135 Published by College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad. This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International License Calculation of the Cross-Section and Neutron Yield for Production Reactions of Gallium-67 Amin Kadhum Amin1* , Huda Majeed Tawfeek2 and Khalid Hadi Mahdi 3 1,2Department of Physics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq. 3Department of Physics, Sciences Faculty, University of Karabuk, Karabuk, Türkiye. Corresponding author* Received: 28 November 2023 Accepted:12 February 2024 Published:20 July 2024 doi.org/10.30526/37.3.3857 Abstract The study of cross-section and the neutron Yield of Gallium–67 isotope is a very necessary choice in the field of nuclear medicine, which is used in radiopharmaceuticals and for medical diagnosis and treatments. The cross-section of 68Zn (p,2n) 67Ga, 67Zn (p, n) 67Ga was calculated for different energies by using different sets of programs using MATLAB language. The cross- section was then used to calculate the neutron yields. The results of the neutron yield distributions have been used to generate polynomial expressions with incident proton energies. We also calculated the stopping power through the Ziegler formula using the computer program (SRIM 2013) to calculate the two reactions mentioned above and also compared the results for stopping powers for the above reactions with the computer program (MATLAB 2017). Then, the neutron yield was calculated for these two reactions to find the best reaction with the highest neutron Yield in our study and use it to calculate the isotope production Yield for these reactions and other results within this study. Keywords: Cross-section, neutron yield, stopping power, polynomial expression. 1. Introduction The cross-section is considered one of the most important physical quantities, that describe nuclear reactions. In practice, these reactions can be calculated by using various mechanisms and models of nuclear reactors]1[. The reaction usually occurs when the target nucleus is bombarded by an accelerated, charged particle, producing a stable or unstable radioactive isotope. The cross-section here describes and marks the nuclear reaction probability ]2, 3[. Units of the cross-section are units of area (the square of the nuclear radius), are measured in units called barns, and are equal to: https://creativecommons.org/licenses/by/4.0/ https://orcid.org/0009-0000-0167-489X mailto:ameen.ali2104m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0002-9983-6419 mailto:huda.m.t@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0002-1995-6892 mailto:khalidaal-shabeeb@karabuk.edu.tr IHJPAS. 2024, 37 ( 3 ) 136 1 barn = 10-28 m2 , 1 barn = 10-24cm2 Microscopic and macroscopic cross-sections are the two types of cross-sections that exist: (1) The microscopic cross-section is the cross-section of a nuclear reaction that takes place between a particle and its nucleus, or between the active region of the nucleus and the beam of the incident particle. It is known as the nuclear reaction's microscopic cross-section (σ), and it is dependent on particle energy. ]4,5[. There are two methods by which the incident particle