Penetration Factor for Nuclear Fusion Reaction in Nonthermal Astrophysical Plasmas

Abstract

The nonthermal effects on the nuclear fusion reaction process are investigated in Lorentzian astrophysical plasmas. The closed expression of the classical turning point in Lorentzian plasmas is obtained by the Lambert W-function. Using the WKB analysis with the effective screening length, the closed expressions of the fusion penetration factor and the cross section for the nuclear fusion reaction in Lorentzian plasmas are obtained as functions of the spectral index, relative kinetic energy, and plasma parameters. It is shown that the nonthermal character of the Lorentzian plasma enhances the fusion penetration factor. In addition, the nonthermal effect on the penetration factor is found to be more significant in plasmas with higher densities. It would be expected that the fusion reaction rates of the p-p chain and the CNO cycle in nonthermal plasmas are always greater than those in thermal Maxwellian plasmas.