New cross sections for the 27 Al(p,x) 7 Be nuclear process: Monitoring proton beam energy via the 22 Na/ 7 Be cross-section ratio between 45 and 200 MeV

. Cross sections are presented for 7 Be produced in the proton bombardment of natural Al up to 200MeV and compared with previous literature data. Cross-section ratios for the 27 Al(p,x) 22 Na and 27 Al(p,x) 7 Be nuclear processes are also presented in the energy region 45 − 200MeV, exploiting our previously reported cross sections for the 27 Al(p,x) 22 Na process. The applicability for energy monitoring of proton beams by exploiting the 22 Na/ 7 Be cross-section ratio is discussed. Monte Carlo simulations in a simpliﬁed geometry provide additional information on activation of an Al monitor foil by secondary neutrons, indicating greater sensitivity to these neutrons by 24 Na as a beam monitor than 22 Na and 7 Be.


Introduction
Cross-section ratios of radionuclides produced in monitor foils, for well-measured nuclear reactions, provide an efficient method for energy monitoring of charged-particle beams [1][2][3]. Such ratios can be invaluable to determine the mean projectile energy as a function of depth inside foil stacks for excitation function measurements and/or stacked targets for radionuclide production (see e.g. [4] for an example of a multi-target stack). The present study was prompted by a need to measure energy shifts inside stacked encap-sulated targets where failure of a capsule occurred. Failure of an upstream target in a target stack can lead to significant shifts in the production energy windows of targets located downstream of the defective one, affecting not only their yields negatively but also increasing coproduced radio-contaminant levels.
In the case of an Al capsule, there already are two wellmeasured proton-induced reactions which cross-section ratio is suitable for monitoring purposes: 27 Al(p,x) 22 Na and 27 Al(p,x) 24 [5]. The premise is that the magnitude of the change of an isotope ratio from the value expected (i.e. when no failure occurred) will provide useful information on a target failure, e.g. at what stage during a bombardment the failure occurred (early on, during the latter stages or somewhere in-between). The proposed method requires the radioassay of the walls of downstream target capsules, punched out and prepared as counting sources.
In the 'ratio method', cross sections of two different nuclear reactions, but originating from the same monitor foil, are normally used. However, data from the same reaction on different foils, shifted in energy but from the a e-mail: szele@atomki.hu same bombardment, can also be useful [6]. The main advantage of cross-section ratios originating from the same measurements is that several common quantities cancel, consequently their associated uncertainties play no role, e.g. foil thickness, accumulated charge, strength of calibration sources, counting geometry, etc.
Unfortunately, the influence of the 27 Al(n,α) 24 Na reaction on the 27 Al(p,x) 24 Na monitor reaction is often not negligible and can be a problem at higher proton energies, when secondary neutron production becomes significant [7][8][9]. For these reasons, we decided to also investigate the 27 Na(p,x) 7 Be process for monitoring purposes, as 7 Be has a convenient half-life of 53.22 d and a sufficiently strong γ -line at 477.6 keV.
Cross sections are presented here for the 27 Al(p,x) 7 Be process. These values are compared with available literature data. The corresponding 22 Na/ 7 Be cross-section ratios are also reported. We also comment on the observed disturbance caused by secondary neutron activation to the 27 Al(p,x) 24 Na process. Results of Monte Carlo simulation studies are presented to shed light on the magnitude of the interference caused by secondary neutron activation in a single Al monitor foil.

Experimental
The experimental details have been described in detail in Ref. [10], so only a few salient aspects will be mentioned here. The primary proton beams were un-collimated and focussed directly onto the foil stacks. Five foil stacks were activated, utilising primary proton beams with nominal energies of 200, 120, 100, 66 and 40 MeV. The stacks were bombarded inside a calibrated Faraday cup. The foil diameter was 20 mm, the stack compositions dominated by Al, which served as both degrader and monitor material. Interspersed with the Al degraders and monitor foils were

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Ni and Mn/Ni-alloy foils, the main aim of which was to measure the 52 Fe excitation function in nat Ni+p and nat Mn+p. The beams were supplied by the separatedsector cyclotron of iThemba LABS, South Africa. After bombardment, the foils were counted repeatedly for their γ -ray emissions, using a calibrated intrinsic Ge detector with a relative efficiency of 13% and a resolution of 1.8 keV FWHM at 1.33 MeV.
The total uncertainties in the cross sections were obtained by summing all the contributing uncertainties in quadrature and were expressed with a 1 standard deviation (lσ ) criterion. In the original paper [10], no energy uncertainties were reported along with the presented cross section data. This has now been rectified, taking into account energy straggling, target foil thicknesses as well as the estimated energy spread of the primary proton beams.