interacts with matter's atoms. The interaction of all particles with the nucleus occurs via processes such as scattering or absorption. A given atom or nucleus's cross-section of absorbing a particle is the microscopic absorption cross-section, or (σa). The following mathematical connection represents the microscopic scattering cross-section, or (σs), and the total cross-section is given by ]6,7[: σT = σa + σs (1) The cross-sections of scattering are calculated from the elastic and inelastic scattering cross-sections (σes, σins): σ scattering = σes + σins (2) (2) The macroscopic cross-section of a homogeneous mixture of nuclides is equal to the total nuclide density added to the microscopic cross-section, and the macroscopic cross-section of the reaction (∑) is obtained by multiplying the microscopic cross-section (σi) by the numerical density (Ni) of the pertinent nuclides (i) in the macroscopic material, which is given by: [3, 8, 9[ ∑ = ∑ Niσi 𝑛 𝑖=1 (3) Where: (N) is the material's atom density (atoms/cm3), (σ) is the microscopic cross-section (cm2), (∑) is the macroscopic cross-section (cm-1), and (n) is the number of nuclides in the homogeneous material. The macroscopic cross-section is the region that all nuclei approach (∑) and is the effective target region within 1 cm2 of matter. As a result, the probability of a nuclear reaction happening when a group of particles passes through a specific unit area is represented by the macroscopic cross-section ]6,10[. 2. Material and Methods The amount that material affects an electrically charged particle's kinetic energy traveling via it is measured by its stopping power. It is frequently connected to a common substance like air or aluminum]11[. The primary causes of the stopping power ability are the target's electrons being ionized, the lowest energy levels being excited, and the target and projectile exchanging charges ] 12, 13, 14[. When a charged particle interacts with oft electrons at the same time, then the attractive coulomb force will give the electron an impulse when the particle passes inside. When energy is transferred to an electron as a result of acquiring an impulse strong enough to move it to an atom's higher energy level (excitation), and if that energy is high enough to release an electron from the atom, it's referred to as (ionization) ]11,15,16 [, the sum of nuclear-stopping power is given by the relationship : Ssum = Sn + Se (4) IHJPAS. 2024, 37 ( 3 ) 137 Where (Se) represents electronic stopping power and (Sn) represents nuclear stopping power. (Sn) Atomic nuclei and electrons from the gas interact with the neutral atoms, bombarding them with a beam of charged objects. The percentage of energy lost in this instance when interacting with atomic nuclei (apart from hydrogen) within a gas medium is as follows ]17]. 