Measurement of 9 Be( 3 He,p i ) 11 B ( i = 0, 1, ..., 9) nuclear reaction cross sections in the 1.0 MeV to 2.5 MeV energy range

In fusion materials research using ion beam analysis techniques, the reactions 9 Be ( 3 He,p i ) 11 B ( i = 0, 1, 2 K ) are relevant to probe Be-related plasma-wall interactions. The cross sections for this reaction have been examined previously; nevertheless, there is a ∼ 40% difference in the studied energy interval between the two most relevant earlier studies. Therefore, a new data set for the differential cross sections 9 Be ( 3 He,p i ) 11 B for the proton groups i = 0, 1, K , 9 is given. The measurements were performed using a thin beryllium ﬁ lm in the laboratory energy range from 1.0 MeV to 2.5 MeV in steps of 50 keV for lab angles from 115 ° to 165 ° to the incoming beam direction in steps of 10 ° . Additional measurements for intermediate angles were performed over the same energy range in steps of 250 keV. The results are in good agreement with one of the previous studies and a benchmarking measurement was performed against the yield of a beryllium thick target at 2.5 MeV for 135 ° .


Introduction
Several technological obstacles have been recognised as fusion reactors, like JET (Joint European Torus), started operating. One of the obstacles is the incomplete knowledge concerning the mechanisms of the interaction between the plasma and the Plasma-wall Facing Components (PFC), which are subjected to high thermal and radiation loads [1][2][3]. PFCs must comply with various safety regulations and standards [4] and so far, as a result of the different experiments in tokamaks around the world, it was considered that beryllium and tungsten-based metal walls are the best options [4].
Ion Beam Analysis (IBA) techniques are relevant in this study as they enable quantitative analysis of erosion and re-deposition and fuel retention processes [5]. Nuclear Reaction Analysis (NRA) using 3 He beams are of particular interest as they allow overcoming the low sensitivity to light elements of Rutherford Backscattering Spectrometry (RBS) and NRA with protons or 4 He beams, or the spectrum complexity of Elastic Backscattering Spectrometry (EBS) [6]. As such, high cross sections 3 He-induced nuclear reactions are being used for quantification of low-Z species, particularly deuterium, lithium, beryllium, boron, and nitrogen [7,8].
In what concerns beryllium, the most energetic ejected protons from the reaction 9 Be( 3 He,p i ) 11 B (Q = 10.32 MeV, i = 0, 1, 2, 3) are easily detected and found isolated from the remaining spectrum. Cross section data required for detecting Be with NRA is limited, but the increasing demand in fusion materials research has increased the need and interest in new measurements of reaction cross sections [9] to fill gaps in databases and increase the accuracy of old measurements. Table 1 summarizes the frame sets of the five main experimental studies conducted to determine the cross sections of the 9 Be( 3 He,p i ) 11 B reactions [6,[10][11][12][13]. The two most recent data sets are directly comparable as they were obtained for the same laboratory angle of 135° [6,13]; however, the two cross sections sets differ significantly, by a ratio of around 1.4. This is one of the reasons why new measurements are a priority.

Previous works
Although more experiments on these reactions have been carried out, they were mainly focused on their theoretical evaluation [11,14,15].

