Abstract
A new systematics was developed that predicted the (n,f) nuclear reaction cross sections for thorium isotopes in the mass number range 228 ≤ A ≤ 234. The TALYS-1.95 and EMPIRE-3.2.3 nuclear computer codes were used to do calculations that validated the results. Semi-empirical formulas are used for a variety of thorium isotopes that divide to the third fission level. The excitation functions of the 228Th (n,f), 229Th (n,f), 230Th (n,f), 231Th (n,f), 232Th (n,f), 233Th (n,f), and 234Th (n,f) nuclear reactions have been calculated at incident neutron energy ranging between 1 and 20 MeV. In addition to evaluated nuclear data files, such as JENDL 3.3, TENDL-2021, ENDF (B-VII.1), JENDL-4, BROND-3.1, EAF-2010, and ROSFOND-2010, experimental data from the EXFOR library were compared with our calculation. Overall, there is good agreement between the new semi-empirical formula, computer codes, evaluated files and experimental data fission cross sections.
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Research ethics: Not applicable.
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Informed consent: Not applicable.
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Author contributions: The author has accepted responsibility for the entire content of this manuscript and approved its submission.
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Use of Large Language Models, AI and Machine Learning Tools: None declared.
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Conflict of interest: The author states no conflict of interest.
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Research funding: Salahaddin University-Erbil, Erbil, Kurdistan Region, Iraq.
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Data availability: Not applicable.
References
1. Podgoršak, E. B.; Ervin, B. Radiation Physics for Medical Physicists; Springer: Berlin, Vol. 1, 2006.Search in Google Scholar
2. Letcher, T. M. Future Energy: Improved, Sustainable and Clean Options for Our Planet; Elsevier: Amsterdam, 2020.Search in Google Scholar
3. Diven, B. C. Fission Cross section of U235 for Fast Neutrons. Phys. Rev. 1957, 105, 1350; https://doi.org/10.1103/physrev.105.1350.Search in Google Scholar
4. Weisskopf, V. Statistics and Nuclear Reactions. Phys. Rev. 1937, 52, 295; https://doi.org/10.1103/physrev.52.295.Search in Google Scholar
5. Qaim, S. M. Activation Cross Sections, Isomeric Cross-Section Ratios and Systematics of (n, 2n) Reactions at 14-15 MeV. Nucl. Phys. A. 1972, 185, 614; https://doi.org/10.1016/0375-9474(72)90036-x.Search in Google Scholar
6. Molla, N. I.; Qaim, S. M. A Systematic Study of (n, p) Reactions at 14.7 MeV. Nucl. Phys. A. 1977, 283, 269; https://doi.org/10.1016/0375-9474(77)90431-6.Search in Google Scholar
7. Qaim, S. M. A Systematic Study of (n, d), (n, n’p) and (n, p n) Reactions at 14.7 MeV. Nucl. Phys. A. 1982, 382, 255; https://doi.org/10.1016/0375-9474(82)90135-x.Search in Google Scholar
8. Qaim, S. M. A Study of (n, nα) Reaction Cross Sections at 14.7 MeV. Nucl. Phys. A. 1986, 458, 237; https://doi.org/10.1016/0375-9474(86)90355-6.Search in Google Scholar
9. Qaim, S. M.; Stöcklin, G. Investigation of (n, t) Reactions at 14.6 MeV and an Analysis of Some Systematic Trends in the Cross-Section Data. Nucl. Phys. A. 1976, 257, 233.10.1016/0375-9474(76)90629-1Search in Google Scholar
10. Qaim, S. M. A Systematic Investigation of (n, 3He) Reactions at 14.6 MeV and an Analysis of the Gross Trend in the Cross-Section Data. Radiochim. Acta 1978, 25, 13; https://doi.org/10.1524/ract.1978.25.1.13.Search in Google Scholar
11. Qaim, S. M. A Systematic of 14 MeV Neutrons Induced Reactions Cross Sections (Review). In Proc. IAEA-Advisory Group Meeting on nuclear Data for Fusion Reactor Technology, Gaussig (GDR), 1988; p 89, AEA-TECDOC-457.Search in Google Scholar