2mp/me = 4x103 (5) Therefore, the energy lost due to interaction with the nucleus is too small, and we could negligible it compared with the loss due to interaction with electrons. For a given thickness, there will be more nuclear interactions in solid targets, (equal to the width of neutron energy), so the nuclear cross-section and the electronic stopping cross-section are comparable. By using the Ziegler formula, the nuclear-stopping power of an alpha particle at a range of energies has been calculated as follows ]18[: MeV (6) Where ( ϵ ) = the reduced ion energy ( MeV ) 2/13/2 2 3/2 12121 2 ))(( 53.32 Energy Reduced ZZMMZZ EM   (7) Where: E is the energy of ion (MeV), M1 is the mass of the projectile (amu), Z1 is the projectile's atomic number, Z2 is the target's atomic number, and M2 is the mass of the target (amu). If the projectiles are entirely stopped inside the target, as well as if all nuclear reactions were two- particle reactions, we obtain a broad neutron spectrum. In a nuclear encounter, there would be a significantly larger loss of kinetic energy [19]. The Ziegler formula was used to calculate the electronic stopping powers (Se) within the parameters of this work, which give correct expressions for the range of energies (10 – 140 Kev)]18[: (8) 2 1 A Low EAS  (9) )] 1000 () 1000/ (1ln[) 1000/ ( 543 EA E A E A SHigh  (10) ) 1 () 1 () 1 ( HighLowe SSS                       102)47.0(ln 1001.0 4.38.61 )1exp(ln 7.1 01.0593.1 23 21 21 for for for Sn IHJPAS. 2024, 37 ( 3 ) 138 Where the coefficients are provided by Ziegler in (Ai) [20- 22] . When a beam of accelerated rays falls on a target, the nuclear reaction that occurs, produce a number (N) of particles per unit time [23[: )()()( bbn EEntY  (11) Where: (σ) is the cross-section reaction, (ε) is the neutron detection efficiency, and (nt) is the number density of target atoms. The yield is then calculated as the beam loses energy while passing through a target that is not infinitesimally thin [23]:     b thr E E n E dX dE EdfEE Y )( )()(  (12) Ethr = Eb - ∆E (13) Where: ∆E is the beam´s energy loss in the target, f is the number of target atoms in each target molecule, )( E dX dE  is the stopping power per target molecule. The thick-target yield, which is given by [22][ 23], is the result of taking the efficiency of ε (E) equal to 1 and assuming that the target is sufficiently thick, with one atom per molecule (i.e., f equal 1).  b thr E E b dXdE dEE EY / )( )(  (14) Where: the reaction threshold energy is (Ethr) ] 24 [. 3. Results and Discussion In this study, the nuclear reaction cross-sections, 68Zn (p,2n) 67Ga and 67Zn (p,n) 67Ga, that are found in the literature are plotted for the specified energy level as illustrated in Figures 1,2, respectively and listed in Tables 1,2. We found via the first figure that the best probability in this reaction occurs with values ranging between (19–30) MeV regarding the energy of incident protons on the isotope (68Zn) where the cross-section after this energy, begins to decrease until the minimum calculated value (24.8 m barn) at the energy value (99.26 MeV). The stopping power values are calculated by (SRIM program -2013) as shown in Figures 3,4 and Table 3. Depending on the values of the cross-section of these reactions and the values of the calculated stopping power based on (Ziegler formula) [18[, as in Figures (3,4), the Neutron Yields for these reactions were calculated according to equation (14) and as in Figures 5,6 and as in Tables 4,5. We found the empirical formula for the results of Neutron Yields, and they were as follows: (y = - 0.1*x^{4} + 26*x^{3} - 2.6e+03*x^{2} + 1.3e+05*x - 1.7e+06) for the68Zn (p,2n) 67Ga,, (y = 1.5*x^{4} – 63*x^{3} – 7.4e+02*x^{2} + 6.5e+04*x – 4.6e+05) for the 67Zn (p,n) 67Ga IHJPAS. 