Method
2.1. 9 Be target A Be target of ITER grade quality (> 99% pure Be, < 1% BeO, < 0.1% C) was used in the measurements. It was produced by the Romanian National Institute for Laser, Plasma and Radiation Physics (INFLPR) [16]. It consisted essentially of a three-layered sample: 500 nm W on Si, with a Be thin film on top of the W. Thin film deposition was performed by the thermionic vacuum arc method (TVA) [17]. The W layer is not continuous indepth, being interrupted by a Ni/W mixed interlayer. The Be layer thickness determination was accomplished through RBS with a 1.75 MeV 4 He + beam, from the shift of the W energy edge when compared to that of a W sample with no evaporated film on top. The spectra taken under normal incidence from the RBS detector, placed at 160°to the incoming beam direction, (with solid angle 1.25 msr and FWHM energy resolution 35 keV) is shown in figure 1. The Be areal density (n Be ) obtained is n Be = (19.2 ± 1.4) × 10 17 atoms/cm 2 , which corresponds to (156 ± 11.3) nm, if we consider the beryllium bulk density (12.35 × 10 22 atoms/cm 3 ). Carbon build-up was periodically verified and the effective energy, considered as the energy of the 3 He particle at half the thickness of the Be layer, was corrected accounting for the energy loss in the accumulated carbon.   [11] 1967 p 2 , p 3 and p 6 to p 9 1-3 15°to 163°13% Lin et al [12] 1981 p 0 to p 8 2.4-6 90°15% Barradas et al [6] 2015 p 0 to p 3 1-2.5 135°10%-20% Provatas et al [13] 2020 p 0 to p 6 1.24-2.87 107°to 164°(2°step) 10% Figure 1. Comparison between the RBS spectra for a pure W sample (green triangles markers) and for the W target with the Be film on top (blue squares markers). NDF simulation curves (full lines) are overlaid to the corresponding experimental points. Yields for the W target were multiplied by 1.2 to aid the visual spectra comparison.
were in the range 2-20 nA, depending on the beam energy. The energetic protons from the 9 Be( 3 He,p i ) 11 B reaction up to i = 11 were detected by three PIPS detectors, mounted on a rotatable plate, and spaced by 20°. A goniometer connected to a stepper motor digitally controlled allowed to command the position of the detectors and therefore perform angular scans under automated computer control, cf figure 2. In front of all three NRA detectors, a 12 μm thick Mylar foil was placed to stop the elastically scattered particles before reaching each detector. This allowed to reduce detector's dead time and protect them against beam-induced radiation damage. The two NRA detectors used to cover the angles between 130°and 165°have a solid angle of (3.6 ± 0.2) msr. For the third detector, covering the angles between 110°and 125°the solid angle is (3.4 ± 0.2) msr. For the NRA detectors, the angle spread due to their finite aperture is ∼1.8°and their active layer thickness is sufficient to detect even the most energetic proton group, p 0 , associated with the ground state of 11 B. For each run, the accumulated charge was obtained by fitting the spectrum of the 3 He ions elastically scattered from W nuclei. The elastic scattering signal was measured with an additional detector placed at a scattering angle of 160°, with the solid angle equal to (1.25 ± 0.05) msr and spread in the scattering angle due to the detector's finite aperture of 1.8°. This detector had no Mylar foil and is identified in figure 2 as 'RBS detector'.

Experimental details
Beamline energy calibration was performed by measuring the gamma yield from the 19 F(p,αγ) 16 O reaction at the resonance energies of 587, 672, 872, 935, 1348, 1375 and 1691 keV.
With the experimental findings, a confidence interval about the expected value of the magnetic flux density B in the beam analysing magnet for each value of the energy E was calculated, and an energy uncertainty was calculated therefrom from the width of the confidence interval. The relative ion beam energy uncertainty was found to be better than 0.3%. The 3 He beam was collimated to a dimension of 0.6 × 0.6 mm 2 in target by two collimation slits and one anti-scattering collimator. The experimental configuration assured an energy resolution of 1 keV, measured by the 991 keV resonance of 27 Al(p,γ) 28 Si reaction (Eγ = 1779 keV, Γ = 0.10 keV). The NDF code [18] was used to fit the spectra of the elastically scattered 3 He ions, taking into account the plural scattering and pile-up effects. A typical NRA spectrum for the angle of 135°is shown in figure 3, together with the identification of the corresponding peaks. Dead time corrections were smaller than 8% for the RBS detector, whereas insignificant for the NRA detectors. Spectra acquisitions were carried out until a gross area uncertainty 10% was obtained for the integral of the spectral peaks under analysis.

Data analysis
The experimental differential cross section, σ, for a particular proton peak, i, is given by: where E̅ is the 3 He beam effective energy, θ is the scattering angle in the laboratory reference frame, y pi is the net spectral intensity of the concerned proton group, e is the elementary charge, n Be the Be areal density, Ω NRA the solid angle of the NRA detector and finally, Q is the accumulated charge during spectrum acquisition. The presence of carbon in the target, with the subsequent production of protons from 12 C + 3 He reactions, interfere with the protons signal from the 9 Be + 3 He reactions. The overlap can occur for 9 Be( 3 He,p 3 ) 11 B with 12 C( 3 He,p 0 ) 14 N, and 9 Be( 3 He,p 6 ) 11 B with 12 C( 3 He,p 1 ) 14 N. When the peaks overlap occurs, individual contributions are obtained from a multi peak Gaussian fit.

