Samples and irradiationsThe stacked-sample activation technique was used for cross-section measurements of proton-induced reactions on enriched germanium (72Ge = 96.42%). Thin metal samples of enriched germanium were prepared at the Forschungszentrum Jülich (FZJ) by the sedimentation technique23. The powdered enriched germanium (supplied by Chemotrade GmbH, Germany) was used to develop thin layers on Al foils of 50 μm thickness and 13 mm diameter (supplied by Goodfellow; chemical purity: 99.0%) as backing material of the sediments. About 40 mg enriched germanium metal powder was suspended in 20 mL of toluene containing a very small amount of Levaprene‐450 (obtained from Arlanxeo, Dormagen, Germany) which possesses high adhesive properties, thereby vastly increasing the stability of the sediment and the attachment to the supportive backing. The supportive backing, a 50 μm aluminum foil, was weighed and fitted between two 10 mm thick Teflon discs screwed together. One of the discs contained a hole of 10 mm diameter forming a 0.785 mL cavity on top of the aluminum backing. The suspension containing the enriched germanium metal was mixed thoroughly, before 0.75 mL of this suspension was transferred into the sedimentation cell, as homogenous and as rapid as possible. Thereafter, the sedimentation cell was carefully placed in a drying oven and the toluene was allowed to evaporate at room temperature for 2 days. After confirming complete dryness (no dark stains left in the sediment), the sedimentation cell was carefully unscrewed and the aluminum backing together with the sediment was removed. The sedimented layers were examined under a microscope and only homogeneous and mechanically stable samples were selected for irradiation. Figure 5 shows the pictures of the surface of two typical samples used in this study as the targets. Passing the quality control, an aluminum cover of 15 mm diameter and 10 μm thickness of known weight was placed on top of each sediment and welted around the aluminum backing. Afterwards, the whole package was weighed, and the exact mass of the sediment was calculated. The exclusive weights of the sediments were found in the range of 2–7 mg. Therefrom the area density was calculated for each sample. The thus prepared enriched germanium sediment, sandwiched between two Al foils, served as the target sample.Figure 5The enriched germanium target developed on aluminum backing without cover. (a) Sample 14 showing a thin sediment on Al backing. (b) Magnified homogeneous sedimentation of sample14. (c). Sample17 showing larger quantity of sediment and Al backing (d) Magnified homogeneous sedimentation of sample 17.Seven samples were stacked together with four thin circular foils (diameter 13 mm) of Cu and one foil of Ti (supplied by Goodfellow; purity: Cu (99.9%); Ti (> 99.6%) and were irradiated at C30-XP. Similarly, thirteen enriched samples together with seven Cu monitor foils were used for irradiation at JULIC and ten samples together with seven Cu monitor foils were irradiated at BC 1710. The flux obtained from each monitor foil was used for the cross section calculations at the respective energy. The energy on each target foil is listed in Table 5. The thicknesses of Cu foils for the three experiments were chosen according to the energy provided by each cyclotron. These Cu and Ti foils served as beam monitors to determine the proton flux and energy along the whole stack. To decrease the energy of protons on each target, additional copper degraders were used (supplied by Goodfellow; purity: 99.9%; thickness: 250 μm and 110 μm). In total three stacks, each with different number of samples, for three different cyclotrons together with several monitor foils, were irradiated. The first stack was irradiated at Jülich Isochronous Cyclotron (JULIC) up to 45 MeV: the second at the BC 1710 cyclotron, and the third at C30-XP. The stacks irradiated at the BC 1710 were mounted in the screw-capped dummy target holder of the beam-line extension constructed a few years ago33. The JULIC is an old established machine at FZJ. It has been in use for many years as the injector of the high-energy cooler synchrotron (COSY). Recently an external target station was constructed at JULIC with an adapter where several target holders can be fitted. In the present measurements, the standard screw-capped dummy target holder, similar to the one at BC 171034, was used to mount the samples and foils in a stacked-form. The beam characterization and beam flux monitoring for the experiments at BC 1710 and JULIC, with protons of primary energies of 16.7 MeV and 45.0 MeV have already been reported. The irradiation at the C30-XP was carried out on a new target system. This is a new machine and is being tuned both for cross section measurements and clinical scale radionuclide production. Some details on beam characterization and flux determination during the present experiment are given here. The extracted beam is of high precision with respect to energy and profile definition. Nevertheless, we checked the effective energy of the proton beam in a foil by the activity ratio method33,34. The 63Zn/62Zn activities formed in Cu monitor foils, mounted