2024, 37 ( 3 ) 139 Figure 1. Cross-section of 68Zn (p,2n) 67Ga. Figure 2. Cross-section of 67Zn (p,n) 67Ga. IHJPAS. 2024, 37 ( 3 ) 140 Figure 3. Stopping power of proton in zinc 68Zn (p,2n) 67Ga Figure 4. Stopping power of proton in zinc 67Zn (p,n) 67Ga Figure 5. Neutron Yield for 68Zn (p,2n) 67Ga IHJPAS. 2024, 37 ( 3 ) 141 Figure 6. Neutron Yield for 67Zn (p,n) 67Ga Table 1. The cross-section of (p,2n) 67Ga 68Zn reaction Proton Energy MeV Cross Section mb Proton Energy MeV Cross Section mb Proton Energy MeV Cross Section mb 19.7 588 36.7 243.3117 53.7 106.5641 20.2 588.25 37.2 233.961 54.2 104.1282 20.7 588.5 37.7 224.6104 54.7 101.6923 21.2 588.75 38.2 208.3333 55.2 99.2564 21.7 589 38.7 181.6667 55.7 96.8205 22.2 589.25 39.2 155 56.2 94.3846 22.7 589.5 39.7 152.3214 56.7 91.9487 23.2 589.75 40.2 149.6429 57.2 89.9744 23.7 590 40.7 146.9643 57.7 89.8462 24.2 590.25 41.2 144.2857 58.2 89.7179 24.7 590.5 41.7 141.6071 58.7 89.5897 25.2 590.75 42.2 143.9375 59.2 89.4615 25.7 591 42.7 143.625 59.7 89.3333 26.2 533 43.2 143.3125 60.2 89.2051 26.7 475 43.7 143 60.7 89.0769 27.2 458.9474 44.2 142.6875 61.2 88.4286 27.7 442.8947 44.7 142.375 61.7 87 28.2 426.8421 45.2 142.0625 62.2 85.5714 28.7 411 45.7 140 62.7 84.1429 29.2 396 46.2 137.5 63.2 82.7143 29.7 381 46.7 135 63.7 81.2857 30.2 366 47.2 132.5 64.2 79.8571 30.7 355.5195 47.7 130 64.7 78.9412 31.2 346.1688 48.2 127.5 65.2 78.7941 31.7 336.8182 48.7 125 65.7 78.6471 32.2 327.4675 49.2 122.6585 66.2 78.5 32.7 318.1169 49.7 120.9512 66.7 78.3529 33.2 308.7662 50.2 119.2439 67.2 78.2059 33.7 299.4156 50.7 117.5366 67.7 78.0588 34.2 290.0649 51.2 115.8293 68.2 78.6207 34.7 280.7143 51.7 114.122 68.7 79.6552 35.2 271.3636 52.2 112.4146 69.2 80.6897 35.7 262.013 52.7 110.7073 69.7 81.7241 36.2 252.6623 53.2 109 70.2 82.7586 IHJPAS. 2024, 37 ( 3 ) 142 . reactionGa 67Zn (p,n) 67 section of-The cross . 2 Table Proton Energy MeV Cross Section mb Proton Energy MeV Cross Section mb Proton Energy MeV Cross Section mb 7.7 669 15.1 399.8 22.5 75.3333 7.9 729.2222 15.3 373 22.7 72.2222 8.1 789.4444 15.5 346.2 22.9 69.1111 8.3 849.6667 15.7 319.4 23.1 66 8.5 909.8889 15.9 298.3333 23.3 65.7778 8.7 943 16.1 283 23.5 65.5556 8.9 949 16.3 267.6667 23.7 65.3333 9.1 955 16.5 252.3333 23.9 65.1111 9.3 961 16.7 237 24.1 63.5 9.5 967 16.9 227 24.3 60.5 9.7 957.2222 17.1 217 24.5 57.5 9.9 947.4444 17.3 207 24.7 54.5 10.1 937.6667 17.5 197 24.9 52.8889 10.3 927.8889 17.7 186 25.1 52.6667 10.5 911.8889 17.9 175 25.3 52.4444 10.7 889.6667 18.1 164 25.5 52.2222 10.9 867.4444 18.3 153 25.7 52 11.1 845.2222 18.5 147.2 25.9 52.4444 11.3 823 18.7 141.4 26.1 52.8889 11.5 827.75 18.9 135.6 26.3 53.3333 11.7 832.5 19.1 129.8 26.5 53.7778 11.9 837.25 19.3 124 26.7 53 12.1 842 19.5 119 26.9 51 12.3 806.2857 19.7 114 27.1 49 12.5 770.5714 19.9 109 27.3 47 12.7 734.8571 20.1 104 27.5 45 12.9 700.8 20.3 99 27.7 42.7778 13.1 668.4 20.5 98.0909 27.9 40.3333 13.3 636 20.7 97.1818 28.1 37.8889 13.5 603.6 20.9 96.2727 28.3 35.4444 13.7 