The 27 Al(p,x) 7 Be excitation function
The measured cross sections for the production of 7 Be in the bombardment of natural Al with protons are shown in Fig. 1, together with some selected experimental data from the literature [11][12][13][14][15][16][17]. Some data sets [18][19][20][21] have been omitted due to the limited space in the figure. The new values of this work are compiled in Table 1. Below 100 MeV, the majority of results from different experiments show reasonably good agreement, the values of Furukawa et al. [12] systematically lower and Miyano [14] systematically higher. Until now, only two groups reported measured cross sections up to 200 MeV (Titarenko et al. [16,17], and Michel et al. [13]). The two datasets of Titarenko not only exhibit rather large differences but also associated high uncertainties. The results of Michel show better agreement with the present work but exhibit rather large scatter above 100 MeV. It is evident that the excitation function is monotonically increasing over the studied energy region, with no discernible structures or peaks.

The 27 Al(p,x) 22 Na excitation function
The 22 Na cross-section data of Ref. [10], extracted from the same γ -ray spectra used to produce the results of Table 1, are available in the EXFOR library (Entry A0497001). These values have been used to calculate the 22 Na/ 7 Be cross-section ratios presented below. This data set was used in the evaluation that led to the recommended 27 Al(p,x) 22 Na monitor excitation function of the IAEA [5], with which it has excellent agreement.

The 27 Al(p,x) 24 Na excitation function
As reported by several previous authors, we also found activation by secondary neutrons to be significant, in particular above 100 MeV. Differences of the order of 10% were found in the overlap region of the 200 MeV and 120 MeV stacks, the larger values obtained with the degraded 200 MeV proton beam. This is why Ref. [10] did not report a measured 27 Al(p,x) 24 Na excitation function. For 22 Na and 7 Be such differences were not observed. We consequently abandoned the idea to utilise the 22 Na/ 24 Na ratios for energy monitoring purposes and decided on the 22 Na/ 7 Be ratios instead. We also agree with a   24 Na reaction to be likely due to the secondary (n,α) reaction.

The 22 Na/ 7 Be cross-section ratio
The experimental 22 Na/ 7 Be cross-section ratios for 27 Al+p are shown in Fig. 2 while the numerical values are compiled in Table 2. The 22 Na/ 7 Be ratios exhibit a monotonically decreasing trend with increasing energy in the 40-200 MeV energy regions. In addition, its range spans a factor of about 20, making it a sensitive monitor for proton energy in a large part of this energy region.

Monte Carlo simulations
Monte Carlo simulations were performed in an attempt to gain a better understanding of the secondary neutron activation of an Al monitor foil in a degraded proton beam. The primary beam was mono-energetic and fixed at 200 MeV, while a single Al foil of 0.1 mm thickness was located at a position where the mean beam energy was 120 MeV. Instead of modelling the entire 200 MeV foil stack used in the actual experiment [10], the upstream target material was modelled as a single, solid degrader. As the majority material in the 200 MeV foil stack of Ref. [10] was Al, a solid Al degrader was specified. A second calculation was performed using Cu as the degrader material. The Al foil (20 mm in diameter) was placed against the degrader, centered on the beam axis. The forward spectra of neutrons emerging from the degraders were obtained from the MCNPX code [23] and found to be in good agreement with similar calculations performed with the FLUKA code [24,25]. Current tallies were set for both the protons and the neutrons passing through the single Al foil. From these simulations, normalized neutron spectra for the energy region 0.8 MeV to the maximum energy of emitted neutrons were obtained as well as the fluence ratio of neutrons to protons passing through the Al foil.
Excitation functions of neutron-induced reactions on 27 Al leading to the formation of 7 Be, 22 Na and 24 Na were taken from the TENDL-2015 library [26]. Effective production cross sections were calculated by folding these excitation functions with the normalized neutron spectra, given byσ where σ n (E) represents the TENDL-2015 data and S n (E) is a normalized neutron spectrum. This allowed the ratio of neutron-induced to proton-induced yields to be calculated as follows: where σ p (120) is the cross-section for the proton-induced reaction at an energy of 120 MeV and N n /N p is the ratio of neutrons to protons passing through the foil. The results are shown in Table 3.
These predictions indicate that the activity induced by secondary neutrons negatively affect 24 Na produced in 27 Al+p (as a monitor for protons) to a much larger extent than 22 Na and 7 Be, in the energy region investigated. Large uncertainties in the TENDL-2015 cross sections used cannot be ruled out, nevertheless, the results are in agreement with experimental observations.

Conclusion
Cross sections for the 27 Al(p,x) 7 Be nuclear processes have been presented up to 200 MeV as well as experimental values for the 22 Na/ 7 Be ratio in 27 Al+p. Admittedly, the results of the Monte Carlo simulations should be interpreted with caution, even though they are in agreement with observations. Nevertheless, there is sufficient evidence that the 22 Na/ 7 Be ratio is better suited than the 22 Na/ 24 Na ratio for proton energy monitoring above about 100 MeV, as the fraction of 24 Na produced by secondary neutrons is substantially higher than in the cases of 22 Na and 7 Be.