Investigation of production of medical ⁸²Sr and ⁶⁸Ge for ⁸²Sr/⁸²Rb and ⁶⁸Ge/⁶⁸Ga generators via proton accelerator

Investigation of production of medical 82 Sr and 68 Ge for 82 Sr/ 82 Rb and 68 Ge/ 68 Ga generators via proton accelerator 1 corresp first-author Corresponding author, ozanartun@beun.edu.tr; Corresponding author, ozanartun@beun.edu.tr; ozanartun@beun.edu.tr Department of Physics, Bülent Ecevit University, Zonguldak 67100, Turkey Department of Physics, Bülent Ecevit University, Zonguldak 67100, Turkey How to operate 82 Sr/ 82 Rb and 68 Ge/ 68 Ga generators used in the positron emission tomography scan process is explained, and the importance of 82 Sr and 68 Ge radionuclides for these generators is revealed. To produce medical 82 Sr and 68 Ge by means of a proton accelerator in an irradiation time of 24 h, a proton beam current of 250 µA, and an energy range E proton =100→5 MeV, the cross sections and the neutron emission spectrum curves of (p, x n) reaction processes on Rb-85, Ga-69 and Ga-71 targets were calculated, and the activities and yields of the product were simulated for the reaction processes. Additionally, the integral yields of the reaction processes were determined via the calculated cross-section curves and the mass stopping power obtained from the X-PMSP program. Furthermore, based on the obtained results, the appropriate reaction processes for the production of 82 Sr and 68 Ge isotopes on Rb-85, Ga-69, and Ga-71 targets are discussed. Radioisotope production Proton accelerator PET Radioisotope generators 1 Introduction 1 Particle accelerators are important because of their applications in different fields, such as radioisotope production in cancer treatment and nuclear battery technology for spacecraft, space probes, and microelectronics [ 1 1 ]. Moreover, for decades, to produce medical radioisotopes used in positron emission tomography (PET), the Los Alamos Neutron Science Center (LANSCE) has produced the medical radioisotopes Sr-82 and Ge-68 for use in PET, and the Ac-225 alpha-emitting isotope for use in radio-immunotherapy by means of available linear accelerators (LINACs) with 800-MeV, 200-MeV, and 100-MeV proton beams [ 2 2 , 3 3 ]. Additionally, photonuclear reactions induced by a laser-Compton light source, e.g., the Extreme Light Infrastructure — Nuclear Physics (ELI-NP), which can be used to produce several isotopes of medical interest, have also been addressed recently [ 4 4 , 5 5 ]. The production of radioisotopes Sr-82 and Ge-68 is important because of its use in strontium-82/rubidium-82 and germanium-68/gallium-68 generators. In fact, for clinical imaging, two generators are widely used in PET, and the major challenge is that the rubidium-82 and gallium-68 radioisotopes have a short half-life to diagnose diseases and calibrate the PET scanner ( T 1/2 =75 s and T 1/2 =68 min, respectively). However, these isotopes, rubidium-82 and gallium-68, include parent isotopes with longer half-lives, such as strontium-82 ( T 1/2 =25.5 d) and germanium-68 ( T 1/2 =271 d), which have been used in cardiac imaging for diagnosing blood flow and in the calibration of PET scanners, respectively [ 2 2 , 3 3 ]. When considering using the daughter radioisotope (i.e., rubidium-82) in PET, the parent isotope, strontium-82, inside generators including an ion exchange column decays to form rubidium-82, and, thus, suitable quantities of rubidium-82 together with a certain solution are obtained by pumping via a generator for the PET scan. To illustrate the behavior in the PET scan, a process can be clearly given by [ 2 2 , 3 3 ]: i) p+ 85 Rb→ 82 Sr+4n (production of Sr-82 on Rb-85 target via (p,4n) reaction) ii) 82 Sr+ e - → 82 Rb+ ν (production of Rb-82 via electron capture) iii) 82 Rb→ 82 Kr+ e + +ν (disintegration to harmless krypton gas in PET scan process) iv) e + +e - →2γ (gamma rays detectable through detector in positron annihilation event ). The purpose of this study is to estimate productions of parent isotopes Sr-82 and Ge-68 used in 82 Sr/ 82 Rb and 68 Ge/ 68 Ga generators. The cross sections and the neutron emission spectrum of (p,xn) reactions on 69,71 Ga and 85 Rb targets were calculated, and the activities, yield of productions, and integral yields of Sr-82 and Ge-68 in a proton beam current of 250 µA and proton energy of as much as 100 MeV were simulated. Based on the simulated and calculated data, the energy ranges of (p, x n) reaction processes for formations of Sr-82 and Ge-68 in a proton accelerator with 100 MeV are discussed. 