12. Abdullah, H. M.; Ahmed, A. H. Empirical Systematics for (n, p) Reaction Cross Sections at 14-15 MeV Neutrons. Indian J. Phys. 2022, 1.Search in Google Scholar
13. Yiğit, M. Analysis of (n, p) Cross Sections Near 14 MeV. Appl. Radiat. Isot. 2018, 135, 115; https://doi.org/10.1016/j.apradiso.2018.01.029.Search in Google Scholar PubMed
14. Mahmud, H. A.; Ahmad, A. H. Empirical Formulae for (n, p) Reaction Cross-Sections at 14-15 MeV Neutrons. Int. J. Mod. Phys. 2022, E 27, 1850079.10.1142/S0218301318500799Search in Google Scholar
15. Abdullah, H. M.; Ahmed, A. H. Semi-Empirical Formula for (n, α) Reaction Cross Sections at 14-15 MeV Neutrons. Appl. Radiat. Isot. 2022, 110396; https://doi.org/10.1016/j.apradiso.2022.110396.Search in Google Scholar PubMed
16. Jhingan, M. L.; Anand, R. P.; Gupta, S. K.; Mehta, M. K. Semi-Empirical Approach for Predicting Neutron-Induced Fission Cross-Sections in the Energy Range 1-18 MeV. Ann. Nucl. Energy 1979, 6, 495; https://doi.org/10.1016/0306-4549(79)90022-7.Search in Google Scholar
17. ViolaJrV. E.; Wilkins, B. D. Fission Barriers and Half-Lives of the Trans-Radium Elements. Nucl. Phys. 1966, 82, 65; https://doi.org/10.1016/0029-5582(66)90524-4.Search in Google Scholar
18. Nix, J. R. The Normal Modes of Oscillation of a Uniformly Charged Drop about its Saddle-Point Shape. Ann. Phys. (N. Y). 1967, 41, 52; https://doi.org/10.1016/0003-4916(67)90199-6.Search in Google Scholar
19. Gadioli, E.; Gadioli, E.; Hodgson, P. E. Pre−Equilibrium Nuclear Reactions; Oxford University Press on Demand: Oxford, 1992.Search in Google Scholar
20. Pearlstein, S. Analysis of (n, 2n) Cross Sections for Medium and Heavy Mass Nuclei. Nucl. Sci. Eng. 1965, 23, 238; https://doi.org/10.13182/nse65-a19557.Search in Google Scholar
21. Abdullah, H. M., Ahmed, A. H. Empirical Formula for (n,f) Reaction Cross Sections of Uranium Isotopes at 1-20 MeV Neutrons. Appl. Radiat. Isot. 202, 111043 (2023).10.1016/j.apradiso.2023.111043Search in Google Scholar PubMed
22. Möller, P.; Sierk, A. J.; Ichikawa, T.; Iwamoto, A.; Mumpower, M. Fission Barriers at the End of the Chart of the Nuclides. Phys. Rev. C. 2015, 91, 24310; https://doi.org/10.1103/physrevc.91.024310.Search in Google Scholar
23. Ericson, T. The Statistical Model and Nuclear Level Densities. Adv. Phys. 1960, 9, 425; https://doi.org/10.1080/00018736000101239.Search in Google Scholar
24. Herman, M.; Herman, M.; Capote, R.; Sin, M.; Trkov, A.; Carlson, B. V; Oblozinsky, P.; Mattoon, C. M.; Wienke, H.; Hoblit, S.; Cho, Y. C.; Nobre, G. P. A.; Plujko, V. A.; Zerkin, V. EMPIRE-3.2 Malta Modular System for Nuclear Reaction Calculations and Nuclear Data Evaluation User’s Manual. 2013.10.2172/1108585Search in Google Scholar
25. Abdullah, H. M.; Ahmed, A. H. Empirical Formulae for (n, p) Reaction Cross Sections at 14-15 MeV Neutrons. Int. J. Mod. Phys. 2022, E 31, 2250049.10.1142/S0218301322500495Search in Google Scholar
26. Koning, A.; Hilaire, S.; Duijvestijn, M. TALYS-1.95, A Nuclear Reaction Program; NRG-1755 ZG Petten: Netherlands, 2019.Search in Google Scholar
27. Koning, A. J.; Hilairey, S.; Duijvestijn, M. TALYS-1.4: A Nuclear Reaction Program. User Manual, NRG, Petten. Eur. Phys. J. A. 2009, 59, 131.Search in Google Scholar
28. James, G. D.; Syme, D. B.; Grainger, J. The Fission Cross Section of 228Th Near Threshold. Nucl. Phys. A. 1984, 419, 497; https://doi.org/10.1016/0375-9474(84)90628-6.Search in Google Scholar
29. Vorotnikov, P. E.; Gladkikh, Z. S.; Davydov, A. V; SM, D.; Ga, O.; Palshin, E. S.; Shigin, V. A.; Shubko, V. M. Cross-Sections for Neutron-Induced Fission of Th-228. Sov. J. Nucl. physics-USSR. 1973, 16, 505.Search in Google Scholar
30. Gokhberg, B. M.; Otroshchenko, G. A.; Shigin, V. A. The Effective Cross Section for Fission of 229Th. In Soviet Physics Doklady, 1960; p 1064.Search in Google Scholar
