The concept of collision strength and a unified kinetic calculation for hard-sphere interactions and inverse square force law interactions

Abstract

With a concept of collision strength and other associated definitions, a unified kinetic theory for both hard-sphere interactions and inverse square force law interactions is developed. Collision frequencies that associate with many kinds of physical terms are calculated and expressed by a series special function Υj(α,x). Among them are arbitrary higher order linear Fokker–Planck coefficients, collision frequency, and energy exchange frequency. In case of a two-temperature system, the total collision rate, energy exchange rate, and collision strength rate are calculated and expressed in a uniform expression. A primitive form of Coulomb logarithm 12Γ(0,hmin) is found by comparing the exact form of equilibration time with Spitzer’s result. Many unifications are found from the unified expression. The threshold value of collision strength has unified activation energy in chemical reaction rate theory and ionization energy in Thomson’s classical ionization theory. An incomplete gamma function has unified Arrhenius exponential coefficient in chemical reaction rate theory and Coulomb logarithm in plasma physics.