2 Calculation and Simulation 1 For an accurate determination of the calculations of nuclear reaction processes of the medical radioisotopes Sr-82 and Ge-68 used in PET for 82 Sr/ 82 Rb and 68 Ge/ 68 Ga generators, the Talys 1.8 code [ 6 6 ] and x -particle mass stopping power (X-PMSP) program [ 7 7 - 9 9 7-9 ] were used for calculating the cross section of reactions and the mass stopping power of target materials. Talys plays a significant role in the field including nuclear reaction because it includes many nuclear reaction models: equilibrium and pre-equilibrium reaction models, optical model, direct model, compound model, and so on, for low and high energies. For each nuclear model, the Talys code has many calculation applications, such as cross sections, double-differential cross sections, level densities, and emission spectra. The Talys code was used in cross sections and neutron emission spectrum calculations of (p, x n) reactions on Rb-85, Ga-68, and Ga-71 targets in the energy range of 1-100 MeV. The calculations of reaction cross sections were performed by using the Fermi gas with constant temperature model for the best input parameters [ 6 6 - 8 8 6-8 , 10 10 ]. In terms of activity, for the produced nuclei x , activity via nuclear reaction on target isotope Y can be expressed by the production rate of nuclei x, the decay rate of x <math id="M1"><mrow><mrow><mo>(</mo><mrow><msub><mi>λ</mi><mi>x</mi></msub><mo>=</mo><mtext>ln</mtext><mn>2</mn><mo>/</mo><msubsup><mi>T</mi><mi>x</mi><mrow><mn>1</mn><mo>/</mo><mn>2</mn></mrow></msubsup></mrow><mo>)</mo></mrow></mrow></math> and the irradiation time T irradiation : <math display="block" id="M2"><mrow><msub><mi>A</mi><mi>x</mi></msub><mrow><mo>(</mo><mi>t</mi><mo>)</mo></mrow><mo>=</mo><msub><mi>λ</mi><mi>x</mi></msub><msub><mi>N</mi><mtext>T</mtext></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow><msub><mi>R</mi><mrow><mi>Y</mi><mo>→</mo><mi>x</mi></mrow></msub><msub><mi>T</mi><mrow><mtext>irradiation</mtext></mrow></msub><mo>.</mo></mrow></math> In Eq. (1), <math id="M3"><mrow><msub><mi>N</mi><mtext>T</mtext></msub><mrow><mo>(</mo><mn>0</mn><mo>)</mo></mrow></mrow></math> is the number of mono-isotopic targets T at the start of the irradiation ( <math id="M4"><mrow><mi>t</mi><mo>=</mo><mn>0</mn></mrow></math> ), <math id="M5"><mrow><msub><mi>R</mi><mrow><mi>Y</mi><mo>→</mo><mi>x</mi></mrow></msub></mrow></math> is expressed by the beam current ( <math id="M6"><mrow><msub><mi>I</mi><mrow><mtext>beam</mtext></mrow></msub></mrow></math> ), the active target volume ( <math id="M7"><mrow><msub><mi>V</mi><mrow><mtext>target</mtext></mrow></msub></mrow></math> ), and the electron charge <math display="block" id="M8"><mrow><msub><mi>R</mi><mrow><mi>Y</mi><mo>→</mo><mi>x</mi></mrow></msub><mo>=</mo><mfrac><mrow><msub><mi>I</mi><mrow><mtext>beam</mtext></mrow></msub></mrow><mrow><msub><mi>z</mi><mtext>p</mtext></msub><msub><mi>q</mi><mtext>e</mtext></msub></mrow></mfrac><mfrac><mn>1</mn><mrow><msub><mi>V</mi><mrow><mtext>target</mtext></mrow></msub></mrow></mfrac><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∫</mo></mstyle><mrow><msub><mi>E</mi><mrow><mtext>back</mtext></mrow></msub></mrow><mrow><msub><mi>E</mi><mrow><mtext>beam</mtext></mrow></msub></mrow></munderover><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mtext>d</mtext><mi>E</mi></mrow><mrow><mtext>d</mtext><mi>x</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><msubsup><mi>σ</mi><mi>x</mi><mrow><mtext>rp</mtext></mrow></msubsup><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mtext>d</mtext><mi>E</mi><mo>,</mo></mrow></math> where <math id="M9"><mrow><msubsup><mi>σ</mi><mi>x</mi><mrow><mtext>rp</mtext></mrow></msubsup></mrow></math> is the residual production cross section of x and <math