Uncertainty analysis
Effective energy (E̅ ): The uncertainty here arises from the contributions of the uncertainties in the beam energy and energy loss through the thickness of the Be layer.
Detection angle (θ): The uncertainty on the detection angle results from the contributions of the target to detector' distance, and the detector angular position.
The spectral intensity of a given proton group (y pi ): The measured quantity for the spectral intensity of a given proton group, results from subtracting an evaluated background quantity, b i , from the integral of the peak of interest, Y i , i.e. y pi = Y i − b i . The background estimation was accomplished using a proprietary implementation of the Statistics-sensitive Non-linear Iterative Peak-clipping algorithm (SNIP) [19]. The statistical uncertainty of the measured peak intensity is given by [20], where (peak width) is the number of channels in the peak and (2) is the number of channels used to determine the left and right boundaries.
For those cases where overlapping peaks need a multi-Gaussian fit procedure, peak areas uncertainties result directly from the fit.
NRA detector solid angle (Ω NRA ): NRA detectors' solid angle, Ω NRA , were experimentally determined. This was done by calculating the ratio between the yields measured by the NRA detectors for 1750 keV 4 He + ions backscattered from the W calibration sample, and that by the fixed RBS detector (with a known solid angle (1.25 ± 0.05) msr). Additionally, a triple source of the alpha emitters 239 Pu, 241 Am and 244 Cm with total activity (0.1 ± 5%) μCi (AMR Radiochemical Centre Amersham ref. AMR 33/R 9206) was used to check the experimental ratios.
Be areal density (n Be ): The uncertainty in Be thickness results from the contributions of the energy shift of the 4 He + backscattered from W under the evaporated Be film and of the uncertainty in the stopping power of the layers of the target. The overall uncertainty in the Be areal density is around 7%. Accumulated charge (Q): As the fitting software NDF does not provide an uncertainty value for the accumulated charge, this was derived analytically from the following formula [21]: where besides the already mentioned parameters, H is the spectrum height, N is the atomic density, δx is the thickness in the target from which backscattering into the energy interval δE takes place (δE is the energy width of one channel in the spectrum), E 0 is the energy of the beam immediately before backscattering and θ inc. the angle of incidence. Equation (2) depends on several parameters, each of these and their associated uncertainty were calculated. There was a sufficiently good agreement between the analytical calculations and fitted charge values to take the calculated uncertainty as a good estimate of the charge uncertainty. This had an average value of 8% across all spectra, varying between 7% and 9%. Table 2 summarizes the relative uncertainties (in %) considered in cross section calculations and the overall uncertainty budget. budget. The final relative uncertainty was computed as the quadratic sum of relative uncertainties.

Results
The differential reaction cross sections calculated for the exit channels p 0 up to p 9 at 135°are presented in figure 4. In the plots from this figure, along with the results of the present work, the data from Provatas et al [13] at 134°up to p 6 are also plotted as well as the data by Barradas et al [6] at 135°up to p 3 , the data by Wolicki et al [10] at 120°and 150°for p 0 and p 1 and the data read from plots by Coker et al [11] at 90°for p 4,5 up to p 9 . As pointed out by some of the previous studies, there is no discernible or obvious resonance structure in these cross sections, which rise smoothly in the energy range from 1 MeV to 2 MeV and typically level off between 2 MeV and 2.5 MeV [11]. The calculated cross sections have a 15.4% average total uncertainty and vary between 0.009 mb/sr and 1.630 mb/sr. Regarding the angular distributions of the cross sections, these are shown in figure 5 for the same proton groups, and energies of 1.5, 2 and 2.5 MeV. The angular distributions are weakly dependent on the emission angle with no significant angular structure showing an overall trend similar to that reported by Provatas et al [13]. Regarding the data from Coker et al [11] it is possible to verify that the agreement with the data determined in this work presents some variations. The mean absolute relative difference between these is around 20% for the beam energy of 2 MeV and increases approximately by 20% for the beam energy of 1.5 MeV. However, comparing the data from Provatas et al [13] and Coker et al [11] these same differences increase to ∼40% and ∼70%, respectively.
A benchmarking measurement was performed by collecting a pure bulk Be spectrum at 135°for a laboratory beam energy of 2.5 MeV. In this case, the charge was measured in the transmission Faraday cup at the entrance of the reaction chamber. Faraday cup calibration was made by previously fitting the spectra of 3 He + elastically backscattered from W for a given accumulated charge in the transmission Faraday cup. For the beam energy of 2.5 MeV, this was made for four independent measurements. For the same accumulated charge in the Faraday cup, the fitting charge in the RBS spectra varied 0.8%, showing it to be a reliable way to measure the accumulated charge on the target. An excellent agreement was obtained between the experimental spectrum and the simulated one for all the proton groups (i = 0, 1, K, 9) when using the differential cross sections from this work (cf figure 6).

