210 © 2025 The Author(s). 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 Production of Californium-252 by Using Reverse Reaction Technology Aqeel L. Oudah1* , Sameera A. Ebrahiem2 and Khalid H. Mahdi 3 1,2Department of Physics, College of Education for Pure Science (Ibn Al-Haitham), University of Baghdad, Baghdad, Iraq. 3Department of Physics, University of Karabuk, Karabuk, Turkey. *Corresponding Author. Received: 11 May 2024 Accepted: 30 July 2024 Published: 20 January 2025 doi.org/10.30526/38.1.4008 Abstract In the current work, Calculate cross sections for 252Cf (α,3n)253Fm reaction Use of interpolation and cross-section sampling published in the international literature to select the appropriate interaction of ground-level energies in a computer-based program (MATALAB-17.0) , in steps of energies (0.2 Million electron volts). Given the importance of the 252Cf isotope and its entry into the industrial and medical fields, there was a need to determine the energy of the incident neutron to produce this isotope, relying on the masses of the entering and leaving particles and the values of angular momentum to obtain an equation and according to the theory of the opposite reaction. The reaction cross sections (253Fm (3n,α) 252Cf) were calculated using the opposite reaction theory for the energy range (3.9789-14.538)MeV. The results show that the probability values increase with the neutron's energy smoothly. The results show that cross-section values are almost constant for the energy range limited to (8.5-14)MeV. The results were plotted and tabulated using MATLAB 17.0. Also, the values obtained for the reaction cross sections 253Fm (3n,α) 252Cf through which the CF is produced. Semi-empirical equations were obtained for the relationship between energy and cross-section. Keywords: Cross-sections, nuclear reactions, radioisotopes, energy, reverse reaction. 1. Introduction Californium is a radioactive, trivalent chemical element.)1( A synthetic chemical element in the periodic table. Its chemical symbol is Cf and the number of protons is 98. It was discovered by bombarding the element curium with alpha particles. It has a few uses. 252Cf has a half-life of 2.6 years and is highly radioactive. It is considered a source of neutrons (1 microgram radiates about 170 million neutrons per minute ). Nine radioactive isotopes have been discovered, the most stable of which are 251Cf with a half-life of 898 days, 249Cf with a half-life of 351 years, and 250Cf with a half-life of 13 years. The rest of the radioactive isotopes have a half-life of less than 2.7 years, most of which are about twenty minutes, and the atomic weight of the isotopes ranges between 237.062 (237Cf) to 256.093 (256Cf). https://creativecommons.org/licenses/by/4.0/ https://creativecommons.org/licenses/by/4.0/ https://doi.org/10.30526/38.1.3501 https://orcid.org/0009-0005-6818-4437 mailto:Aqeel.Awda2204m@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0002-1900-2810 mailto:sameera.a.i@ihcoedu.uobaghdad.edu.iq https://orcid.org/0000-0002-1995-6892 mailto:khalidaal-shabeeb@karabuk.edu.tr IHJPAS. 2025, 38 (1) 211 2. Materials and Methods 2.1. Radioisotope Production Isotopes are substances with nuclei that have an equal number of protons and a varying number of neutrons. The physical characteristics of an element's isotopes differ from their chemical counterparts but are the same in the number of nucleons. Because of this, each isotope is distinguished by its mass number. In addition, some isotopes are unstable and are liable to radioactive decay. Radioactive isotopes are the name given to these isotopes (2) Figure 1 shows two groups of elements, the elements with the same number of neutrons (isotones) and elements with the same mass number (isobars). The lines in the figure show how the number of nucleons changes in the different types of radioactive decay, where the coordinate represents the number of neutrons N and the coordinate represents the atomic number Z. All radioactive elements have