id="M10"><mrow><msub><mi>z</mi><mtext>p</mtext></msub></mrow></math> represents the projectile charge number [ 6 6 , 8 8 ]. Also, <math id="M11"><mrow><msub><mi>V</mi><mrow><mtext>target</mtext></mrow></msub></mrow></math> can be given by the effective target thicknesses <math display="block" id="M12"><mrow><msub><mi>V</mi><mrow><mtext>target</mtext></mrow></msub><mo>=</mo><msub><mi>S</mi><mrow><mtext>beam</mtext></mrow></msub><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∫</mo></mstyle><mrow><msub><mi>E</mi><mrow><mtext>back</mtext></mrow></msub></mrow><mrow><msub><mi>E</mi><mrow><mtext>beam</mtext></mrow></msub></mrow></munderover><msup><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mtext>d</mtext><mi>E</mi></mrow><mrow><mtext>d</mtext><mi>x</mi></mrow></mfrac></mrow><mo>)</mo></mrow></mrow><mrow><mo>−</mo><mn>1</mn></mrow></msup><mtext>d</mtext><mi>E</mi><mtext>     </mtext><mo>,</mo></mrow></math> here <math id="M13"><mrow><msub><mi>S</mi><mrow><mtext>beam</mtext></mrow></msub></mrow></math> is the product of the beam surface [ 6 6 ]. In addition to the Talys code, another program, X-PMSP, was used to determine the integral yields of reaction processes from reaction cross sections and the mass stopping powers of target materials. It can calculate the mass stopping powers and ranges of 98 elements for proton, deuteron, triton, he-3, and alpha particles in the energy range between 1 and 1000 MeV. The mass stopping powers of Rb-85, Ga-68, and Ga-71 targets for protons can be calculated by means of the velocity of the incident particle β( v/c ), as follows: <math display="block" id="M14"><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mtext>d</mtext><mi>E</mi></mrow><mrow><mi>ρ</mi><mtext>d</mtext><mi>x</mi></mrow></mfrac></mrow><mo>)</mo></mrow><mo>=</mo><mn>0.3071</mn><mfrac><mrow><mi>Z</mi><msup><mi>z</mi><mn>2</mn></msup></mrow><mrow><mi>A</mi><msup><mi>β</mi><mn>2</mn></msup></mrow></mfrac><mrow><mo>[</mo><mrow><mn>13.8373</mn><mo>+</mo><mtext>ln</mtext><mrow><mo>(</mo><mrow><mfrac><mrow><msup><mi>β</mi><mn>2</mn></msup></mrow><mrow><mn>1</mn><mo>−</mo><msup><mi>β</mi><mn>2</mn></msup></mrow></mfrac></mrow><mo>)</mo></mrow><mo>−</mo><msup><mi>β</mi><mn>2</mn></msup><mo>−</mo><mtext>ln</mtext><mrow><mo>(</mo><mi>I</mi><mo>)</mo></mrow><mo>−</mo><mfrac><mi>δ</mi><mn>2</mn></mfrac></mrow><mo>]</mo></mrow><mo>,</mo></mrow></math> where A and Z are the mass and the proton number of the target, respectively, and z and I denote the atomic number of the incident particle and the mean ionization potential of the target material, respectively. The density effect correction ( δ ) for different X ( <math id="M15"><mrow><mi>log</mi><mrow><mo>(</mo><mrow><mi>β</mi><mo>/</mo><msqrt><mrow><mn>1</mn><mo>−</mo><msup><mi>β</mi><mn>2</mn></msup></mrow></msqrt></mrow><mo>)</mo></mrow></mrow></math> ) values is given by <math display="block" id="M16"><mtable columnalign="left"><mtr><mtd><mi>i</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>δ</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><mn>4.6052</mn><mi>X</mi><mo>+</mo><mi>a</mi><msup><mrow><mo>(</mo><mrow><msub><mi>X</mi><mn>1</mn></msub><mo>−</mo><mi>X</mi></mrow><mo>)</mo></mrow><mi>m</mi></msup><mo>+</mo><mi>C</mi><mtext>     </mtext><mo stretchy="false">(</mo><msub><mi>X</mi><mn>0</mn></msub><mo><</mo><mi>X</mi><mo><</mo><msub><mi>X</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mi>i</mi><mo stretchy="false">)</mo><mtext> </mtext><mi>δ</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><mn>4.6052</mn><mi>X</mi><mo>+</mo><mi>C</mi><mtext>                                   </mtext><mo stretchy="false">(</mo><mi>X</mi><mo>></mo><msub><mi>X</mi><mn>1</mn></msub><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mi>i</mi><mi>i</mi><mi>i</mi><mo stretchy="false">)</mo></mtd></mtr><mtr><mtd><mrow/></mtd></mtr><mtr><mtd><mi>δ</mi><mrow><mo>(</mo><mi>X</mi><mo>)</mo></mrow><mo>=</mo><mi>δ</mi><mrow><mo>(</mo><mrow><msub><mi>X</mi><mn>0</mn></msub></mrow><mo>)</mo></mrow><mo>×</mo><msup><mn>10</mn><mrow><mn>2</mn><mrow><mo>(</mo><mrow><mi>X</mi><mo>−</mo><msub><mi>X</mi><mn>0</mn></msub></mrow><mo>)</mo></mrow></mrow></msup><mtext>                         </mtext><mrow><mo>(</mo><mrow><mi>X</mi><mo>≤</mo><msub><mi>X</mi><mn>0</mn></msub></mrow><mo>)</mo></mrow><mi>，</mi></mtd></mtr></mtable></math> where a, X 1 , X 0 , and C are the constants of the medium [ 7 7 ]. However, the integral yields of the reaction processes for the irradiation time t and the projectile current I can be calculated by the reaction cross section ( <math id="M17"><mrow><mi>σ</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow></mrow></math> ) and the mass stopping power <math id="M18"><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mtext>d</mtext><mi>E</mi></mrow><mrow><mtext>d</mtext><mrow><mo>(</mo><mrow><mi>ρ</mi><mi>x</mi></mrow><mo>)</mo></mrow></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></math> in (MeVcm 2 /g) for the activation equation: <math display="block" id="M19"><mrow><mi>A</mi><mo>=</mo><mfrac><mrow><msub><mi>N</mi><mtext>A</mtext></msub><mi>H</mi></mrow><mi>M</mi></mfrac><mi>I</mi><mrow><mo>(</mo><mrow><mn>1</mn><mo>−</mo><msup><mi>e</mi><mrow><mo>−</mo><mi>λ</mi><mi>t</mi></mrow></msup></mrow><mo>)</mo></mrow><munderover><mstyle mathsize="140%" displaystyle="true"><mo>∫</mo></mstyle><mrow><msub><mi>E</mi><mn>1</mn></msub></mrow><mrow><msub><mi>E</mi><mn>2</mn></msub></mrow></munderover><mfrac><mrow><mi>σ</mi><mrow><mo>(</mo><mi>E</mi><mo>)</mo></mrow><mtext>d</mtext><mi>E</mi></mrow><mrow><mrow><mo>(</mo><mrow><mfrac><mrow><mtext>d</mtext><mi>E</mi></mrow><mrow><mtext>d</mtext><mrow><mo>(</mo><mrow><mi>ρ</mi><mi>x</mi></mrow><mo>)</mo></mrow></mrow></mfrac></mrow><mo>)</mo></mrow></mrow></mfrac><mtext>     </mtext><mo>,</mo></mrow></math> where λ and H are the decay constant of product and isotopic abundance of target nuclei, respectively. M represents the atomic weight of target material, and <math id="M20"><mrow><msub><mi>N</mi><mtext>A</mtext></msub></mrow></math> is Avagadro’s number [ 8 8 ]. 2.1 Material and methodology 2 In the current work, to produce parent isotopes Sr-82 and Ge-68 of daughter isotopes Rb-82 and Ga-68 for 82 Sr/ 82 Rb and 68 Ge/ 68 Ga generators on Rb-85, Ga-68, and Ga-71 targets, simulations of the reaction processes under particular conditions were performed to define activity and yield results for (p, x n) reactions in the energy range E proton =100→5 MeV. Ga-68, Ga-71, and Rb-85 targets were assumed to have > 99% purity and uniform thickness and density in reaction processes. During the (p, x n) reaction processes, it was assumed that there were no losses in the yield and activity of the reactions. The effective target thicknesses of Rb-85, Ga-71, and Ga-69 were 8.270 cm, 2.076 cm, and 2.017 cm in the energy range E proton =100→5 MeV, respectively. Considering the proton energy range and beam current of the accelerator made it possible to adjust the most-suitable target thicknesses by code. The densities of the target materials were 1.530 g/cm 3 (for Rb-85) and 5.910 g/cm 3 (for Ga-71 and Ga-69), and the area of all target materials was approximately 1.00 cm 2 . Moreover, to irradiate the target materials, a proton accelerator with a proton beam current of 250 µA in the energy range E proton =100→5 MeV was used, and the irradiation time of the target materials Rb-85, Ga-71, and Ga-69 for all reaction processes was 24 h and the cooling time of the target materials was 24 h. The maximum produced heat in the targets for the production of Sr-82 and Ge-68 was approximately 23.750 kW. Under these conditions, the yields of product and activities in proton-induced reactions on Rb-85, Ga-71, and Ga-69 targets were simulated for 24 different reactions, including 85 Rb(p,4n) 82 Sr, 71 Ga(p,4n) 68 Ge, and 69 Ga(p,2n) 68 Ge [ 2 2 , 3 3 , 6 6 ]. 3 Results and discussion 1 To assess the importance of the production of Sr-82 and Ge-68 used in 82 Sr/ 82 Rb and 68 Ge/ 68 Ga generators, the cross sections of 24 different (p, x n) reactions on Rb-85, Ga-71, and Ga-69 target materials were calculated. The proton energies with the maximum cross sections of reactions were also determined. Based on the obtained energy values, the neutron emission spectrum results of reactions were calculated, and the neutron emission energies of reactions were estimated. Moreover, the activities and yields of product of the reactions were simulated under particular conditions using a proton accelerator in the energy range E proton =100→5 MeV. Additionally, the integral yields of reactions were determined by the obtained cross sections and the mass stopping powers of the targets. On the basis of our results, we discussed suitable productions of Sr-82 and Ge-68 in (p, x n) reaction processes. 