Collision integral for elastic scattering of electrons and phonons

The form of the collision integral describing elastic scattering of electrons and phonons by crystal defects is discussed once again. It is shown that in the absence of detailed balance for the transition probability $(W_{kk'}\ne W_{k'k})$, the collision integral does not contain Fermi or Bose factors (1$\mp$n$_k$) contrary to the point of view widespread in the literature. It turns out to be independent of the type of particle statistics and to be linear in occupation numbers, $I_k=\Sigma_k'(W_{kk'}n_k'–W_{k'k}n_k)$. A proof is given of the $H$-theorem on the increase in entropy of a system of elastically scattered electrons and phonons.