Discussion
In this work, we found that-despite the similar trends in the behaviour of the calculated cross-sections, both in energy and angle-there is a quantitative discrepancy relative to the work of Provatas et al [13].
The former attributed this discrepancy to some possibly unaccounted systematic uncertainty in the work of Barradas et al [6], e.g. inaccuracies in the product (solid angle)×(beam fluence) and/or in the determination of the Be areal density. However, the thorough measurements and uncertainty analysis reported here indicate that none of these factors explains the discrepancy. Instead, there is quite a good agreement between the present data and the data of Barradas et al [6], with the data for p 0 and p 1 at 135°sitting between that reported by Wolicki et al [10] for 120°and 150°. Furthermore, the present data set displays a trend like the excitation curves reported by Coker et al [11] for p 4,5 to p 9 at 90°.

Conclusions
In the present work, the differential cross sections of the 9 Be( 3 He,p i ) 11 B reaction for the first ten proton groups (i = 0, 1, K, 9), were measured in the 1.0 MeV to 2.5 MeV energy range and at angles between 110°and 165°in steps of 5°, with a careful and thorough evaluation of uncertainties. These vary between 0.009 mb/sr and 1.630 mb/sr with an average total uncertainty of 15.4%. The present results were compared with the most relevant literature. Among these, the ones of Barradas et al [6] and of Provatas et al [13] were also focused on providing data sets for NRA analysis on fusion-related materials research. An excellent agreement was found with the results from Barradas et al [6] in the overlapping analysis; however, the discrepancy by a factor of 1.4 in  [13] at 134°( grey diamonds markers), Barradas et al [6] at 135°(blue X's markers), Wolicki et al [10] at 120°and 150°(cyan squares and green right-leaning triangle markers, respectively). Data extracted from Coker et al [11] at 90°(green triangle markers). With the exception for this last data set, data for comparison was retrieved from the IBANDL database [22]. the cross section values for p 0 up to p 6 persists towards the work of Provatas et al [13], for all the analysed angles. The thorough uncertainty budget of the current experiment and the fact that the recorded trends-energy dependency and angular distributions-are similar suggests there may be a yet unidentified systematic deviation in Provatas et al [13] data set. Finally, the results were benchmarked by measuring the first ten proton groups yields at 135°from a thick Be target bombarded by 2.5 MeV 3 He and using the new cross-sections to simulate and fit this spectrum with NDF: the excellent agreement achieved is a hallmark of the adequacy of the cross sections reported. Figure 5. Angular distribution of the differential cross sections of the 9 Be( 3 He,p i ) 11 B, i = 0, 1, K, 9 reactions at three laboratory beam energies (from the left to the right), 2.5 MeV (red circles markers), 2.0 MeV (blue squares markers), and 1.5 MeV (green diamonds markers). Solid markers correspond to the present data whereas data from Provatas et al [13] is plotted for 9 Be( 3 He,p i) 11 B, i = 0, 1, K, 6 with open markers. Data from Coker et al [11] is also plotted for Be( 3 He,p i ) 11 B, i = 2, 3, 6, K, 9 (open triangles markers) at the laboratory beam energy of 2 MeV and 1.5 MeV. Data used for comparison was retrieved from the IBANDL and EXFOR databases [22].

Data availability statement
All data that support the findings of this study are included within the article (and any supplementary files).  . NRA spectrum from a Be thick target irradiated with 2.5 MeV 3 He + ions. The detector was placed at 135°to the incoming beam direction behind a 12 μm thick Mylar foil to stop the backscattered particles. The background was subtracted using the SNIP algorithm. Simulated NRA spectrum is shown superimposed (red line).