3.1 Calculation of cross section 2 In the description of the production parent isotopes Sr-82 and Ge-68 used in 82 Sr/ 82 Rb and 68 Ge/ 68 Ga generators, the cross sections for 24 different reactions on Rb-85, Ga-71, and Ga-69 target materials were calculated in the 1-100-MeV energy range, and the results are presented in Figs. 1 Figs. 1 - 3 3 . For the medical radioisotope Sr-82 on the Rb-85 target, the calculated cross-section curves and the experimental data in the literature are shown in Figure 1 Figure 1 , which illustrates nine reactions. As is clearly visible in Fig. 1 Fig. 1 , 85 Rb(p,n) 85 Sr, 85 Rb(p,4n) 82 Sr, 85 Rb(p,3n) 83 Sr, and 85 Rb(p,5n) 81 Sr reactions include few experimental results, and the calculated cross-section result for 85 Rb(p,n) 85 Sr reaction is in good agreement with the findings of Kiss et al. (2008) [ 11 11 ] and Levkovski (1991) [ 12 12 ]. In the 85 Rb(p,3n) 83 Sr reaction, the theoretical cross-section result is more consistent with the results of Levkovski (1991) than the data reported by Kastleiner et al. (2002) [ 13 13 ]. Although the theoretical cross-section curve of the 85 Rb(p,4n) 82 Sr reaction is similar to the result of Kastleiner et al. (2002), the maximum cross-section values of both results are approximately 45 MeV, but the experimental cross-section result of Horiguchi et al. (1980) [ 14 14 ] has a maximum cross-section value at an ~50 MeV incident proton energy. In the 85 Rb(p,5n) 81 Sr reaction, the theoretical cross-section results and the experimental cross-section results (Horiguchi et al., 1980; Kastleiner et al., 2002) are fairly low, and the maximum cross-section value is ~58 MeV. The cross-section results for (p,x) 86 Sr, (p,6n) 80 Sr, (p,7n) 79 Sr, and (p,8n) 80 Sr reactions reach values that are too low compared with other reactions. As can be observed, (p,n), (p,2n), (p,3n), (p,4n), and (p,5n) reactions have cross-section curves; in particular, the 85 Rb(p,2n) 84 Sr reaction has the highest cross-section values at 19 MeV, and the cross-section curve of this reaction is intersected by 85 Rb(p,n) 85 Sr and 85 Rb (p,3n) 83 Sr at 14 MeV and 27 MeV proton incident energies, respectively. 85 Rb(p,n) 85 Sr and 85 Rb(p,3n) 83 Sr reactions in 85 Rb(p,xn) reactions create contamination for production of Sr-84. Similarly, the 85 Rb(p,3n) 83 Sr reaction is intersected by 85 Rb(p,2n) 84 Sr and 85 Rb(p,4n) 82 Sr at 27 MeV and 43 MeV proton incident energies, respectively. In the case of the 85 Rb(p,4n) 82 Sr reaction, the cross-section curve of this reaction is cut by 85 Rb(p,3n) 83 Sr behind 43 MeV. However, the cross-section values for the 85 Rb(p,5n) 81 Sr reaction are not enough to cut off 85 Rb(p,4n) 82 Sr reaction. The calculated cross-section curves and the experimental results of Levkovski (1991) and Porile et al. (1963) [ 15 15 ] for (p, x n) reactions on the Ga-69 target are shown in Fig. 2. Fig. 2. To produce the radionuclide Ge-68, the 69 Ga(p,2n) 68 Ge reaction process has two experimental results, as reported by Levkovski (1991) and Porile et al. (1963). The calculated result agrees well with both the experimental data from threshold energy to 17 MeV; the cross-section values of these two experimental results, however, are higher than the calculated results. For the 69 Ga(p,n) 69 Ge reaction, three experimental data together with the results of Levkovski (1991) and Porile et al. (1963) are available, and the experimental result of Johnson et al. (1967) [ 16 16 ] is in good agreement with the theoretical cross-section curves in the energy range between 3 MeV and 6 MeV. In the production of Ge-68, beyond 25 MeV, 69 Ga(p,n) 69 Ge and 69 Ga(p,3n) 67 Ge reactions make up contamination in the 69 