a half-life, Where the half-life is the time during which half of the nuclei of the current radioactive isotope decay and it can vary from 10 -8 seconds for short-lived radioisotopes and up to 1014 years for long-lived radioisotopes. The different radioactive isotopes of some elements also have multiple types of half-life, decay pathways, and decay types. Naturally or as a result of artificially modifying the atom unstable nucleation of radioactive isotopes can occur. In some cases, a cyclotron is used. In other instances, a nuclear reactor produces radioactive isotopes used in the medical field in diagnosis, treatment, and other industrial fields. A nuclear reactor is the best way to produce neutron-rich radioactive isotopes used in technological advances such as molybdenum-99., while cyclotrons are the most appropriate way to produce proton-rich radio- isotopes like fluorine) 3,4). practical releasing radiation is called radioactive decades. The process of radioactive decay for each radioactive isotope is unique and is measured by a period called the half-life (5-7). Figure 1. Describes groups of elements and the path of decay(7). 2.2. Cross Sections The interaction of the neutron with the target nucleus in a reaction does not depend on the type of nucleus, but rather on the energy for neutrons. Therefore, the absorption of thermal neutrons in some materials is much greater than the absorption of fast neutrons. In addition to the type of interactions (7). This probability of an interaction between neutrons is called a microscopic cross- section σ. The values of these cross-sections change with changes in neutron energies(8,9). Cross sections have several types:  Microscopic cross sections.  Macroscopic cross sections. IHJPAS. 2025, 38 (1) 212 Microscopic cross sections (σ) are the target and effective areas presented by a single nucleus of the bombardment particle. Microscopic cross-sections can also be defined as follows (10): σ= R/I (1) σ : Microscopic cross- section-section (cm2)(11,12). R: Numbers of reactions per unit time per nucleus. I: Numbers incident particles per unit times per unit area. While the macroscopic cross sections (∑) are the effective target areas represented by the cores containing cm2 of material, another meaning is that these are microscopic and macroscopic cross sections and expressed in cm2 or pens (1 barn = 10-24 cm2). A neutron will interact with a given volume of matter, and this depends on the microscopic cross sections on the number of nuclei within that volume. In other words, all macroscopic cross sections are the probability of certain interactions occurring / units travel of the neutron. (∑) where this microscopic cross section (σ) is related to the following relationship (11). ∑ = N * σ (2) ∑ : Macroscopic section (cm-1). N: Atoms densities of material(atoms/cm 3). This neutron interacts with an atom of matter by scattering first and absorbing second. Microscopic absorption cross sections, σa, is the probability that a particular atom will absorb a neutron. The scattering probability of neutrons from the nucleus is the microscopic scattering cross section, σ s. So the total cross section’s σT is given by the following relationship(12,13): σT = σa + σs (3) (14,15) σ a = σ c + σ f (4) (16) The reaction cross sections B(n,α)A can be calculated from reaction cross sections. If reaction cross sections A(α,n)B are measured by the opposite reaction method: 𝜎(α,n) g α,n α2 = σ (n,α) g n,αn2 (5) σ(α,n) and σ(n,α) are the cross sections of (α,n) and (n,α) interactions, respectively, g and the statistical factor which is the de-Broglie wavelength divided by 2π and (20) are given by:  = ħ MV (6) Where ħ= h /2π is Dirac- constant, h is plank-constant, M is mass and V is velocity. 3. Results and Discussion In the current study, cross sections were measured by the inverse reaction method 252Cf (α,3n)253Fm This is to obtain the production of chloronium from the reaction253Fm (3n,α) 252Cf This is due to the status that CF enjoys and its great importance, as californium is a radioactive, trivalent chemical element that contains 98 protons. CF is used as an important neutron source that helps in detecting natural ores and minerals such as gold and silver through the neutron IHJPAS. 