27 Al(d,alpha) and 27 Al(d,p) Nuclear Reaction Cross Sections at Ed<2MeV Measured at Three Backward Scattering Angles Related to NRA


 The cross-sections of deuteron-induced nuclear reactions suitable for ion beam analysis, measured in different laboratories, are often significantly different. In the present work, differential cross-sections of 27 Al(d,p) and 27 Al(d,α) reactions were measured, and the cross sections benchmarked with thick target spectra obtained from pure aluminium for the first time in two independent laboratories. The 27 Al(d,p) and (d,alpha) differential cross-sections were measured between 1.4 and 2 MeV at scattering angles of 165°, 150°, and 135° in the VDGT laboratory in Tehran (Iran), and the same measurements for detector angle of 150° were repeated from scratch, including target making, with independent equipment on the SAFIR platform at INSP in Paris (France). The results of these two measurements at 150° are in good agreement, and for the first time a fitted function is proposed to describe the Al-cross sections for which no suitable theoretical expression exists. The obtained differential cross-sections were validated through benchmarking, by fitting with SIMNRA deuteron-induced particle spectra obtained from a high purity bulk Al target at both labs for deuteron incident energies between 1.6 and 2 MeV. The thick target spectra are well-reproduced. The evaluated and benchmarked cross sections have been uploaded to the ion beam analysis nuclear data library database (www-nds.iaea.org/ibandl/).


1-Introduction:
Ion beam analysis (IBA) has been widely used to analyze quantitatively and with high sensitivity the composition and elemental depth profiles in the surface regions of solids. For light element analysis, suitable nuclear reactions can be found and in particular, deuteron-induced reactions, (d,p) or (d,α), often have high Q-values and appreciable cross-sections. In many cases of Nuclear Reaction Analysis (NRA) of thin films, isolated reaction particle peaks may be obtained with judicious choice of scattering angle, incident beam energy, and filtering foils in front of the charged particle detector. However, in general, NRA generates complex spectra with overlapping peaks, especially from thick samples. Knowledge of the cross-sections for the cases of isolated peaks is already useful for designing experiments to determine elemental contents of thin films. Many such cross-sections, for example 16 O(d,p0) 17 O, 16 O(d,p1) 17 O, 12 C(d,p0), 14 N(d,α0), have been carefully measured at energy and angular ranges of analytical interest [1][2][3][4]. It is sometimes possible to analyse several light elements simultaneously by NRA. Knowledge of the cross-sections of reactions that are not necessarily of primary interest for thin film analysis, is then often needed for cases in which targets contain elements giving rise to reactions that produce particle groups that interfere with the primary analytical peak, and even more so in thick target NRA where the broadening of the particle spectra from the non-zero target thickness leads to a much greater probability of elemental interferences. Furthermore, accurate experimental nuclear reaction cross-sections are required to provide proper parameters for appropriate approximations and expressions of theoretical nuclear reaction mechanism models [5][6][7].
Because oxygen is the most abundant element in the earth's crust and because of the universal importance of oxides in earth sciences and materials science, accurate cross-sections for 16 O and 18 O nuclear reactions have been determined [1,8]. The second most abundant element is silicon, and although it is an intermediatemass element from the point of view of IBA, it also has nuclear reactions of analytical interest that have been determined [2,9] .
Aluminium is the third most abundant element that is widely used in industry for its mechanical and electrical properties, decorative applications, and its resistance to environmental aggression especially after suitable electrochemical passivation. Aluminium is also widely present in the alumina-silicate rocks that constitute so much of the earth's upper crust. In many thin film systems, such as III-Nitrogen semiconductors developed amongst other things for UV-C light emitting diodes destined to replace UV mercury lamps in mass sterilisation applications for COVID mitigation, and thin conformal alumina films or nanolaminates grown by Atomic Layer Deposition where aluminium is an essential component, absolute determination of the Al content is paramount for developing improved materials. There is a wealth of deuteron-induced charged particle reactions on 27 Al with high Q-values that may be exploited in NRA for analysis of aluminum or encountered as interferences in NRA of aluminium-containing materials. [10][11][12][13][14][15][16][17][18][19][20] There is a further motivation for good knowledge of Al cross sections: even if analysis of Al is not the main objective of a measurement, reaction products from Al may interfere with the signals from other reactions of interest and to be able to fully fit a complex NRA spectrum, all of the cross sections involved need to be known. Detailed knowledge of the cross-sections of these reactions is thus a significant interest in the field of NRA. The compound nucleus 29 Si contains too many close levels to be able to be treated satisfactorily within R-Matrix theory, and too few to be able to be handled satisfactorily with a statistical approach. At present, the best we can obtain is well measured experimental cross-sections [10][11][12][13][14][15][16].
In this work, we have determined the cross-sections for the 27 Al (d,p0+1,2+3,4,5+6, 9,10,11,12) and 27 Al(d, α0, 1,2,3,4) reactions at an energy below 2 MeV and at 150° scattering angle in two completely independent measurements in two different laboratories: the Van De Graaff Lab in Tehran (VDGT) and the SAFIR platform of the Institut des NanoSciences de Paris (INSP). The 27 Al(d,p) and (d,α) cross-sections were also determined at 135° and 165° at VDGT. From our measured data and a critical evaluation of previous measurements, we propose a set of recommended cross-sections for NRA and demonstrate their validity through benchmarking experiments in a thick pure aluminum target in both laboratories.