31. Petit, M.; Aiche, M.; Barreau, G.; Boyer, S.; Carjan, N.; Czajkowski, S.; Dassié, D.; Grosjean, C.; Guiral, A.; Haas, B.; Karamanis, D.; Misicu, S.; Rizea, C.; Saintamon, F.; Andriamonje, S.; Bouchez, E.; Gunsing, F.; Hurstel, A.; Lecoz, Y.; Lucas, R.; Bauge, E.; Billebaud, A.; Perrot, L. Determination of the 233Pa (n,f) Reaction Cross Section from 0.5 to 10 MeV Neutron Energy Using the Transfer Reaction 232Th (3He, P) 234Pa. Nucl. Phys. A. 2004, 735, 345; https://doi.org/10.1016/j.nuclphysa.2004.02.017.Search in Google Scholar
32. Goldblum, B. L.; Stroberg, S. R.; Allmond, J. M.; Angell, C.; Bernstein, L. A.; Bleuel, D. L.; Harke, J. T.; Gibelin, J.; Phair, L.; Scielzo, N. D.; Swanberg, E.; Wiedeking, M.; Norman, E. B. Indirect Determination of the Th230 (n,f) and Th231 (n,f) Cross Sections for Thorium-Based Nuclear Energy Systems. Phys. Rev. C-Nuclear Phys. 2009, 80, 44610; https://doi.org/10.1103/physrevc.80.044610.Search in Google Scholar
33. Meadows, J. W. The Fission Cross Sections of 230Th, 232Th, 233U, 234U, 236U, 238U, 237Np, 239Pu and 242Pu Relative to 235U at 14.74 MeV Neutron Energy. Ann. Nucl. Energy. 1988, 15, 421; https://doi.org/10.1016/0306-4549(88)90038-2.Search in Google Scholar
34. Blons, J.; Mazur, C.; Paya, D.; Ribrag, M.; Weigmann, H. The Asymmetric Deformation of 231Th And 233Th. CEA-CONF-5122; CEA Centre d’Etudes Nucleaires DE Saclay: France, 1980.Search in Google Scholar
35. James, G. D.; Lynn, J. E.; Earwaker, L. G. Nuclear Spectroscopy of Highly Deformed 231Th. Nucl. Phys. A. 1972, 189, 225; https://doi.org/10.1016/0375-9474(72)90292-8.Search in Google Scholar
36. Muir, D. W.; Veeser, L. R. Neutron-Induced Fission Cross Sections of 230Th and 231Pa. In Proceedings of the 3rd Conference on Neutron Cross-Sections and Technology, Vol. 1; Knoxville, TN, 1971; p. 292.Search in Google Scholar
37. Kazarinova, M. I.; Zamyatin, Y. S.; Gorbachev, V. M. Fission Cross Sections for Th230, Pu240, Pu241, and Am241 by Neutrons with Energies of 2.5 and 14.6 MeV. Sov. J. At. Energy 1961, 8, 125; https://doi.org/10.1007/bf01481207.Search in Google Scholar
38. Shcherbakov, O.; Donets, A.; Evdokimov, A.; Fomichev, A.; Fukahori, T.; Hasegawa, A.; Laptev, A.; Maslov, V.; Petrov, G.; Soloviev, S.; Tuboltsev, Y.; Vorobyev, A. Others: Neutron-Induced Fission of 233U, 238U, 232Th, 239Pu, 237Np, natPb and 209Bi Relative to 235U in the Energy Range 1-200 MeV. J. Nucl. Sci. Technol. 2002, 39, 230; https://doi.org/10.1080/00223131.2002.10875081.Search in Google Scholar
39. Lisowski, P. W.; Ullmann, J. L.; Balestrini, S. J.; Carlson, A. D.; Wasson, O. A.; Hill, N. W. Neutron induced fission cross section ratios for 232Th, 235,238 U, 237Np, and 239Pu from 1 to 400 MeV. National Bureau of Standards: Washington, DC (United States); Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States); Los Alamos National Laboratory (LANL), Los Alamos, NM (United States). https://www.osti.gov/biblio/6967752.Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Original Papers
- An overview of production routes of the non-standard positron emitter 86gY with emphasis on a comparative analysis of the 86Sr(p,n)- and 86Sr(d,2n)-reactions
- Study on empirical formulae for (n,f) reaction cross sections of thorium isotopes between 1 and 20 MeV
- Radiolytic alterations to neptunium extraction and redox in 30 % tri-n-butyl phosphate
- Utilities of ionic liquid extraction with astatine ions and its extraction mechanism
- Gamma irradiation synthesis and characterization of Poly(N-vinyl-2-pyrrolidone/acrylic acid) superabsorbent hydrogels for treatment of ink waste
- Application of XRD, SEM-EDX and FTIR techniques for mineral characterization of geological ores
- Elucidating the effect of CdO–Na2O exchange on structure, mechanical and radiation shielding improvements of B2O3–P2O5–Na2O glass
- Alpha emitters concentration of natural radionuclides and lung cancer cases in blood of smokers and non-smokers using passive detector