Solution with third-order accuracy for the electron distribution function in weakly ionized gases and intrinsic semiconductors

Summary  An explicit solution for the isotropic componentf 0(v) of the electron distribution functionf(v, μ) in a weakly ionized gas (or an intrinsic semiconductor) in steady-state and uniform conditions and for dominant elastic collisions is given to withinO(ε 4)=O(m 2/M 2), wherem andM are the masses of the electron and of the molecule, respectively. Since in the preceding, companion paper the componentsf 1(v),f 2(v) andf 3(v) of the expansion off(v, μ) in Legendre polynomials have been shown to be of the orderε 1 ε 2 ε 3, respectively, and have been expressed as functions off 0(v), the distribution functionf(v, μ) is explicitly known with third-order accuracy. This is beyond the best preceding expression, that by Chapman and Cowling, which has first-order accuracy only.