Calculation of Astrophysical S-factor and Thermonuclear Reaction Rates for (p,n) Medium Elements Reactions

The cross-sections of (p,n) medium elements reactions as a function of proton energies such as ⁴⁵Sc(p,n)⁴⁵Ti, ⁴⁸Ti(p,n)⁴⁸V, ⁵¹V(p,n)⁵¹Cr, ⁵²Cr(p,n)⁵²Mn, ⁵⁵Mn(p,n)⁵⁵Fe, ⁵⁶Fe(p,n)⁵⁶Co, ⁵⁹Co(p,n)⁵⁹Ni, ⁶²Ni(p,n)⁶²Cu, ⁶³Cu(p,n)⁶³Zn, and ⁶⁶Zn(p,n)⁶⁶Ga have been interpolated near threshold up to 10 MeV in step of 0.05 MeV using MATLAB program. Weighted averages of cross-sections have been used to calculate the astrophysical S-factor and thermonuclear reaction rates as a function of the center of mass energy, E_c.m. and T₉ respectively. Polynomial expressions have been used to fit the calculated astrophysical S-factor and thermonuclear reaction rates to determine the astrophysical S-factor at various Ec.m. and thermonuclear reaction rates at various T₉ from best fitting equations with minimum Chi-Square. Empirical formulae of reactions set ⁴⁵Sc(p,n)⁴⁵Ti, ⁴⁸Ti(p,n)⁴⁸V, ⁵⁵Mn(p,n)⁵⁵Fe, ⁵⁹Co(p,n)⁵⁹Ni, ⁶⁶Zn(p,n)⁶⁶Ga and reactions set ⁴⁸Ti(p,n)⁴⁸V, ⁵¹V(p,n)⁵¹Cr, ⁵⁹Co(p,n)⁵⁹Ni, ⁶³Cu(p,n)⁶³Zn, ⁶⁶Zn(p,n)⁶⁶Ga have been used to calculate the astrophysical S-factor as a function of Ec.m. and Z and thermonuclear reaction rates as a function of T₉ and Z of target nucleus. The results have been compared with the adopted data that have been calculated from the fitting equations which have a good agreement.