Document Type
Original Article
Abstract
The study utilized weighted averages of cross sections in millibarn for (p,γ) reactions of 74Ge, 88Sr, 89Y, 90Zr, and 107Ag medium target elements from the EXFOR nuclear data library and compares them with evaluated from TALYS 1.95 nuclear model code. These averages were employed to develop empirical formulas for the astrophysical S-factor, covering proton energies up to 5 MeV, and thermonuclear reaction rates up to 20×109 K T9 (T9 is the temperature in units of 109K). Polynomial formulas have been utilized to accurately model the calculated astrophysical S-factor and thermonuclear reaction rates, achieving the optimal fit with a low chi-square value. Novel polynomial equations were discovered that establish a relationship between the astrophysical S-factor and the energy of protons, as well as the atomic number. Additionally, these equations establish a relationship between thermonuclear reaction rates and the temperature (T9) and atomic number of the target elements. The results demonstrate that the newly derived empirical formulae exhibit a substantial level of agreement with the previously established ones, which were determined through the use of fitting equations. The study provides reliable empirical formulas for key reaction rates and variables, a significant achievement in nuclear astrophysics, validated against established models like TALYS 1.95. Some of the most important isotopes for understanding the weak s-process in large stars and their utility in nuclear physics include 74Ge, 88Sr, 89Y, 90Zr, and 107Ag, these isotopes give a best formulae for each of the astrophysical S-factor and thermonuclear reaction rates.
Keywords
Keywords: Cross-sections (p, γ) reactions; Astrophysical S-factor; Thermonuclear reaction rates; TALYS 1.95; Empirical formulae.
How to Cite This Article
Hussein, Mohammed Issa
(2024)
"New Empirical Formulae for some (p,γ) Reactions of Astrophysical S-factor and Thermonuclear Reaction Rates,"
Polytechnic Journal: Vol. 14:
Iss.
1, Article 11.
DOI: https://doi.org/10.59341/2707-7799.1829
References
[1] Monpribat E, Martinet S, Courtin S, Heine M, Ekstr€om S, Jenkins DG, et al. A new 12C + 12C nuclear reaction rate: impact on stellar evolution. Astron Astrophys 2022;660:1e12. https://doi.org/10.1051/0004-6361/202141858.
[2] Jose J. Stellar explosions hydrodynamics and nucleosynthesisvol. 218. Taylor & Francis Group, LLC; 2016. 992e992 p. Science. ISBN: 978-1439853061.
[3] Abdul Aziz A. Charged-particle induced thermonuclear reaction rates of light nuclei (MSc. Thesis). Malaysia: University of Malaya; 2008.
[4] Hingu A, Prajapati PM, Mukherjee S, Pizzone RG, Katovsky K. Erratum to: astrophysical S factor and reaction rate of 92,94 Mo(p, g) relevant to the p-process. EPJ Web Conf 2023;275:2017. 202327502017. https://doi.org/10.1051/epjconf/
[5] Kailas S. Thermonuclear reaction rates from (p,n) reaction on targets with A¼92-122. J Astrophys Astr 1986;7:53e7. https:// doi.org/10.1007/BF02715027. Table 6 presents a comparison of the available experimental data with the theoretical results of the thermonuclear reaction rates of 74Ge. 4. Conclusions In the present work, the more recent cross-section of (p,g) reactions of the 74Ge, 88Sr, 89Y, 90Zr, and 107Ag elements are used to calculate the astrophysical Sfactor and thermonuclear reaction rates at energies upto5MeV.Theobtainedastrophysical S-factor and thermonuclear reaction rates have been formalized usingafittingprocedure;aswellanempiricalformula has been established that combines the variation of the astrophysical S-factor with proton energy and target atomic number, and the variation of thermonuclear reaction rates with T9 and target atomic numberaswell.Theestablishedsystematicregarding these variations gave resultsinreasonableagreement with thecalculated weighted averageofastrophysical S-factor and thermonuclear reaction rates. Ethics information The article is theoretical data analysis and all the ethical issues have been taken as consideration. Funding There is no funding for the present work. Author contribution Data collection, statistical analysis, writing first draft and review, and revision are performed by the author “Mohammed Issa Hussein”. Conflict of interest There is no conflict of interest to publish this work.
[6] Roughton NA, Intrator TP, Peterson RJ, Zaidins CS. Thicktarget measurements and astrophysical thermonuclear reaction rates: alpha-induced reactions. At Data Nucl Data Tables 1983;28(November):341e53. https://doi.org/10.1016/ 0092-640X(83)90021-9.