2-Experimental setup and procedure
The experimental setups at VDGT and INSP are significantly different. We present here the main experimental features of each laboratory.

2-1-1-Chamber and data acquisition
At VDGT, cross sections and benchmarking spectra were measured in the 30º left beamline of the 3MV Van de Graaff electrostatic accelerator, equipped with a chamber developed for accurate and reliable RBS/NRA measurements [24]. A beam of 20-40nA was directed into a beam spot of 1.5 × 1.5 mm 2 . The energy resolution is estimated to be about 1 keV. Under these conditions, deadtime was less than 10% and pileup was minimized.
The pressure of the chamber was about 2×10 -6 mbar during the measurements. The detection system for all of the measurements consisted of three 25mm 2 ×300 µm thick surface barrier detectors installed at 135º, 150º, and 165º degrees from the incident beam direction. The angular spread of each detector was less than 3°, with solid angles  of 1-2 msr. Integrated beam charge Q of 10C was usually sufficient to obtain adequate statistics.

2-1-2-Calibration energy of the accelerator:
We determined beam energy from the field strength of the analyzing magnet, measured with an NMR fluxmeter [25]. The energy calibration of the accelerator was determined from the reaction threshold energy at 1880.44 ± 0.02 keV in the 7 Li(p,n) 7 Be reaction. The target was a pressed LiF pellet with a 10 µg/cm 2 silver coating for charge evacuation and neutrons were detected with a BF3 detector.

2-1-3-Target preparation:
The thin Al target must be of appropriate thickness, stable both in atmosphere and under the beam in vacuum, and should also be amorphous to avoid unwanted channeling effects [26]. To achieve these requirements, physical vapor deposition (PVD) was chosen from amongst the different methods for thin Al target preparation [27]. Pure Al was evaporated onto a microscope slide which had been prepared by dipping into a mixture of water and detergent under ultrasonic agitation. The PVD system was a model VE-770 with a base pressure of about 10 -6 mbar, equipped with a coiled tungsten filament. The obtained film was floated onto water and then fished over an 8mm diameter hole in a thin metal sheet. Finally, 10 ± 0.5 nm of Ag was deposited onto the thin self-supporting vacuum evaporated Al film as an internal reference [24,28].

2-1-4-Characterization of the thin target
The thin target thickness is determined by RBS [29] with an uncertainty of less than 5%, due to uncertainties in Q×Ω, in possible deviations of the 27 Al(,) 27 Al cross section from the assumed Rutherford cross section and in fitting the simulated spectrum to the measured spectrum. The thickness of target was only used for determination of deuteron beam energy loss through the target. The thickness and stoichiometry of the Al/Au target were measured at the three detection angles of 135º, 150º, and 165º by alpha particle beams of 1.8 MeV. This measurement was simulated with SIMNRA 7.03 by using the Chu and Yang straggling model and Ziegler/Biersack stopping power [30]. Typical simulated and measured spectra are shown in Fig. 1. In target characterization with the alpha beam, the areal density ratio was calculated by equation [1]: where N corresponds to the areal density of the target and Y to the experimental yield (net area under the peak). Here, NA rather than [A] is used to represent the areal density of species A, in order to simplify the expressions. The average of these ratios from different detection angles was estimated by assuming the Rutherford cross section for reaction of alpha particles with Ag and Al, and applying a correction for the energy loss in the thin target. Using this ratio eliminates uncertainty due to solid angle, dead time, and charge measurement for the differential nuclear cross section measurements.