571.2 21.1 95.3636 28.5 33 13.9 543.5 21.3 94.4545 28.7 32.4 14.1 520.5 21.5 92.25 28.9 31.8 14.3 497.5 21.7 88.75 29.1 31.2 14.5 474.5 21.9 85.25 29.3 30.6 14.7 451.5 22.1 81.75 29.5 30 14.9 426.6 22.3 78.4444 --------------- ------------------- Table 3. The stopping power of proton (1.5 – 98.5 MeV) in Zinc. Proton Energy MeV Stopping Power MeV/(mg/cm) Proton Energy MeV Stopping Power MeV/(mg/cm2) Proton Energy MeV Stopping Power MeV/(mg/cm2) 1.5 0.0933 36.5 0.0102 69.5 0.0063 2.5 0.0689 37.5 0.01 70.5 0.0062 3.5 0.0556 38.5 0.0098 71.5 0.0062 4.5 0.0471 39.5 0.0096 72.5 0.0061 5.5 0.0411 40.5 0.0095 73.5 0.0061 6.5 0.0366 41.5 0.0093 74.5 0.006 7.5 0.0332 42.5 0.0091 75.5 0.0059 8.5 0.0303 43.5 0.009 76.5 0.0059 9.5 0.028 44.5 0.0088 77.5 0.0058 10.5 0.026 45.5 0.0087 78.5 0.0058 IHJPAS. 2024, 37 ( 3 ) 143 11.5 0.0244 46.5 0.0085 79.5 0.0057 12.5 0.0229 47.5 0.0084 80.5 0.0057 13.5 0.0216 48.5 0.0083 81.5 0.0056 14.5 0.0205 49.5 0.0081 82.5 0.0056 15.5 0.0195 50.5 0.008 83.5 0.0055 16.5 0.0186 51.5 0.0079 84.5 0.0055 17.5 0.0178 52.5 0.0078 85.5 0.0054 18.5 0.0171 53.5 0.0077 86.5 0.0054 19.5 0.0165 54.5 0.0076 87.5 0.0053 20.5 0.0159 55.5 0.0075 88.5 0.0053 21.5 0.0153 56.5 0.0074 89.5 0.0052 22.5 0.0148 57.5 0.0073 90.5 0.0052 23.5 0.0143 58.5 0.0072 91.5 0.0052 24.5 0.0139 59.5 0.0071 92.5 0.0051 25.5 0.0134 60.5 0.007 93.5 0.0051 26.5 0.0131 61.5 0.0069 94.5 0.005 27.5 0.0127 62.5 0.0068 95.5 0.005 28.5 0.0124 63.5 0.0067 96.5 0.005 29.5 0.012 64.5 0.0067 97.5 0.0049 30.5 0.0117 65.5 0.0066 98.5 0.0049 31.5 0.0115 66.5 0.0065 ----------------- ----------------- 32.5 0.0112 67.5 0.0064 ----------------- ------------------ 33.5 0.0109 68.5 0.0064 ----------------- ----------------- .Ga67(p,2n) Zn68 The neutron yield of .Table 4 Proton Energy MeV Neutron Yield*106 (n/ 106 proton) Proton Energy MeV Neutron Yield*106 (n/ 106 proton) Proton Energy MeV Neutron Yield*106 (n/ 106 proton) 19.7 0.0182 36.7 0.5952 53.7 0.8684 20.2 0.0367 37.2 0.6068 54.2 0.8752 20.7 0.0556 37.7 0.6181 54.7 0.8819 21.2 0.0747 38.2 0.6286 55.2 0.8886 21.7 0.0941 38.7 0.6379 55.7 0.8951 22.2 0.1139 39.2 0.6459 56.2 0.9015 22.7 0.134 39.7 0.6538 56.7 0.9077 23.2 0.1544 40.2 0.6616 57.2 0.9139 23.7 0.1752 40.7 0.6694 57.7 0.9201 24.2 0.1963 41.2 0.6772 58.2 0.9263 24.7 0.2177 41.7 0.6848 58.7 0.9326 25.2 0.2395 42.2 0.6926 59.2 0.9389 25.7 0.2616 42.7 0.7005 59.7 0.9452 26.2 0.2819 43.2 0.7085 60.2 0.9515 26.7 0.3002 43.7 0.7165 60.7 0.9579 27.2 0.3181 44.2 0.7245 61.2 0.9643 27.7 0.3357 44.7 0.7326 61.7 0.9706 28.2 0.3528 45.2 0.7408 62.2 0.9768 28.7 0.3695 45.7 0.7489 62.7 0.983 29.2 0.3859 46.2 0.7569 63.2 0.9891 29.7 0.4018 46.7 0.7648 63.7 0.9952 30.2 0.4173 47.2 0.7727 64.2 1.0011 30.7 0.4325 47.7 0.7804 64.7 1.0071 31.2 0.4475 48.2 0.7881 65.2 1.013 31.7 0.4622 48.7 0.7957 65.7 1.019 32.2 0.4768 49.2 0.8032 66.2 1.025 IHJPAS. 