2025, 38 (1) 213 activation technique. It is also used in neutron radiography of aircraft and weapon components to detect corrosion. Table 1. Cross section of alpha particle incident by step 0.2MeV for 252Cf (α,3n)253Fm reaction( p.work). Alpha Energy (MeV) X- Sections (mb) p.w. Alpha Energy (MeV) X- Sections (mb) p.w. Alpha Energy (MeV) X- Sections (mb) p.w. 29.5 0.7462 33.3 1.8279 37.1 3.2571 29.7 0.7953 33.5 1.9796 37.3 3.2472 29.9 0.8444 33.7 2.1313 37.5 3.2373 30.1 0.8935 33.9 2.283 37.7 3.2275 30.3 0.9426 34.1 2.4346 37.9 3.2176 30.5 0.9917 34.3 2.5863 38.1 3.2078 30.7 1.0408 34.5 2.738 38.3 3.1979 30.9 1.0899 34.7 2.8897 38.5 3.1881 31.1 1.139 34.9 3.0341 38.7 3.1782 31.3 1.1882 35.1 3.0547 38.9 3.1683 31.5 1.2373 35.3 3.0752 39.1 3.1585 31.7 1.2864 35.5 3.0957 39.3 3.1486 31.9 1.3355 35.7 3.1162 39.5 3.1388 32.1 1.3846 35.9 3.1368 39.7 3.4316 32.3 1.4337 36.1 3.1573 39.9 3.7908 32.5 1.4828 36.3 3.1778 40.1 4.1501 32.7 1.5319 36.5 3.1984 ---------- ---------- 32.9 1.581 36.7 3.2189 ---------- ---------- 33.1 1.6763 36.9 3.2394 ---------- ---------- Table 1 shows the range of alpha energy incident on the target nucleus, 252Cf, between 29.5 and 40.1 (MeV). It is shown that the behavior of the cross sections begins to increase until it reaches a cross-section of 4.1501 mbarn as shown in fig.1 by using MATLAB program The evaluation of cross sections recalculated by spline(22,23), fitting and interpolate. The percentage was calculated from the appropriate equation for the distribution of cross sections of the alpha energy range, as follows: y = 1.1e-5*x α 7 - 0.0028*x α 6 + 0.3*x α 5 - 17*x α 4 + 6.1e+2*x α 3 - 1.3e+4*x α 2 + 1.5e+5*x α - 7.5e+5 where y is the cross sections, xα is the neutron energy. Table 2. Cross sections of neutron Incident of 253Fm (3n,α) 252Cf reaction( p.work). Neutron energy (MeV) X- Sections (mb) p.w. Neutron energy (MeV) X- Sections (mb) p.w. Neutron energy (MeV) X- Sections (mb )p.w. 3.9789 0.2838 7.565 0.6375 11.1511 1.2241 4.1782 0.3024 7.7643 0.6951 11.3504 1.2319 4.3774 0.3211 7.9635 0.7528 11.5496 1.2386 4.5766 0.3398 8.1627 0.8105 11.7488 1.2349 4.7758 0.3585 8.3619 0.8682 11.948 1.2311 4.9751 0.3771 8.5612 0.9259 12.1473 1.2274 5.1743 0.3958 8.7604 0.9835 12.3465 1.2236 5.3735 0.4145 8.9596 1.0412 12.5457 1.2199 5.5728 0.4332 9.1589 1.0989 12.745 1.2161 5.772 0.4518 9.3581 1.1538 12.9442 1.2124 5.9712 0.4705 9.5573 1.1617 13.1434 1.2086 6.1704 0.4892 9.7565 1.1695 13.3426 1.2049 6.3697 0.5079 9.9558 1.1773 13.5419 1.2011 6.5689 0.5265 10.155 1.1851 13.7411 1.1974 6.7681 0.5452 10.3542 1.1929 13.9403 1.1936 6.9673 0.5639 10.5534 1.2007 14.1396 1.305 7.1666 0.5826 10.7527 1.2085 14.3388 1.4416 IHJPAS. 2025, 38 (1) 214 Neutron energy (MeV) X- Sections (mb) p.w. Neutron energy (MeV) X- Sections (mb) p.w. Neutron energy (MeV) X- Sections (mb )p.w. 7.3658 0.6012 10.9519 1.2163 14.538 1.5782 In Table 2, the cross sections for the reaction (3n, a) were calculated using the reverse reaction technique and according to the following equation: X(n,α)= 0.33068487 Tα Tn X(α,n) Which depends on the atomic masses of each of the products and reactants(24-26), by calculating Q-value and Eth, and by relying on the spin and parity values of each of the products, reactants (27,28), and the complex nucleus to calculate the g-factor(29,30). Where gα,n=1 and gn,α=1/4 These data are listed in Table 2 and plotted in Figure 2 in addition to the sixth-order semi- empirical formula, using the program (MATLAB version R (2017). From the data, we noticed the increase in cross sections from (0.2838 mbarn) to (1.5782 mbarn) and this increase is smooth. We deduced that the greatest potential for production 252Cf by bombarding 253Fm by Resonance neutrons (Its power ranges from 1-100 MeV). In Table 2; It was found that the values of the cross sections increase with the increase in the energy of the neutron incident on the target material 253Fm as shown in Figure 2. From Figure 2 a sixth-order semi-empirical equation is obtained for the relationship between neutron energy with cross sections and the following y = - 7.5e-06*xn 6 + 0.00071*xn 5 - 0.022*xn 4 + 0.31*xn 3 - 2.2*xn 2 + 7.8*xn – 10 where y is the cross sections, xn is the neutron energy. Figure 2. The cross sections as a function of alpha energy for 252Cf (α,3n)253Fm reaction. IHJPAS. 