The Maxwell — Boltzmannian Approach to the Nuclear Reaction Rate Theory



One of the central problems in the theory of cosmological and stellar nucleosynthesis (and in the reaction theory of controlled thermonuclear fusion in the laboratory as well) is the determination of reaction rates. Up till now the theories of nuclear kinetics are equilibrium theories with a strict Maxwell-Boltzmannian approach to the evaluation of reaction rates. It is the purpose of the present paper to investigate in some detail the relation between the macroscopic nuclear reaction probability and the microscopic nulcear reaction cross section on the base of equilibrium-thermo-dynamic arguments. Via the formulation of the Boltzmann equation the general form of the nuclear reaction probability is derived, the fundamental physical assumptions for this equilibrium reaction probability are discussed, and the most general collision probability integral will be evaluated in closed form for all convenient values of the parameter by using random variables.