in the stack, were considered for determining the accuracy of energy. The activities of these radionuclides were determined non-destructively by γ-ray spectrometry, converted to decay rates with necessary corrections, and finally extrapolated to the end of bombardment (EOB). The mean energy of the proton beam in the front Cu foil as well as in the subsequent foils was determined by comparing the experimentally obtained ratios with the values calculated theoretically from the IAEA recommended excitation functions of the reactions natCu(p,x)63Zn (energy range 7–20 MeV), natCu(p,x)62Zn (energy range 20–45 MeV)35. The deduced energy agreed well with the value derived from the accelerator parameters. Keeping the uncertainties of the cross sections in mind we fixed the primary energy of the extracted proton beam of the cyclotron as 24.2 ± 0.3 MeV. The effective proton flux was determined by using the reactions natCu(p,x)62Zn, natCu(p,x)65Zn (energy range 7–20 MeV) and natTi(p,x)46Sc (energy range 20–30 MeV), as monitor reactions. A comparison of the monitor reaction cross sections over the investigated respective energy regions derived in this work and the recommended data of the IAEA is given in Fig. 6. The data fits very well within the limits of uncertainties. Those monitor reactions were chosen owing to their nearly stable excitation function and better recommended precision over the proton energy range of this work. The proton flux was determined using the measured decay rates of 62Zn, 65Zn and 46Sc at EOB and the recommended cross-section values of the respective monitor reactions35. The proton flux values from the above three monitors agreed with the average value within 2–6%. The energy degradation was calculated by the computer program, STACK, written at FZJ and based on the energy-range relation36.
Table 5 Measured cross sections for the formation of 71As and 72As in proton irradiation of enriched 72Ge at three cyclotrons at FZJ.Figure 6A comparison of the monitor reaction cross sections derived over the investigated energy regions in this work and the IAEA recommended data.Radioactivity measurementThe radioactivity of a relevant radionuclide formed in irradiated enriched germanium-sample or in monitor foil was measured nondestructively using several high-purity germanium (HPGe) gamma-ray detectors, supplied by ORTEC, coupled with the necessary electronics and Maestro data acquisition software. The energy resolutions (FWHM) of the detectors used at 1332.5 keV of 60Co were 1.9–2.5 keV. The standard point sources 22Na, 54Mn, 57Co, 60Co, 137Cs, 152Eu, and 241Am, supplied by Eckert and Ziegler, Berlin, were used for efficiency calibration of the γ-ray detectors. The uncertainty in the activity of each source was specified as 3%. The γ -ray spectra measured were analyzed by the GammaVision37 software. A typical gamma ray spectrum is shown in Fig. 7. The major γ-rays from 72As and 71As are labeled. The background was subtracted to get the net area for each γ -ray. Samples were counted at various distances, viz. 10, 20, 30 and 50 cm from the surface of the detector, depending on the half-life and activity of the irradiated sample. The dead time of the system was kept below 5%. For all the above counting distances, the effect of the sample size on the efficiency and also the random coincidence loss became almost negligible. Measurements were carried out in several parallel steps, depending on the half-life of the product. The activity of short-lived radionuclides was measured within 2–3 h after EOB. Special attention was paid to attenuation of γ -ray as well as to detector efficiency for that gamma line. During the counting the Al-cover (10 μm thick) side of the germanium-sediment was always kept downward, i.e., facing the detector to minimize the absorption in Al. The further absorption of the low energy gamma lines in both the sample and the Al-cover was estimated; it amounted to about 0.05% and 0.03%, respectively. Parallel to this measurement, the monitor foils were also measured on the other detectors whose efficiencies were known for the given distances. In the second step of counting, the radioactivity of each of the two radionuclides 72As (T1/2 = 26.0 h) and 71As (T1/2 = 65.30 h) was determined.Figure 7Typical γ-ray spectrum of an enriched 72Ge sample irradiated with 24 MeV protons. The most important peaks originating from 72As and 71As (given in Table 2) are marked in the diagram.Experimental cross sectionsThe experimental nuclear reaction cross sections were measured using thin samples of 72Ge metal in the stacked-sample activation arrangement covering the energy range from 7.3 to 45 MeV. The beam profile and flux measurements were carried out by using Cu and Ti monitor foils. The production cross sections for the monitor reactions are well-established as described above. A photograph of two typical thin samples of enriched 72Ge (Sample 14, Sample 17), prepared in our laboratory, is shown in Fig. 5. Irradiations were done at three different cyclotrons at FZJ. The radioactivity of each product was determined via high-resolution γ-ray spectrometry. A typical γ-ray spectrum of an enriched Ge sample irradiated