2025, 38 (1) 215 Figure 3. The cross sections as a function of neutron energy for 253Fm (3n,α) 252Cf reaction. 4. Conclusion It was found from this study that the values of probability increase with the increase of neutron until it reaches a constant stage and for the energy range that ranges between 9.3581-14.3388 MeV. In other words, the probability of obtaining a CF isotope is higher with an increase in the energy of neutrons, as CF is used for diagnosis and treatment. Acknowledgment Firstly, I would like to extend my sincere thanks to my professors in this field for being the basis and first supporter of this work, as I relied in my research on most of her scientific writings, including scientific research, university dissertations, and dissertations, and also directed me to the appropriate publishing houses. In addition to relying on its scientific information in physics, I also do not forget to give credit to the rest of the researchers and authors whose scientific publications I benefited from in my research (G. Henriksen, S. Messelt), in addition to other things mentioned in the sources below, also do not forget to thank my institution very much. The first in my studies at the Ibn Al-Haitham College of Education for Pure Sciences, to allow me the opportunity to publish my research with ease and without complications. Conflict of Interest The authors declare that they have no conflicts of interest. Funding There is no funding for the article. Ethical Clearance The local ethical committee at the University of Baghdad approved the project. References 1. PODGORŠAK, Ervin B. Radiation physics for medical physicists. Berlin: Springer, 2006. IHJPAS. 2025, 38 (1) 216 2. Chaidir P, Daya AS, Indra S, Fany T, Ahid N, Fernanto R, Anung P. Scaled-up production of 131I radioisotope using dry distillation method for radiopharmaceutical application. J Phys Conf Ser 2022;2193(1). IOP Publishing https://10.1088/1742-6596/2193/1/012020 3. Szkliniarz K, Sitarz M, Walczak R, Jastrzębski J, Bilewicz A, Choiński J, Zipper W. Production of medical Sc radioisotopes with an alpha particle beam. Appl Radiat Isot. 2016;118:182-189 https://doi.org/10.1016/j.apradiso.2016.07.001 4. Schlyer DJ, Van den Winkel P, Ruth TJ, Vora MM, Pillai M, Haji-Saeid M. Cyclotron produced radionuclides: Principles and practice. IAEA Technical Reports Series. 2008;465. 5. Qaim SM., Spahn I., Scholten B., Neumaier B. Uses of alpha particles, especially in nuclear reaction studies and medical radionuclide production. Radiochim Acta. 2016;104(9):601-624. https:// 10.1515/ract-2015-2566 6. Acylo A, editor. Cyclotron produced radionuclides—physical characteristics and production methods. IAEA. 2009. 7. Henriksen G, Messelt S, Olsen E, Larsen RH. Optimization of cyclotron production parameters for the 209Bi (α, 2n) 211At reaction related to biomedical use of 211At. Appl Radiat Isot. 2001;54(5):839-844 https://10.1016/s0969-8043(00)00346-8 8. Meyerhof WE, Valk HS. Elements of nuclear physics. 1967;2314: 233-246. 9. Ebrahiem SA, Sarsam MN, Youhana HM, Abd-Al-Hameed NT. Determining of cross-sections for 16O (n, α) 13C reaction from cross-sections of 13C (α, n) 16O for the ground state. Ibn Al-Haitham J Pure Appl Sci. 2017;26(1):109-115. 10. Ebrahiem SA, AL-khalidi SH. Interaction Samarium and Holmium with Charged ed Particles (Alpha particles). Mustansiriyah J Sci Educ.2016;17(5):399-414. 