Estimation of the effect of Tsallis non-extensive statistics on the 14C(n,γ)15C reaction rate

The total cross-section of the radiative neutron capture reaction 14 С( n ,γ 0+1 ) 15 C—for energies ranging from 10 meV to 5 MeV—is considered. Calculations performed in the framework of the modified potential cluster model with forbidden states show an agreement of total cross-section σ (23.3 keV) = 4.75 μb with the presently recommended value 4.86(48) μb by Ma et al., 2020. The efficiency of carbon isotope 15 C production is illustrated by the 14 С( n ,γ 0+1 ) 15 C reaction rate calculated at temperatures from T 9 = 0.001 to T 9 = 10. The conventional Maxwell–Boltzmann weighted reaction rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m1"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mfenced open="〈" close="〉" separators="|"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mi>v</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mtext>MB</mml:mtext> </mml:msub> </mml:mrow> </mml:math> of the present work is comparable, with less than 10% accuracy, with the latest calculations by Ma et al., 2020 and Bhattacharyya et al., 2021. The estimation of non-extensive effects is implemented using our data on the reaction rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m2"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mfenced open="〈" close="〉" separators="|"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mi>v</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mtext>MB</mml:mtext> </mml:msub> </mml:mrow> </mml:math> as reference values. The efficiency of carbon isotope production in radiative capture reactions 12-14 С( n ,γ) 13-15 C is estimated based on the calculated reaction rates. The influence of the Maxwellian-weighted 12-14 C( n ,γ) 13-15 C reaction rates on the ratios 12 C/ 13 C and 13 C/ 14 C is examined. Tsallis statistics is applied for the first time to the calculation of the 14 С( n ,γ 0 ) 15 C reaction rate with values of non-extensive parameter 0.7 ≤ q ≤ 1.3 on the background of Maxwell–Boltzmann statistics corresponding to q = 1. The reaction rate <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="m3"> <mml:mrow> <mml:msub> <mml:mrow> <mml:mfenced open="〈" close="〉" separators="|"> <mml:mrow> <mml:mi>σ</mml:mi> <mml:mi>v</mml:mi> </mml:mrow> </mml:mfenced> </mml:mrow> <mml:mi>q</mml:mi> </mml:msub> </mml:mrow> </mml:math> shows a factor ∼4 increase for q = 0.7 and a factor ∼0.6 decrease for q = 1.3 compared to q = 1.