energies. Currently, an in-progress version of this detector array is operated in an inverted orientation and in the same experimental setup as the liquid scintillator array used for analysis described in this work, and an example 12 C(n,n ′ γ) cross section shape from this inverted in-progress detector array is shown in Fig. 7. The agreement between γ-only measurements from liquid scintillator and CLYC detectors and of the n-γ analysis technique suggests that these detectors should be capable of expanding scattering measurement capabilities far beyond what can be done with liquid scintillators alone. Future work on neutron scattering eventually focus on results from the CoGNAC experimental setup.

Conclusions
Neutron scattering is currently one of the leading sources of uncertainty in simulations of neutron transport owing to either disagreement between literature data and nuclear data evaluations, or a complete lack of needed data. Carbon, aluminum, and iron are three particularly common elements, and thus understanding the relevant nuclear data for the most naturally-abundant isotopes of these nuclei is of fundamental importance. In this work we showed the experimental configuration, analysis path, and preliminary results for C, Al, and Fe measurements of inelastic neutron scattering at the WNR facility at LANL using a 54-detector liquid scintillator array. Despite the deficiencies of these detectors in terms of pulse-integral resolution and range of PSD applicability, high-quality measurements of the 12 C(n,n ′ γ) cross section were extracted EPJ Web of Conferences , 01004 (2023) 284 ND2022 https://doi.org/10.1051/epjconf/202328401004 using n-γ and γ-only data. Multiple preliminary inelastic scattering channel cross sections were also reported for both 27 Al and 56 Fe. Lastly, an in-development detector of CLYC scintillators (CoGNAC) was described in this work, with preliminary γ-only data for the 12 C(n,n ′ γ) data from these detectors shown as well. The success of these early measurements in the LANL neutron scattering campaign appear promising, and impactful future measurements going from light elements to actinides are expected.

Acknowledgments
CoGNAC development work and initial n-γ analysis on C and Fe data was funded by the Los Alamos National Laboratory LDRD program through LDRD Project 20210329ER. Acquisition and analysis of data on Al was funded by NA-22 via Proposal ID 0000260569 submitted to DOE-FOA-0002440. Acquisition of the Fe data shown in this work was funded by Proposal ID 0000017653 submitted to DOE-FOA-17-1763.