Ga(p,2n) 68 Ge reaction. The cross-section result of 69 Ga(p,3n) 67 Ge is lower than the (p,n) and (p,2n) reactions on the Ga-69 target. Because the 69 Ga(p,x) 70 Ge, 69 Ga(p,4n) 66 Ge, 69 Ga(p,5n) 65 Ge, and 69 Ga(p,4n) 64 Ge reactions have cross-section values that are too low, these reactions do not affect the production of the 69 Ga(p,2n) 68 Ge reaction in terms of contamination. For an accurate determination of the production of nuclei, the comparisons of the theoretical cross section and the experimental data by Levkovski (1991) [ 12 12 ], Porile et al. (1963) [ 15 15 ], Johnson et al. (1964) [ 16 16 ], and Humes et al. (1963) [ 17 17 ] for (p,xn) on Ga-71 target material are shown in Figure 3 Figure 3 . For the 71 Ga(p,n) 71 Ge reaction, there are two experimental data by Johnson et al. (1964) and Humes et al. (1963). The calculated cross-section result of this reaction is in considerably good agreement with the results of Johnson et al. (1964), but Humes et al. (1963) have only one data point at 5 MeV that is different from the theoretical result. Unfortunately, there are no experimental measurements of the 71 Ga(p,2n) 70 Ge reaction in literature. The calculated cross-section result of the 71 Ga(p,3n) 69 Ge reaction agrees with Levkovski’s (1991) data, and the maximum cross section for this reaction is at ~29 MeV incident proton energy. In the case of the most important reaction, it is clear that 71 Ga(p,4n) 68 Ge has low cross-section curves compared with (p,n), (p,2n), and (p,3n), and the cross-section curves of these three reactions cut 71 Ga(p,4n) 68 Ge at ~33 MeV, ~38 MeV, and ~45 MeV proton incident energies. 3.2 Calculation of differential cross section of (p,xn) reactions 2 Here, the determination of the cross section of the (p, x n) reactions is quite important to estimate the incident proton energy values; hence, the incident proton energies corresponding to the maximum cross section for suitable (p, x n) reactions were determined by cross-section calculations, as shown in Figs. 1 Figs. 1 - 3 3 . The differential cross-section (DX) calculations for (p, x n) reactions on Rb-85, Ga-69, and Ga-71 targets are presented in Figs. 4(a)-(c) Figs. 4(a)-(c) . For the Rb-85 target, the calculated DX results of the 85 Rb(p,n) 85 Sr, 85 Rb(p,2n) 84 Sr, 85 Rb(p,3n) 83 Sr, 85 Rb(p,4n) 82 Sr, and 85 Rb(p,5n) 81 Sr reactions are given by Figure 4(a) Figure 4(a) as a function of neutron energy. DXs of these reactions have evaporation peaks in the energy range between 0.5 MeV and 1.5 MeV. Except for 85 Rb(p,n) 85 Sr, the DX values of the other reactions reach as much as 1000 mb/MeV. Similarly, in Figs. 4(b) and (c) Figs. 4(b) and (c) , the calculated DX results on Ga-69 and Ga-71 targets reach the maximum values for all reactions in the energy range 0.5-1.0 MeV. This clearly indicates that the DX values of 85 Rb(p,4n) 82 Sr, 69 Ga(p,2n) 68 Ge, and 71 Ga(p,4n) 68 Ge reactions in the production of Sr-82 and Ge-68 are 975.54 mb/MeV at ~0.94 MeV neutron emission energy, 455.72 mb/MeV at ~0.59 MeV, and 743.77 mb/MeV at ~0.85 MeV. 3.3 Simulation of activity and yield of product 2 To analyze (p, x n) reactions on Rb-85, Ga-69, and Ga-71 targets in E proton =100→5 MeV, 24-h irradiation time, and proton beam current of 250 µA by means of a proton accelerator, the simulated activities and yield of products for 24 different (p, x n) reactions under certain conditions were considered, and the simulations are shown in Figs. 5 Figs. 5 - 7 7 . In the simulations, there are nine (p, x n) reactions on the Rb-85 target, and among these reactions, the highest activities are (p,3n) 83 Sr (~4800 MBq) and (p,5n) 81 Sr (~1265 MBq) at the end of 24 h. (p,2n) 83 Sr and (p,x) 86 Sr reactions have no activity values, because 83 Sr and 86 Sr are natural isotopes of Sr. (p,7n) 79 Sr and (p,8n) 78 Sr reactions have constant activities during the irradiation time, because the half-lives of 79 Sr and 78 Sr isotopes (T 1/2 =2.25 min and T 1/2 =2.65 min) are short compared with the irradiation time (hour); therefore, the activities of these two isotopes seem to be straight lines. A similar situation is observed for 65 Ge and 64 Ge ( T 