Comparative Role of 14C(n,γ)15C and 14C(p,γ)15N Reactions in the Production of 15N: Maxwell–Boltzmann and Tsallis Frameworks

The radiative capture reactions 14C(n,γ0+1)15C and 14C(p,γ0)15N are investigated within a framework of the modified potential cluster model. A comprehensive review of recent experimental and theoretical studies of the 14C(n,γ)15C reaction is presented, including comparisons with ANC-based approaches and recent ab initio calculations. For the 14C(p,γ0)15N reaction, elastic scattering phase shifts, interaction potentials, total cross-sections, astrophysical S-factors, and reaction rates are calculated up to Ec.m. = 5 MeV. The analysis includes two resonances at 1/2+(2S1/2) at Ex = 11.615(4) MeV and 3/2+(2D3/2) at Ex = 13.390(10) MeV. The zero-energy astrophysical S-factor is estimated as S(0) ≈ 4.5(1) keV·b. Reaction rates for both capture processes are calculated over the temperature range T9 = 0.01–10 within the Maxwell–Boltzmann and non-extensive Tsallis statistical frameworks. A phenomenological sensitivity analysis based on Tsallis statistics is performed to investigate how assumed deviations from Maxwell–Boltzmann energy distributions modify the neutron and proton capture reaction rates and their cross-over temperatures. Numerical results reveal a new relationship between neutron and proton capture at Asymptotic Giant Branch stars shell temperatures T9 ≈ 0.02–0.15, relevant to 15N production in neutron-rich environments.