On the relative velocity distribution for general statistics and an application to big-bang nucleosynthesis under Tsallis statistics

Abstract: The distribution function of the relative velocity in a two-body reaction of nonrelativistic uncorrelated particles is derived for general cases of given distribution functions of single particle velocities. The distribution function is then used in calculations of thermonuclear reaction rates. As an example, we take the Tsallis non-Maxwellian distribution, and show that the distribution function of the relative velocity is different from the Tsallis distribution. We identify an inconsistency in previous studies of nuclear reaction rates within Tsallis statistics, and derive revised nuclear reaction rates. Utilizing the revised rates, accurate results of big bang nucleosynthesis are obtained for the Tsallis statistics. For this application it is more difficult to reduce the primordial 7Li abundance while keeping other nuclear abundances within the observational constraints. A small deviation from a Maxwell-Boltzmann distribution can increase the D abundance and slightly reduce 7Li abundance. Although it is impossible to realize a 7Li abundance at the level observed in metal-poor stars, a significant decrease is possible while maintaining a consistency with the observed D abundance.