2024, 37 ( 3 ) 144 32.7 0.4911 49.7 0.8107 66.7 1.031 33.2 0.5051 50.2 0.8181 67.2 1.0371 33.7 0.5189 50.7 0.8254 67.7 1.0431 34.2 0.5324 51.2 0.8328 68.2 1.0493 34.7 0.5455 51.7 0.84 68.7 1.0555 35.2 0.5584 52.2 0.8472 69.2 1.0619 35.7 0.571 52.7 0.8543 69.7 1.0684 36.2 0.5833 53.2 0.8614 70.2 1.075 Ga67(p,n) Zn67 The neutron yield of .5 Table Proton Energy MeV Neutron Yield*105 (n/ 106 proton Proton Energy MeV Neutron Yield*105 (n/ 106 proton Proton Energy MeV Neutron Yield*105 (n/ 106 proton 7.7 0.0423 15.1 2.3037 22.5 2.9995 7.9 0.089 15.3 2.3416 22.7 3.0094 8.1 0.1402 15.5 2.377 22.9 3.0189 8.3 0.196 15.7 2.41 23.1 3.028 8.5 0.2566 15.9 2.4412 23.3 3.0371 8.7 0.3202 16.1 2.471 23.5 3.0463 8.9 0.385 16.3 2.4995 23.7 3.0555 9.1 0.4512 16.5 2.5266 23.9 3.0647 9.3 0.5188 16.7 2.5522 24.1 3.0738 9.5 0.5879 16.9 2.577 24.3 3.0824 9.7 0.6573 17.1 2.6009 24.5 3.0907 9.9 0.7271 17.3 2.624 24.7 3.0987 10.1 0.7972 17.5 2.646 24.9 3.1064 10.3 0.8675 17.7 2.6671 25.1 3.1141 10.5 0.9375 17.9 2.687 25.3 3.1219 10.7 1.0068 18.1 2.7059 25.5 3.1297 10.9 1.0753 18.3 2.7236 25.7 3.1375 11.1 1.143 18.5 2.7408 25.9 3.1454 11.3 1.2097 18.7 2.7575 26.1 3.1534 11.5 1.2777 18.9 2.7736 26.3 3.1615 11.7 1.347 19.1 2.7891 26.5 3.1697 11.9 1.4175 19.3 2.804 26.7 3.1779 12.1 1.4893 19.5 2.8185 26.9 3.1858 12.3 1.5589 19.7 2.8324 27.1 3.1934 12.5 1.6262 19.9 2.8459 27.3 3.2008 12.7 1.6911 20.1 2.8588 27.5 3.2079 12.9 1.7537 20.3 2.8713 27.7 3.2147 13.1 1.8141 20.5 2.8836 27.9 3.2211 13.3 1.8723 20.7 2.896 28.1 3.2272 13.5 1.928 20.9 2.9083 28.3 3.2329 13.7 1.9814 21.1 2.9206 28.5 3.2383 13.9 2.0327 21.3 2.9328 28.7 3.2435 14.1 2.0824 21.5 2.9449 28.9 3.2487 14.3 2.1304 21.7 2.9566 29.1 3.2539 14.5 2.1767 21.9 2.9679 29.3 3.2589 14.7 2.2211 22.1 2.9788 29.5 3.2639 14.9 2.2636 22.3 2.9893 ------------- --------- 3. Conclusion The present study detailed a theoretical investigation to study the cross-section and the neutron yield of the Gallium – 67 isotopes by using (MATLAB 2017) and (SRIM 2013) programs, where we IHJPAS. 2024, 37 ( 3 ) 145 studied some of the isotopes that affect the Cross-Section, stopping power, and neutron yields of Gallium-67 and their properties. Regarding the Cross-Section of the proton, the best results are with higher energy values (about 29.3 MeV) in Zinc. Concerning the stopping power, we got the best results (0.0933 MeV / (mg/cm2) with lower energy (1.5 MeV) from the Proton isotope in zinc. Regarding the neutron yield, the proton isotope had the best results (70 MeV) in Zinc. Acknowledgment I extend my thanks to the College of Education for pure science Ibn Al-Haitham, University of Baghdad for assisting in completing this work by opening private laboratories and providing scientific facilities by the staff of the Physics Department to help support the research project. Conflict of Interest The authors declare that they have no conflicts of interest. Funding None. References 1. Audi, G. and Wapstra, A.H.. The 1995 update to the atomic mass evaluation. Nuclear Physics A. 1995, 595(4), 409-480. https://doi.org/10.1016/0375-9474(95)00445-9 2. Jawad, E.A.; Jassim, M.K.; Tawfeek, H.M. Calculating the Sputtering Yield of Lithium, Sodium and Krypton Bombarded by Same Target Ion Using TRIM Simulation Program. Ibn AL-Haitham Journal for Pure and Applied Science. 2017, 29, 3, 26-35. https://doi.org/10.1063/5.0172339. 3. Meyerhof, W.E. Elements of Nuclear Physics. McGraw–Hill. 1967, 22, 174. 4. Samira, A.E.; Firas, M.H.; Mustafa, K.J.; Huda, M.T. 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