Neutron production in the interaction of 200-MeV deuterons with Li, Be, C, Al, Cu, Nb, In, Ta, and Au

. Double-di ﬀ erential neutron production cross sections (DDXs) for 200-MeV deuteron induced reactions on Li, Be, C, Al, Cu, Nb, In, Ta, and Au were measured at forward emission angles ranging from 0 ◦ to 25 ◦ by means of a time of ﬂight (TOF) method with EJ301 liquid organic scintillators. The measured DDXs were compared with JENDL-5 and TENDL-2021 nuclear data, and theoretical model calculations using DEURACS and PHITS codes. It was found that the JENDL-5 and DEURACS calculation are in better agreement with the measured DDXs than the PHITS calculation, while TENDL-2021 fails to reproduce both the spectral shape and magnitude of the measured DDXs for all the targets.


Introduction
Intensive fast neutron sources using deuteron accelerators have been proposed for irradiation tests of fusion reactor materials, radioisotopes production for medical use, transmutation of long-lived radioactive nuclear waste, and so on. Neutron production data from various materials bombarded by deuterons are required for the design of such accelerator-based neutron sources. However, the experimental data, e.g. double-differential neutron production cross sections (DDXs), are not sufficient. Several experimental data of thick target neutron yields (TTNYs) have been taken at incident deuteron energies ranging from 5 to 40 MeV [1], while DDX data measured with thin target are very limited [1]. The DDX data are more useful for direct benchmark tests of theoretical models than TTNY data. Meanwhile, some deuteron nuclear data for energies up to 200 MeV are currently available: JENDL/DEU-2020 [2], JENDL-5 [3], TENDL-2021 [4] , FENDL-3.2b [5] , ENDF/B-VIII.0 [6] , and JEFF-3.3 [7] . Most of them are created based on theoretical model calculations. Therefore, experimental DDX data over wide ranges of incident energy and target mass number are strongly required for validation of nuclear data and theoretical models.
Under these situations on deuteron nuclear data, the DDXs were systematically measured for six targets(Li, * e-mail: watanabe@aees.kyushu-u.ac.jp * * Present affiliation: Japan Atomic Energy Agency (JAEA) * * * Present affiliation: National Institute for Quantum Science and Technology (QST) Be, C, Al, Cu, and Nb) at 102 MeV and forward angles from 0 • to 25 • at the Research Center for Nuclear Physics (RCNP), Osaka University [8] in our previous work. The present work is its extension to higher incident energy of 200 MeV. The forward-angle DDXs are measured for nine targets(Li, Be, C, Al, Cu, Nb, In, Ta, and Au) at 200 MeV for further investigation of the incident energy dependence of neutron production from deuteron bombardment. Moreover, the experimental data are compared with theoretical model calculations with PHITS (Particle and Heavy Ion Transport System) [9] and DEURACS (Deuteron-induced Reaction Analysis Code System) [10], and the latest nuclear data (JENDL-5 [3] and TENDL-2021 [4]) as benchmark tests. It should be noted that the result of Li has already been reported in ND2019 [11].

