New Empirical Formulae for some (p,γ) Reactions of Astrophysical S-factor and Thermonuclear Reaction Rates

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

• cross-sections (p, γ) reactions; astrophysical s-factor; thermonuclear reaction rates; talys
• 1.95; empirical formulae.