2-2-Experimental work in INSP Lab:
At INSP Lab in Paris, the 30° right beamline of the 2.5 MV Van de Graaff electrostatic accelerator of SAFIR (Système d'Analyse par Faisceaux d'Ions Rapides) platform was employed for our measurement.
The accelerator energy, read from the Generating Voltmeter signal, was calibrated by using the narrow nuclear resonances of the 27 Al (p, γ) 28 Si reaction at 991.88 keV, the 13 C(p,γ) 14 N reaction at 1747.6 keV and the 15 N(p,γ) 12 C reaction at 426.1 keV. In each case, the gamma rays were detected with a BGO scintillation detector at 0° [31,32]. Because of the very high energy resolution of the beamless than 250eV full width half maximum energy spread over the range reported here, excitation curves were fitted with SPACES [33] so as to compensate for small distortions of the excitation curve due to surface contaminants and oxidation.
The treatment of the GVM signal has been implemented into Labview rather than in analogue electronic circuits, giving an energy calibration that is highly linear and practically independent of temperature.
A similar method to that used at VDGT was employed at INSP for preparation of the thin self-supporting targets. An EDWARDS FL 400 and VINCI technologies PVD 4E were used for Al and Au evaporation respectively. The preparationfloating and fishing -and characterization of the target were the same as at VDGT Lab in Tehran, with the exception that here we have used Au rather than Ag as the internal standard for the INSP targets, and subsequently the areal density ratio was taken into account as in the differential cross section measurement. Also, absolute values of the areal densities NAl and NAu were determined by comparing with the standard Bi-implanted Si reference with an uncertainty of 2%-3% in the same RBS measurement. Scanning electron microscopy (SEM) images of the surface of from Au/Al target, shown in

3-1-The differential nuclear cross section measurement value at VDGT Lab in Tehran:
Among the nuclear reactions that can be used to characterize Al, 27 Al(d,p0+1,2+3,4,5+6,9,10,11,12) 28 Al and 27 Al(d,α0,1,2,3,4) 25 Mg were selected for measurements of the deuteron induced reaction cross sections since these particle groups can be identified and their intensities estimated under reasonable experimental conditions. The cross sections were measured with 10 keV steps, for energies ranging from 1.3-2 MeV.
In order to discriminate between high Q-value (d,p) and (d,α) groups in a single measurement setup, we placed a 4µm thick mylar filter in front of the detector. The judicious choice of mylar thickness, to minimize interferences in the thin target spectra, was found through SIMNRA simulations. The discrimination is illustrated in Fig. 3, comparing a real measured spectrum with 4 m mylar, with a simulated spectrum without filter. Clearly, interference between the particles from 27 Al(d,p0+1) 28 Al and 27 Al(d,α0) 25 Mg, and from 27 Al(d,p4) 28 Al and 27 Al(d,α3) 25 Mg is eliminated. Eq. (2): where Ed, YAl or Ag, θ and (∆ ) θ , Ag represent incident deuteron beam energy, the experimental yield of Al or

3-2-The differential cross section measurement at INSP Lab in Paris:
The experiments were done with three different experimental setups, as follows: for (d,α) reaction measurements, we used the 4µm-thick mylar in front of the 300 µm-thick surface barrier detector and repeated these measurements without mylar in front of the detector. For (d,p) reaction measurements, in the third configuration, a 100µm-thick mylar was chosen in front of a 500 µm-thick pin diode detector at scattering angle of 150º. Typical experimental alpha particle and proton spectra from the 27 Al(d,α) 25 Mg and 27 Al(d,p) 28 Al reactions are shown in Fig. 8-a and Fig. 9-a, respectively.  The differential cross-sections were determined by using equation [1], just replacing Ag by Au: where θ, YAl and Au, Ed(Au), Ed(Al) correspond to the scattering angle, integrated yields (Au and Al) as obtained from the experimental spectra, the energy at the surface of the Au layer, and the energy at half of the Aluminium thickness (including energy loss in the Au film), respectively. represents the areal density of Au versus Al present in the target, measured by RBS.

3-3-Uncertainties
Using the measured ratio and normalizing the cross section measurement to the corresponding Rutherford cross-section, the uncertainties owing to solid angle, detector angular settings, dead time, and charge measurement were eliminated [35]. The uncertainty of the ratio was estimated to be about 3% according to the counting statistics. The corresponding statistical uncertainties of ( dσ dΩ ) θ, (Al) were estimated to be 4%-9% according to the error propagation formulas.
The measured differential cross section at INSP Lab with error bars at scattering angle 150º for the 27 Al(d,α0-

4-2-Comparison with previous studies
Although we are not aware of previous measurements for 135° (other than [34], for (d,), discussed above) and 165° scattering angles, several data sets exist for 150°. Comparison of the cross sections measured here with available aluminum (d,p) and (d,) cross-sections at 150º is presented in Fig. 11. As mentioned in [10], the measurements of Ref. [13] barely overlaps with previous studies, and the data from [16] are underestimated by a factor of about 2, so they are no longer considered here. The differential cross section values in Ref [21] show systematic differences from the other data, beyond the uncertainties given in the paper, both for 27 Al(d,p0+1,2+3,4,5+6) 28 Al and 27 Al(d, α0,1,2,3,4) 25 Mg. Data in Ref. [10] are in acceptable agreement with our data except for a small energy shift. We attribute this energy shift to the energy loss of the incident beam in the target, which was not taken into account in [10]. The four retained datasets have been plotted in Fig. 12 for the 150° scattering, with the data from Ref. [10] corrected for the energy loss in the target, using the target thickness supplied in that publication.  27 Al(d,p0+1,2+3,4,5+6) 28 Al reactions [10,21].

4-3-Evaluation of 150° cross section measurements
Since there is no suitable nuclear reaction model for these reactions, the question arises as to how to represent the best averaged values of the data to propose a single recommended cross section at any energy within the measured range. We have taken the approach of fitting a freely chosen mathematical function to all of the data, weighted inversely according to their reported uncertainties.
The four retained datasets were therefore fitted with 8-term and 20-term Fourier series, and a spline interpolation algorithm, shown in Fig. 12.
The differences between the fitted functions are small but the 20-term Fourier series allows the data to be represented with good fidelity and not too many fitted parameters. This is shown in Fig. 13.

4-3-1-Fourier series equations
One of the advantages of fitting the data with the Fourier series is that the theoretical function can be expressed easily and used as a reference model in future works. The actual Fourier series are written as follows [36]: Theoretically, the Fourier coefficients and can be evaluated as follows: Considering the N=20 Fourier series, the coefficients for all of the cross sections reported here (in addition to the 150° collection) were calculated and are presented in Table 1. The goodness of fit is given by the coefficient of correlation R which describes the proportion of the variation of the data described by the fitted function [37]. R 2 is above 0.96 for the highest cross sections, and above 0.9 even for the lower cross sections which are statistically noisier.

5-Benchmarking the Evaluated cross sections
The measured cross sections are validated by a benchmarking exercise [38,39], in which the cross sections are used in an independent experiment. For NRA cross sections, this almost always consists in obtaining thick target NRA spectra from a well-defined (often mono-elemental) target and verifying the extent to which the measured cross sections reproduce the observed spectra when included in an established NRA simulator such as SIMNRA. To our knowledge, only the 27 Al(d,p) 28 Al cross-sections have been benchmarked, by obtaining and fitting thick target spectra, for just one incident energy and one scattering angle [10], whilst there have been no benchmarking experiments at all for 27 Al(d,) 25 Mg cross sections.
The goal of the present work is to benchmark the 27 Al(d,p) 28 Al and 27 Al(d,) 25 Mg cross sections at three scattering angles, 135°, 150°, and 165°, and with various incident beam energies in two different laboratories.
For the experimental part of benchmarking, charged particle spectra were obtained from a thick pure aluminium target under deuteron irradiation. For the simulation part of benchmarking, the SIMNRA 7.03 code is applied with the Chu and Yang straggling model and Ziegler/Biersack stopping power.

Lab in Tehran
For benchmarking the 27 Al(d,p) 28 Al and 27 Al(d,) 25 Mg cross sections at VDGT Lab in Tehran, we used a thick pure Al target with a thin Ag layer deposited on it for the self-normalization process. No mylar was used in front of the detector. Other experimental parameters are as explained in section 2-1. The results of benchmarking for Ed=1600-1900keV at the scattering angles of 135°, 150° and165°, with an incident energy interval of 100keV, are shown in Fig. 14, Fig. 15, and Fig. 16 , respectively. At 150°, the three cross section data sets (VDGT data, INSP data, and fitted data) have been incorporated into the SIMNRA library. Overall, the agreement between the simulated and measured spectra is satisfying.

5-2-Benchmarking of measured data for 27 Al(d,p) 28 Al reactions at INSP Lab in Paris:
For benchmarking the 27 Al(d,p) 28 Al cross sections at INSP Lab in Paris, Au rather than Ag deposited on the thick pure Aluminum target acted as the internal reference. Moreover, a new multi-holder detector at INSP lab was designed (Fig. 17), which included three 1cm 2 Hammamatsu S3590-09 PIN diodes, with depletion depth of 300m, as detectors at 135°, 150° and 165°. A 100µm mylar foil in front of each detector ensured the elimination of the alpha particles from the spectrum.
The benchmarking results are displayed in Fig. 18 for Ed=1700-2000keV with an energy step of 100keV, at the scattering angle of 150° for VDGT data, INSP data, and fitted data sets. Figures 19 and 20 present the benchmarking results for Ed=1500-1800keV with an energy step of 100keV at the scattering angles of 165° and 135°, respectively. The simulation at these angles employed the measured VDGT cross section data. In general, the correspondence between the simulations and the measured thick target spectra was very satisfying.
The range of measured cross-sections used for simulating the spectra was 1. We note that the recommended cross sections for 135° and 165° are the first 27 Al(d,p) and 27 Al(d,) cross sections to be benchmarked at these angles for NRA.

7-Acknowledgements
We are particularly indebted to S. Steydli (INSP) for assistance in mechanical and vacuum aspects, and H.