On distribution function of free and bound electrons in equilibrium Coulomb system

Abstract

In classical thermodynamics, the velocity distribution function of particles is always Maxwell distribution
for any density. This is due to the fact that the dependences on the pulses and coordinates in the
expression for the total energy are separated. Integration over coordinates leads to the appearance of a
configuration integral, and the remaining part is divided into the product of Maxwell distribution
functions. In the case of formation of bound states (molecules) in an atomic gas, the full phase space of
the relative motion of two particles is divided into two parts. The first corresponds to negative energies of
relative motion (molecular component), and the second to positive (free atoms). The velocity distribution
function remains Maxwellian, if we ignore the fact of separation of the phase space. It can be assumed
that for free atoms the velocity (kinetic energies) distribution may be different from Maxwell. For
plasmas, the assumption of the non-Maxwellian velocity distribution function of free electrons was made.
The influence of the non-Maxwell electron distribution function on the recombination coefficient is
estimated.