Experiment
The experiment was conducted at the N0 course in RCNP. The experimental procedure was almost the same as in our previous measurement with 102 MeV deuteron beam [8].
The experimental setup is schematically illustrated in Fig. 1. A pulsed deuteron beam accelerated to 200 MeV was transported to the neutron experimental hall and bombarded a target thin foil placed in the beam swinger magnet. The nine targets used in the measurement were all natural isotopes, i.e., Li, Be, C, Al, Cu, Nb, In, Ta, and Au. The deuterons passing through the target were delivered to a Faraday cup. The beam current was changed from 3 to 45 nA, depending on target species and neutron detection angles. Emitted neutrons from the target were detected by two different-size EJ301 liquid organic scintillators (50.8 mm by 50.8 mm and 127 mm by 127 mm in diameter and length, which hereafter will be referred to as 50.8-mm EJ301 detector and 127-mm EJ301 detector, respectively) located at two different distances of 7 m and 20 m, respectively. The 50.8-mm EJ301detector was used for the measurement of the low-energy component, and placed at the shorter distance of 7 m. On the other hand, the 127-mm EJ301 detector with higher intrinsic efficiency was situated at the longer distance of 20 m, so that high-energy neutron spectra were measured with high energy resolution. The neutron DDXs were measured at six angles (0 • , 5 • , 10 • , 15 • , 20 • , and 25 • ) for Li, Be, C, Al, Cu, Nb, and Au, and five angles (0 • , 5 • , 10 • , 20 • , and 25 • ) for In and Ta by moving the target along the beam trajectory in the swinger magnet. The emitted neutrons were transported to the 100-m TOF tunnel through a movable collimator. The position of the collimator was changed depending on the target position. A clearing magnet was installed in the collimator to remove background components of charged particles. The energies of emitted neutrons were determined by the conventional TOF method. The 50.8-mm EJ301 detector was removed from the neutron beam line in the measurement with the 127-mm EJ301 detector. Since the magnetic field of the clearing magnet influenced the photomultiplier tube in the 50.8-mm EJ301 detector located at 7 m, the magnet was switched off and a 5 mm thick NE102A plastic scintillator was additionally mounted in front of the 50.8-mm EJ301 detector as a veto detector for background charged particles.

Data analysis
The data analysis procedure is the same as in our previous works [8,11].
The light outputs from the EJ301 detectors were calibrated with two kinds of standard RI sources, 137 Cs and 241 Am/Be, and the thresholds of the 50.8-mm and 127-mm EJ301 detectors were set to be 0.49 MeVee and 4.3 MeVee, respectively. At low neutron energies below 15 MeV, the number of background gamma-ray events was comparable to that of neutron events in the measurement with the 50.8-mm EJ301 detector. Both the events were well separated by the pulse shape discrimination with the two-gate integration method [12].
The neutron TOF spectrum obtained after subtraction of gamma events was converted to the energy spectrum. Then, the experimental DDX was finally derived from the energy spectrum using the target thickness, the solid angle subtended by the detector, the deuteron beam current, the neutron detection efficiency, and the attenuation correction of neutron fluxes. The neutron detection efficiency calculated with the SCINFUL-QMD code [13] was employed. The attenuation of neutron fluxes in air at 7 m and 20 m was estimated by PHITS calculation with JENDL/HE-2007 [14,15]. Finally, both the DDXs measured at 7 m and 20 m were merged smoothy at 12 MeV. As a result, each experimental DDX shown in Fig. 2 is composed of the DDX measured at 7 m in the energy range ≤ 12 MeV and that measured at 20 m above 12 MeV.
Uncertainties of the measurements include both systematic and statistical errors. The total systematic error was estimated to be 12%, which consists of the detection efficiencies calculated by the SCINFUL-QMD code(10%), the solid angle(<1%), the attenuation correction in air estimated by the PHITS calculation(3%), and the effect of neutron scattering from the swinger magnet, the floor, the wall, and the collimator(<6%). It should be noted that only the statistical error is presented as the experimental error bar in the subsequent figures. Figure 2 shows the experimental DDXs of the nat C target for all emission angles from 0 • to 25 • . Each neutron spectrum has a characteristic broad peak around 100 MeV corresponding to half the incident energy, and the peak becomes sharper and sharper toward 0 • . This trend leads to very steep angular distribution of producted neutrons. The broad peak can be explained by neutron emission from elastic and non-elastic deuteron breakup reactions as discussed later in section 4.3. It was found that the observed energy and angular distributions of produced neutrons for the other targets are similar to those for nat C in Fig.2.

Experimental results
The measured 0 • -DDXs for all the targets are compared in Fig. 3. A characteristic peak around half the incident energy is clearly observed for all the target, and the peak yield increases gradually with increasing target atomic number. Differences in the energy spectrum shape among the targets are seen in the energy range less than 60 MeV, where the neutron yield increases as the target atomic number increases. Particularly, the increase is noticeable in the emission energy range below 20 MeV for heavier targets than nat Cu. This spectral component is expected to be formed by the statistical decays via evaporation process as discussed later.