with 24 MeV protons is shown in Fig. 7. Further details of the measurements are given above in the section Methods and Analytical Procedures. The measured cross sections and the associated uncertainties are summarized in Table 5. In a few samples irradiated at JULIC, at proton energies above 35 MeV a very weak activity of 70As (T1/2 = 52.6 min) formed via the 72Ge(p,3n)70As reaction was also detected. However, due to rather poor counting statistics we did not analyse its production cross section.Nuclear reaction cross section calculationsNuclear reaction cross sections were calculated by using the three models, namely TALYS, EMPIRE and ALICE-IPPE. The nuclear model code TALYS26 version 1.96 was used, adopting an equidistant excitation energy grid. TALYS 1.96 consists of several nuclear models to analyze all the possible nuclear reaction mechanisms over the energy range of 1 keV to 200 MeV. In the calculations, considerable parametrisation was done in an attempt to obtain good agreement with the experimental data. The particle transmission coefficients were generated via the spherical optical model by using the ECIS-06 code38 with global parameters: for neutrons and protons from Koning and Delaroche39; for the optical model parameters (OMP) of complex particles (d, t, 3He) the code made use of a folding approach, building up the OMPs from the neutron and proton potential. The proton optical model was adjusted by using the recommended range of the parameter (rvadjust = 0.9). For OMP of alpha particles the TALYS default reference parameter set was adopted. Width fluctuation calculations were carried out for the compound nuclear part of the excitation function. The gamma-ray transmission coefficients were calculated through the energy-dependent gamma-ray strength function according to Kopecky and Uhl40 for E1 radiation, and according to Brink41 and Axel42 for all the other transition types. For the pre-equilibrium contribution in the nuclear reactions, a two-component exciton model of the TALYS code was used. The collective contributions from giant resonances and surface effects in exciton model were also calculated. The onset energy for multiple pre-equilibrium processes was set to 20 MeV. The energies, spins, parities, and branching ratios of the discrete levels were based on the RIPL-3 database43. The spin cutoff factor for the ground state was set equal to 1. The vibrational enhancements and shell correction energies were taken into account for calculations. In the continuum region, the level density was calculated by the geometry dependent superfluid model (GDSFM)44, using its slightly modified new version in TALYS 1.96. The basic physical and numerical parameters and the reaction mechanisms are given in the manual of TALYS 1.96. The calculated results from the global library of TALYS, i.e. TENDL-202127 were also compared. The detailed description of adopted parameters and all analytical nuclear model calculations are given in the manual of TALYS 1.96 that is available at the official website of the International Atomic Energy Agency (IAEA). (iaea.org)45For comparison, another nuclear model code EMPIRE 3.2 was also employed. The code was developed by Herman et al.25 under international cooperation. The calculations were done by using the discrete levels taken from the RIPL-3 level file, based on the 2007 version of ENSDF. EMPIRE specific level densities were used and exciton model calculations were done with PCROSS. The cluster emissions given by Iwamoto-Harada model were adopted. Monte Carlo preequilibrium model (HMS)44 was used by assuming the isotropic angular distribution of the compound nucleus.For purely precompound model calculations ALICE-IPPE was used that contains the generalized super fluid model for level densities.The cross section calculations for the production of 72As and 71As by using the above mentioned three nuclear model codes as well as TENDL-2021 data are compared and discussed above with the experimental data.UncertaintiesThe total uncertainty in the cross sections measured in the present work was estimated by the sum of both statistical and systematic errors46. The statistical errors included in each cross-section value contain the individual uncertainties in: counting statistics (1–5%), true coincidence correction (< 2%), decay data, especially γ-ray intensities (1.9–8.4%) and sample homogeneity (up to 5%). The uncertainty of the net peak area was (1.5–5%), obtained from the analysis of the weak and unsmooth peaks, from where, the uncertainty associated with the peak area was calculated manually. The uncertainty in the measurement of the beam flux varied for the three cyclotrons (3–6%). The systematic errors include the detector efficiency (2.5–5.5%), nuclear data (5–6%), and reference cross sections (4–5%). The overall total uncertainty in the cross sections for 72As and 71As is estimated as (11–13%). The energy uncertainty of the proton beam also varied (2–5%) for the three cyclotrons that became gradually higher as the beam got degraded in each foil.
Excitation functions of 72Ge(p,xn)72,71As reactions from threshold up to 45 MeV for production of the non-standard positron emitter 72As