11. Youhana HM, Sarsam MN, Ebrahiem SA. Study of Cross Sections for 10 Li 10 Reaction From Cross Sections of Li a, n) Reaction Using the Reciprocity Theory for the Ground State. Ibn Al-Haitham J Pure Appl Sci. 2009;22(1):(1609-4042) 12. Ali TA, Ebrahiem SA. Study of the cross-sections of neutron interaction with lithium isotopes according to the reaction of the reverse reaction. AIP Conf Proc. 2023;3018(1). 13. Basdevant JL, Rich J, Spiro M. Fundamentals in nuclear physics: From nuclear structure to cosmology. Springer Science & Business Media. 2005;45(15):55-67. 14. Hamadani HT, Younis TA, Ebrahiem SA. Evaluation of The Nuclear Data on (α, n) Reaction for Natural Molybdenum. Ibn Al-Haitham J Pure Appl Sci. 2017;23(3):76-85. 15. Youhana HM, Ebrahiem SA. Determining of Cross Sections for 22Na (n, α) 19F reaction from Cross Sections of 19F (α, n) 22Na reaction using the reciprocity theory for the ground state. Ibn Al-Haitham J Pure Appl Sci.. 2009;22(2):144-156. 16. Ali TA, Ebrahiem SA. Study of the cross-sections of neutron interaction with lithium isotopes according to the reaction of the reverse reaction. AIP Conf Proc. 2023;3018(1). AIP Publishing https:// doi.org/10.1063/5.0172831. 17. Muehlhause CO. Neutron Fields: Production, Transport Character, and Detection: Neutron Physics. KH Beckurts and K. Wirtz. Translated from the second German edition (1964) by L. Dresner. Springer- Verlag, New York, 1964. x+ 444 pp. Illus. $17. Science. 1965;148(3669):489-489. 18. Waly BH, Ebrahiem SA. Study of the nuclear properties of an aluminum isotope in the production of third cycle elements. AIP Conf Proc. 2022;2437(1). 19. Mohammed NA. Ebrahiem SA. Assessment of radiation risk parameters for natural radon in three Iraqi institutions for February AIP Conf Proc. 2020;2307(1). AIP Publishing. https://doi.Org /10.1063/5.0035396. 20. Sathik NP, Ansari MA, Singh BP, Prasad R. Measurement and analysis of excitation functions for alpha induced reactions on iodine and cesium. Pramana. 1996;47(4):401-410. https://iopscience.iop.org/article/10.1088/1742-6596/2193/1/012020 https://doi.org/10.1016/j.apradiso.2016.07.001 file:///C:/Users/lenovo/Downloads/10.1515/ract-2015-2566 file:///C:/Users/lenovo/Downloads/10.1515/ract-2015-2566 https://10.0.3.248/s0969-8043(00)00346-8 https://doi.org/10.1063/5.0172831 https://doi.org/10.1063/5.0172831 IHJPAS. 2025, 38 (1) 217 21. Abbood NM, Ebrahiem SA. Study of Nuclear Properties of High Purity Germanium. Ibn Al-Haitham J Pure Appl Sci. 2020;33(1):31-39. https://doi.org/10.30526/33.1.2374 22. 22.Hiba MA, Hadi JM, Naz TJ, Sameera AE. Neutron yield for (70Zn) by bombarding of alpha particles. Acad Sci J. 2014;10(3-part 2). 23. Muslim RA, Mahdi KH, Ebrahiem SA. Study of Properties for Ca (a, n) Ti Reactions and n-Yield for Ca Isotopes (A= 41-50). Appl. Phys. 2014;23(13): 34-56. 24. Firestons R, Shirley VS. Table of isotopes eighth edition, Newyork. 1999. 25. Ebrahiem SA, Abbas IA, Ibraheim AM. Ameer MA. Cross Sections Calculations of 33S (n, α) 30 Si reaction by using the inverse reaction for the first excited state. Cross Sections. 2013;7(2):162-167. 26. Abbas IA, Ibraheim AM, Abbas SA, Ebrahiem SA. Calculation the Cross Sections for64Cu (n, p) 64Ni Reaction By Reciprocity Theory. J Univ Anbar Pure Sci. 2013;7(2). 27. Ebrahiem SA, Sarsam MN, Youhana HM, Abd-Al-Hameed NT. Determining of cross-sections for 16O (n, α) 13C reaction from cross-sections of 13C (α, n) 16O for the ground state. Ibn Al-Haitham J Pure Appl Sci. 2013;26(1):109-115. 28. Youhana HM, Ebrahiem SA. Determining of cross-sections for 22Na (n, α) 19F reaction from cross- sections of 19F (α, n) 22Na reaction using the reciprocity theory for the ground state. Ibn Al-Haitham J Pure Appl Sci. 2009;22(2). 29. Ebrahiem A,Mahdi KH, Tawfeeq H M. Calculation the Cross Sections of 3He(n,p)3H reaction for ground state using reciprocity theorem . J Kufa-Phys. 2010;23(12):123-143. 30. Hamadani HT, Younis TA, Ebrahiem SA. Evaluation of The Nuclear Data on (α, n) Reaction for Natural Molybdenum. Ibn Al-Haitham J Pure Appl Sci. 2010;23(3), 76-85. https://doi.org/10.30526/33.1.2374