Comparison with model calculations and nuclear data
In Fig. 4, the measured DDXs for nat Cu are compared with model calculations with PHITS [9] as well as deuteron nuclear data of JENDL-5 [3] and TENDL-2021 [4]. The deuteron nuclear data in JENDL-5 was created based on the model calculation using DEURACS [2,10], and the cross sections calculated with the TALYS code [4] were compiled in TENDL-2021. The PHITS code consists of a combination of different models to describe the total reaction cross section, the dynamical and subsequent evaporation processes. In the present calculation, the MWO model [16] is chosen for calculation of total reaction cross sections. INCL4.6 [17] and the generalized evaporation model (GEM) [18] are employed in simulating the dynam-  ical process including deuteron breakup reaction and the subsequent evaporation process, respectively. As can be seen in Fig. 4, the JENDL-5 data denoted by the red solid lines are in the best agreement with the experimental data, especially in the broad peak region around 100 MeV at small angles less than 15 • . With an increase in emission angle, JENDL-5 tends to underestimate the experimental DDX data at emission energies from 20 MeV to 100 MeV, particularly at 20 • and 25 • . The spectral shape of TENDL-2021 plotted by the blue dotted curves is quite different from the experimental one. It should be emphasized that TENDL-2021 underestimates remarkably the measured DDX data around the broad peak around 100 MeV at small angles less than 15 • . As a result, the steep angular distribution of the broad peak cannot be reproduced by TENDL-2021 data at all. The PHITS calculation is in overall agreement with the measured DDXs except in the high energy range above 150 MeV as shown by the green dashed lines in Fig. 4. In addition, the PHITS calculation underestimates the cross section in the broad peak region around 100 MeV at emission angles of 10 • , 15 • and 20 • .
We have investigated the reaction mechanisms of deuteron-induced reactions using DEURACS calculation. DEURACS can consider the following reaction processes: elastic breakup(EBU) reaction, non-elastic breakup(NBU) reaction, single-proton transfer(pTR) reactions to bound states in the residual nuclei, and statistical decay(SD) processes followed by the NBU process and deuteron absorption. In DEURACS, the EBU and NBU reactions are described by the continuum discretized coupled channel theory and the Glauber model, respectively. In addition, DWBA is employed for the pTR reaction, and the exciton and Hauser-Feshbach models are applied to the SD processes. Figure 5 presents the results of nat C, 27 Al, 93 Nb, and 197 Au at 0 • . The orange dot-dashed curves and blue dotted ones represent the EBU component and the NBU plus pTR components, respectively. The green dashed curves denote the SD components including the prequilibrium process. The sum of them is given by the red solid lines. The DEURACS calculations show excellent agreement with the experimental data over a wide range of emission energy, except in the low energy range between 20 and 60 MeV. This analysis indicates that the main component in the broad peak comes from the NBU process. As the target atomic number increases, the contribution from the EBU process is enhanced because Coulomb breakup is expected to become dominant for nuclei with high atomic number like 197 Au.

Summary and outlook
We have measured systematic DDX data of 200-MeV (d, xn) reactions on nine targets(Li, Be, C, Al, Cu, Nb, In, Ta, and Au) at emission angles ranging from 0 • to 25 • . The measured data were compared with the model calculations (PHITS and DEURACS) and nuclear data (JENDL-5 and TENDL-2021). It was found that JENDL-5 data based on DEURACS calculations reproduce the experimental data better than TENDL-2021 data and PHITS calculations In the future, further improvement of the reaction models used in DEURACS will be necessary for better reproducibility of various experimental data. Using the improved DEURACS, we plan to perform detailed data analyses focusing on the incident energy dependence of neutron production from deuteron-induced reactions for energies up to 200 MeV.