1/2 =30.9 s and T 1/2 =63.7 s). The activity value of (p,4n) 82 Sr increases with increasing irradiation time, and its activity reaches ~157.81 MBq in 24 h of irradiation time. In the case of (p,xn) reactions on Ga-69 and Ga-71 target materials, the (p,3n) reaction has a high activity compared with other reactions for both targets, except for the (p,n) 69 Ge reaction with an irradiation time of more than 15 h. Because Ge-70 and Ge-72 are stable isotopes of Ge, there are no activities, as shown in Figures 6 Figures 6 and 7 7 . Additionally, the activity of the 69 Ga(p,n) 69 Ge reaction has the highest values in 24 h (~1698.9 MBq); furthermore, the production of 69 Ge for the Ga-71 target with the (p,3n) reaction also has the highest activity (~3716.7 MBq). For the Ge-68 radionuclide used in PET, the activities of 69 Ga(p,2n) 68 Ge and 71 Ga(p,4n) 68 Ge reactions are ~16.63 MBq and ~9.03 MBq in 24 h. However, the yields of product of (p, x n) reactions on Rb-85, Ga-69, and Ga-71 targets as a function of irradiation time under the conditions mentioned in the activity simulations were simulated and are shown in Figures 8 Figures 8 - 10 10 . In the productions of radionuclides Sr on the Rb-85 target ( Fig. 8 Fig. 8 ), there are a few interesting reactions compared with the activities of such reactions as (p,5n) 81 Sr and (p,6n) 80 Sr. The (p,5n) 81 Sr reaction has the highest yield values up to 2 h of irradiation time; however, its yield curve decreases as a sharp curve, reaching zero at 6.2 h. There are similar states for (p,6n) 80 Sr, (p,7n) 79 Sr, and (p,8n) 78 Sr. This is mainly because 80 Sr, 79 Sr, and 78 Sr isotopes produced by 85 Rb(p,6n), 85 Rb(p,7n), and 85 Rb(p,8n) reactions have half-lives of 106.3 min, 2.25 min, and 2.65 min, respectively; thus, these radioisotopes disappear up to a few hours because of decay. In other words, the productions of 79 Sr and 78 Sr isotopes are performed by 85 Rb(p,7n) and 85 Rb(p,8n) reactions at the highest amount in the first few minutes of irradiation, but at the end of 1 h, the yields of product of 79 Sr and 78 Sr isotopes are close to zero, because new productions of 79 Sr and 78 Sr isotopes are not available. This is because the target material has not been changed up to the end of irradiation time ( <math id="M21"><mrow><msub><mi>t</mi><mrow><mtext>irradiation</mtext></mrow></msub><mo>→</mo><mn>24</mn><mtext> h</mtext></mrow></math> ). The (p,n) 85 Sr, (p,3n) 83 Sr, and (p,4n) 82 Sr reactions during the irradiation process have almost constant yield values of 9.08 MBq/mA, 617.64 MBq/mA, and 25.95 MBq/mA, respectively. In the production of radionuclides of Ge on Ga-69 and Ga-71 targets, when Figures 9 Figures 9 and 10 10 for product of yield are compared with each other, the yields of product of Ge-69 have two different values (p,n) 69 Ge (228.09 MBq/mA) and (p,3n) 69 Ge (499.04 MBq/mA). The yields of Ge-69 on the Ga-71 target are higher than that of production on Ga-69. In contrast to this reaction, the productions of the radionuclides 65,66,67,68 Ge on the Ga-69 target have higher yield values than on the Ga-71 target. Moreover, the 69 Ga(p,n) 69 Ge, 69 Ga(p,2n) 68 Ge, 71 Ga(p,3n) 69 Ge, 71 Ga(p,n) 71 Ge, and 71 Ga(p,4n) 68 Ge reactions have almost constant yield values during irradiation time, i.e., 228.10 MBq/mA, 2.77 MBq/mA, 499.04 MBq/mA, 37.80 MBq/mA, and 1.50 MBq/mA, respectively. However, the yield values of the 69 Ga(p,3n) 67 Ge, 69 Ga(p,4n) 66 Ge, 71 Ga(p,5n) 67 Ge, and 71 Ga(p,5n) 67 Ge reactions approach zero with increasing irradiation time. 3.4 Integral yield calculations for (p,xn) reactions 2 To estimate the integral yields of (p, x n) reactions on Rb-85, Ga-69, and Ga-71 targets using Eq. (6), cross-section results were used that were obtained from Figs. 1 Figs. 1 - 3 3 and the mass stopping powers of the target materials ( Fig. 11 Fig. 11 ) calculated by the X-PMSP program for targets. The integral yield calculations were performed in certain conditions, such as irradiation time of 24 h, proton beam current of 250 µA, and the energy range of 1-100 MeV. Isotopic enrichment of each target material was taken into account in the calculations of