[7] Wu D, Wang NY, Guo B, He CY, Tian Y, Tao X, et al. New measurement of the 74Ge(p,g)75As reaction cross sections in the p-process nucleosynthesis. Phys Lett Sect B Nucl Elem Part High-Energy Phys 2020;805:1e5. https://doi.org/10.1016/ j.physletb.2020.135431.
[8] Quinn SJ, Spyrou A, Simon A, Battaglia A, Couder M, Deyoung PA, et al. Probing the production mechanism of the light p-process nuclei. Phys Rev C e Nucl Phys 2013;88(1): 1e5. https://doi.org/10.1103/PhysRevC.88.011603.
[9] Sauerwein A, Endres J, Netterdon L, Zilges A, Foteinou V, Provatas G, et al. Investigation of the reaction 74Ge(p,g)75As using the in-beam method to improve reaction network predictions for p nuclei. Phys Rev C e Nucl Phys 2012;86(3): 1e13. https://doi.org/10.1103/PhysRevC.86.035802.
[10] Galanopoulos S, Demetriou P, Kokkoris M, Harissopulos S, Kunz R, Fey M, et al. The 88 Sr (p, g) 89 Y reaction at astrophysically relevant energies. Phys Rev C 2003;67(1): 015801. https://doi.org/10.1103/PhysRevC.67.015801.
[11] Harissopulos S, Spyrou A, Lagoyannis A, Axiotis M, Demetriou P, Hammer JW, et al. Cross section measurements of proton capture reactions relevant to the p process: the case of 89Y(p,g)90Zr and 121,123Sb(p,g)122,124Te. Phys Rev C e Nucl Phys 2013;87(2):1e15. https://doi.org/10.1103/ PhysRevC.87.025806.
[12] Tsagari P, Kokkoris M, Skreti E, Karydas AG, Harissopulos S, Paradellis T, et al. Cross section measurements of the 89Y(p, g)90Zr reaction at energies relevant to p-process nucleosynthesis. Phys Rev C e Nucl Phys 2004;70(1):1e10. https:// doi.org/10.1103/PhysRevC.70.015802.
[13] Spyrou A, Quinn SJ, Simon A, Rauscher T, Battaglia A, Best A, et al. Measurement of the 90,92Zr(p,g)91,93Nb reactions for the nucleosynthesis of elements near A¼90. Phys Rev C eNucl Phys 2013;88(4):88e93. https://doi.org/10.1103/ PhysRevC.88.045802.
[14] Khaliel A, Mertzimekis TJ, Asimakopoulou E-M, Kanellakopoulos A, Lagaki V, Psaltis A, et al. First crosssection measurements of the reactions Ag107,109(p,g) Cd108,110 at energies relevant to the p process. Phys Rev C 2017;96(3):1e7. https://doi.org/10.1103/PhysRevC.96.035806.
[15] Li JY, Li ZH, Li ET, Bai XX, Su J, Guo B, et al. New determination of the astrophysical 13C(p, g) 14N S(E) factors and reaction rates via the 13C(7Li, 6He) 14N reaction. Eur Phys J A 2012;48(2):1e7. https://doi.org/10.1140/epja/i201212013-x.
[16] Angulo C, Arnould M, Rayet M, Descouvemont P, Baye D, Leclercq-Willain C, et al. A compilation of chargedparticle induced thermonuclear reaction rates. Nucl Phys A 1999;656(1):3e183. 00030-5. https://doi.org/10.1016/S0375-9474(99).
[17] Meyerhof WE. Elements of nuclear physics. New York, USA: McGraw-Hill Book Company; 1967. ISBN: 9780070417458.
[18] Bevington PR, Robinson DK. Data reduction and error analysis for the physical sciences. McGraw-Hill Education; 2003. ISBN: 978-0072472271.
[19] Koning A, Hilaire S, Goriely S. TALYS: modeling of nuclear reactions. Eur Phys J A 2023;59(131). https://doi.org/10.1140/ epja/s10050-023-01034-3.
[20] Belgaid M, Tassadit A, Kadem F, Amokrane A. Semiempirical systematics of (n, p) reaction cross sections at 14.5 MeVneutronenergy. Nucl InstrumMethods Phys Res Sect B Beam Interact Mater Atoms 2005;239(4):303e13. https:// doi.org/10.1016/j.nimb.2005.05.053.
Follow us: