Investigation of cross sections of deuteron induced nuclear reactions on selenium up to 50 MeV

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Introduction
The main motivation for the present measurement was to produce a more complete and reliable database for activation cross-sections of deuteron induced nuclear reactions useful for practical applications and can also serve as a base for improvement of the description by theoretical codes.
In the literature only a few works containing data on deuteron induced activation cross sections on selenium were found. Some of the earlier measurements were done on enriched monoisotopic targets (Miskel [1], Debuyst [2], Paans [3], Qaim [4], Dmitriev [5] and Vakilova [6] are limited to low energy and all are related to study of medical radioisotope production and nuclear reaction mechanisms or nuclear structure studies. We present here for the first time experimental activation cross section data on natural selenium up to 50 MeV together a e-mail: ditroi@atomki.hu (corresponding author) with a comparison with the earlier experimental results and with predictions of the latest model codes.

Experimental technique and data evaluation
The activation cross sections on natural selenium (for isotopic composition see Table 1) were measured by using the activation method and the standard stacked foil irradiation technique combined with off-line high-resolution gammaray spectrometry. The irradiation, the activity measurement and the data evaluation were similar as described in more detail in our earlier works on systematic study of deuteron induced nuclear reactions on numerous targets (around 650 reactions induced on 62 target elements). Thin Se targets (2.5-3.8 μm) were evaporated onto high purity aluminum (99.9%) backings (50.5 μm thickness), and covered with 50.5 µm Al for protection against contamination and surface loss. The backings and the cover foils served also as recoil catchers and were used for monitoring the beam parameters (beam current and energy).
The Se target foils were interleaved with Al (102.6 μm), Ti (10.9 μm) additional energy degrader and/or monitor foils. The Ti foils also served to follow the recoiled radionuclei from the Al monitors. The stack composition is presented in Table 2. Irradiation was performed at the Cyclone 110 cyclotron of the Université Catholique in Louvain la Neuve (LLN) at 50 MeV deuteron energy with a beam current of 20 nA for 40 min. The large number of monitor foils allowed us to follow the beam intensity and the energy degradation along the stack in detail via the simultaneous re-measurement of the excitation functions of the 27 Al(d,x) 24,22 Na. The good reproduction of the standard monitor data is illustrated in Fig. 1. The 24 Na excitation function was measured inde- pendently for the target backing/cover Al foils and for the thick Al degraders and show acceptable agreement. The activity of the irradiated samples was measured without chemical separation by using the well-calibrated gammaspectrometry set-ups at VUB Brussels. The decay of activity of the samples was followed by series of measurements to identify and to separate complex gamma-lines and to follow the cumulative effects after decay of short-lived isomeric states and/or parent nuclei. The energy degradation along the stack was initially determined by a stopping calculation and was confirmed on the basis re-measured excitation function of monitor reactions. For initial calculation home made codes STOPPING and STACK have been used, which are based on the Ziegler's tables. For the associated error estimation also the Ziegler's SRIM code was used. The uncertainties on the cross-sections were estimated by using the error propagation of the formula used for calculation (except non-linearly contributing time depending factors). The uncertainties of the contributing factors were: number of bombarding particles (7%), gamma intensity data (3%), detector efficiency (5%), peak area (0.1-10%), number of the target nuclei (5%). The uncertainty of the energy scale was calculated by taking into account the energy uncertainty of the primary beam, the pos-sible variation in the target thickness and the effect of beam straggling. The used nuclear data were taken from NUDAT 2.6. More details on the experiment and the data evaluation are collected in Table 2.

Theoretical calculations
The cross sections of the investigated reactions were calculated using the modified pre-compound model codes ALICE-IPPE (Dityuk et al. [17]) and EMPIRE-II (Herman [18]). During the recent analyses of several (d,p) reactions we were confronted with a large underestimation of the measured cross sections by the code results. We came to the conclusion that the experimentally observed cross sections of the (d,p) reaction cannot be reproduced below 20-30 MeV with the available statistical model codes. It is well known that for the (d,p) reactions at low energies the direct stripping process play a very important role. To achieve better description of available data for (d,p) reactions a phenomenological enhancement factor K has been introduced, as energy dependent and estimated to describe the whole set of the observed (d,p) cross sections for medium and heavy nuclei. By this improvement, in the ALICE IPPE-D and EMPIRE-D code versions [19] for deuteron induced reactions, the direct (d,p) channel is increased strongly and this is reflected in changes for all other reaction channels in both codes.
The EMPIRE-D and TALYS model codes predict acceptable well the near-threshold section of the neutron emitting reactions. The ALICE-D predictions are less satisfactory for this energy because of the much simple model of the lowenergy discrete levels of the nuclei in question. For determination of the cross sections in the vicinity of the local maxima, a ratio of the level densities of competing channels is important. The seen differences in calculations are the consequences of differences of the default level-density parameters of the particular codes. Discrepancies between calculations with experiment can be improved by the proper adjustments of input parameters. The comments on the (d,pxn) reactions are similar to those discussed above. However, a special attention is paid to the (d, p) reaction. This reaction is dominated by the direct breakup mechanism without the formation of intermediate pre-equilibrium states of the nucleus.  Tables 3, 4 and 5. The isotopic cross sections presented in some earlier published studies were normalized to natural Se abundance.

Cross sections of residual radionuclides of bromine
The radioisotopes of bromine are produced only by direct (d,xn) reactions. The contributing reactions and the reaction Q-values were presented in Table 1. Due to the long cooling time needed for transfer of the irradiated targets form LLN to VUB, the formation of short-lived 83,84m,84g Br could not be confirmed.

The nat Se(d,xn) 82 Br process
As the higher energy metastable state of 82 Br has a short half-life (T 1/2 = 6.13 min, IT: 97.6%) we present cumulative cross-sections for the ground state (T 1/2 = 35.282 h), measured after 82m Br total decay (Fig. 2). The formation on 82 Br occurs only through the (d,2n) reaction on 82 Se. Our data point near the threshold seems to be shifted, when compared to the earlier experimental data and to the theory. This discrepancy is partly explained by the large energy uncertainty   into account the significantly lower gamma-line intensities and the lower production cross section the contribution of the decay of 77 As was neglected. The theoretical predictions slightly overestimate the experimental data.

The nat Se(d,xn) 76 Br process
Most of the gamma-lines of 76 Br (16.2 h, ε: 100%) and 76 As (26.24 h, β-: 100%) are common as both decay to 76 Se. A few independent lines with low intensity exist but we couldn't identify them in our spectra. Due to the difference in half-life we estimate that in our last series of spectra the contribution of the shorter-lived 76 Br to common gamma-lines can be neglected, taking also into account the ratio of cross sections finally derived. In our last series of spectra, the strongest line of 76 As (559 keV) was identified in the high energy samples, and cross sections for production of 76 As could be deduced (see Sect. 4.3.1). For correction of the 76 As contribution in the 559 keV gamma-line in the first series of gamma-spectra (used to derive 76 Br cross sections) we fitted our experimental cross section data to the prediction of ALICE-D, and we calculated the 76 As contribution to the 559 keV line (because the ALICE-D prediction is the closest to the experimental values in Fig. 9). The correction was around 5% in average and we deduced cross section for production of 76 Br (Fig. 5). No earlier experimental data were found. Our data show less pronounced differences than the calculated values in contributions of reactions on the different stable Se isotopes and especially the 76 Se(d,2n) reaction seems

The nat Se(d,xn) 75 Br process
The excitation functions of the nat Se(d,xn) 75 Br (96.7 min) reaction are shown in Fig. 6. The earlier experimental cross sections of the 74 Se(d,n) reaction measured by Qaim et al. [4] for energies below 18 MeV were normalized to natural Se isotopic composition. From the theoretical descriptions the EMPIRE-D estimation is acceptable.

Cross sections of residual radionuclides of selenium
The radioisotopes of selenium are produced by direct (d,pxn) reactions and decay of parent isobaric bromine radionuclides. The contributing reactions and the reaction Q-values are presented in Table 1.

The nat Se(d,x) 75 Se process
We can deduce cumulative cross sections for production of 75 Se (119.78 d). It includes the complete decay of parent 75 Br (96.7 min, ε: 100%) (Fig. 7). No earlier experimental data were found. The theoretical data, especially the EMPIRE are in good agreement with the experimental results.

The nat Se(d,x) 73 Se process
The measured cross sections for production of 73g Se (7.15 h) are cumulative as they were measured after complete decay of short-lived 73 Br (3.4 min, ε: 100%) and 73m Se (39.8 min, ε: 27.4 %, IT: 72.6 %) (Fig. 8). No earlier experimental data were found. All theoretical codes give acceptable trend, TENDL and EMPIRE give good prediction up to 40 MeV, over this energy the ALICE prediction is better.

Cross sections of residual radionuclides of arsenic
The radioisotopes of arsenic are produced by direct (d,2pxn) reactions and by decay of parent selenium isotopes. The con-tributing reactions and the reaction Q-values are presented in Table 1.

The nat Se(d,x) 76 As process
To get production cross sections for 76 As (26.24 h, β − : 100%) we have used the activity derived from the 559 keV gamma-line signals assessed in the last series of measurements. The contributions of the contaminating, common gamma-line of 76 Br (16.2 h, ε: 100%) were small as estimated on the basis of cross sections and the elapsed time after EOB. Statistically reliable signals for the 559 keV line were identified only in the high energy samples (Fig. 9). Significant disagreement can be observed in the predictions of the different theoretical codes. Some of our data points (i.e. The possible reason could be that the corresponding spectra have been measured by different cooling times and measuring times than the others, and the peak counts were under 100, which could make large statistical error.

The nat Se(d,x) 74 As process
The 74 As (17.77 d) is produced only directly. The experimental and theoretical data are shown in Fig. 10. No earlier experimental data were found. ALICE-D gives the best and acceptable prediction.

The nat Se(d,x) 72 As process
The 73 As (80.30 d) is produced directly and through the decay of the 73m Se (39.8 min, ε: 27.4%, IT: 72.6%) and 73g Se (7.15 h, ε: 100%) parent isomeric states. The cumulative cross sections are shown in Fig. 11. The ALICE-D and TENDL-2019 give the best description.

The nat Se(d,x) 71 As process
We could obtain cumulative cross sections for production of 71 As (65.30 h) (Fig. 12), including direct production and complete decay of short-lived parent 71 Se (4.74 min, ε:    [20] for 75 Se and 74 As production. The former is lower and the latter is higher than our new data.

Activation file
Selenium is used with bismuth in brasses to replace more toxic lead. Like lead and sulfur, selenium improves the machinability of steel at concentrations around 0.15% [21]. Selenium produces the same machinability improvement in copper alloys. The recently measured data can be useful for nuclear activation related applications (activation analysis, accelerator technology).

Nuclear reaction theory
As was shown in several of our recent investigations the description of activation cross sections of the deuteron induced reactions by model codes is not very successful, due to e.g the fact that the (d,p) reactions are not handled correctly. The D-versions of the EMPIRE and ALICE codes try to improve on it. New experimental data are vitally impor-  tant to test the present predictions and to further improve the reaction codes and the input parameters.

Production of medical isotopes
Several of the investigated activation products have applications in nuclear medicine [22][23][24]. The main important production routes of these isotopes are summarized in Table 6. The production mostly requires monoisotopic targets to assure the radionuclide purity. The present cross section data combined with theoretical results that describe properly the experiments on nat Se can be useful to estimate production routes yields. The data can also serve as a basis to derive monoisotopic cross sections in the energy range where only one reaction contributes.

Summary and conclusion
The excitationfunctions for nat Se(d,x) reactions resulting in formation of 82 Br(m+), 80m Br, 77 Br(m+), 76 Br(m+), 75 Br, 75 Se(cum), 73 Se(cum), 76 As, 74 As, 73 As(cum), 72 As, 71 As (cum) were measured up to 50 MeV in the frame of a systematic study of deuteron induced threshold reactions. The experimental cross section and deduced yield data were compared with some earlier measured low energy values and are showing good agreement. Model calculations were done with the ALICE-IPPE-D and EMPIRE-D code. The ALICE-D and EMPIRE-D theoretical calculations, completed with the TALYS results from TENDL-2019 on-line library, describing with varying success the shape and the absolute values of the experimental data, especially for (d,2pxn) reactions leading to As radioisotopes. The obtained experimental data provide a basis for improved model calculations and for applications in radioisotope production, in dose calculations, in waste handling, in charged particle activation analysis for thin layer application and for nuclear data validation.

Data Availability Statement
This manuscript has no associated data or the data will not be deposited. [Authors' comment: The datasets generated during and/or analysed during the current study are not publicly available yet but are available from the corresponding author on reasonable request].
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