integral yield reactions. The production of Sr isotopes on Rb-85 is shown in Fig.12(a) Fig.12(a) , and the integral yields of (p,n) 85 Sr, (p,3n) 83 Sr, (p,4n) 82 Sr, and (p,5n) 81 Sr reactions have high values (see Fig.1 Fig.1 ) of 150 MBq/µA, 16000 MBq/µA, 350 MBq/µA, and 4000 MBq/µA at 100 MeV, respectively. Fig.12(a) Fig.12(a) , for the production of medical Sr-82, clearly shows that Sr-82 formed approximately 95% up to 60 MeV of proton incident energy; especially, after 40 MeV, the production of Sr-82 steeply increased at this energy, but the production of Sr-85 and Sr-83 in (p, x n) reactions was saturated. Then, Sr-81 was involved in these (p, x n) reactions beyond 45 MeV. The integral yields of Ge-68 for Ga-71 and Ga-69 targets are shown in Figs. 12(b) and (c) Figs. 12(b) and (c) . The integral yield results of 69 Ga(p,n) 68 Ge and 71 Ga(p,4n) 68 Ge reactions are 40 MBq/µA and 15 MBq/µA, respectively; these results indicate that the integral yield value for the 69 Ga(p,n) 68 Ge reaction is lower than that of 71 Ga(p,4n) 68 Ge. Additionally, the production of Ge-68 in the 69 Ga(p,2n) 68 Ge reaction reaches approximately 85% at 30-MeV proton incident energy; the production of Ge-68 in the 71 Ga(p,4n) 68 Ge reaction, however, is saturated at ~55 MeV. Furthermore, the production of Ge-68 in the (p, x n) process begins at 12 MeV on the 69 Ga target, as in Fig.12(b) Fig.12(b) . In contrast, the formation of Ge-68 in (p,4n) on the Ga-71 target begins at 32 MeV, as in Fig.12(c) Fig.12(c) . Therefore, based on integral yield, it can be said that the 69 Ga(p,2n) 68 Ge reaction is more suitable than that of 71 Ga(p,4n) 68 Ge in terms of the incident proton energy and yield values of the reactions. Moreover, in addition to the Ge-69 radionuclide, there is contamination of the 71 Ga(p,n) 71 Ge reaction in production of Ge-68 on the Ga-71 target beyond 3 MeV, as in Figure 12(c) Figure 12(c) , compared with the Ga-69 target. 4 Summary 1 The cross-sections and DXs of (p,xn) reaction processes were calculated to produce the radionuclides Sr-82 and Ge-68 used in PET for strontium-82/rubidium-82 and germanium-68/gallium-68 generators by means of a proton accelerator. The activities and yields of the product of (p, x n) processes on Rb-85, Ga-69, and Ga-71 targets were simulated under particular conditions, such as under an irradiation time 24 h and a proton beam current of 250 µA. Additionally, the integral yields of these reaction processes were determined by the calculated cross-section curves and the mass stopping powers via X-PMSP. The results obtained from calculations clearly show that the emission spectrum curves for the suitable (p, x n) reactions on Rb-85, Ga-68, and Ga-71 targets have the highest values in the energy range between 0.5 and 1.0 MeV. For the productions of Sr-82 and Ge-68, the DX values of the 85 Rb(p,4n) 82 Sr, 69 Ga(p,2n) 68 Ge, and 71 Ga(p,4n) 68 Ge reactions are 975.54 mb/MeV at ~0.94 MeV neutron emission energy, 455.72 mb/MeV at ~0.59 MeV, and 743.77 mb/MeV at ~0.85 MeV. Upon taking the yields of the product into account, the productions of the radionuclides 65,66,67,68 Ge on the Ga-69 target have higher yield values than on the Ga-71 target. Furthermore, as another result, the yield values of the (p,6n) 80 Sr, (p,7n) 79 Sr, (p,8n) 78 Sr, (p,n) 85 Sr, (p,3n) 83 Sr, and (p,4n) 82 Sr reactions up to end of irradiation are almost constant. 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Rev . 130 , 1522 ( 1963 ). doi: 10.1103/PhysRev.130.1522 http://doi.org/10.1103/PhysRev.130.1522 (p, n) Cross Sections at 6.75 MeV 10.1007/s41365-018-0474-1 2017-12-23 2018-03-24 2018-04-08 2018-08-28 2018-10-01 2021-04-11 © China Science Publishing & Media Ltd. (Science Press), Shanghai Institute of Applied Physics, the Chinese Academy of Sciences, ChineseNuclear Society and Springer Nature Singapore Pte Ltd. 2018 This is a post-peer-review, pre-copyedit version of an article published in Nuclear Science and Techniques. The final authenticated version is available online at: http://dx.doi.org/10.1007/s41365-018-0474-1 http://dx.doi.org/10.1007/s41365-018-0474-1 . 2018 Nuclear Science and Techniques 10 29