2.3.2.1 Scattering Probability

For a more detailed description of the collisions a probability that an electron is scattered per unit time from band $n$ having quasi-momenta $\hbar\vec{k}$ to a state in band $n^{'}$ with quasi-momenta $\hbar\vec{k}^{'}$ is assumed. This probability is obtained from the corresponding microscopic theory. The scattering probability is denoted as $S(\vec{k},\vec{k}^{'},\vec{r},t)$ and introduced as follows^2.18. The probability that an electron with quasi-momenta $\hbar\vec{k}$ and coordinate $\vec{r}$ has been scattered during an infinitesimal time interval $dt$ to an infinitesimal volume of the quasi-momenta space $d\vec{k}^{'}$ around $\vec{k}^{'}$ is equal to:

$$S(\vec{k},\vec{k}^{'},\vec{r},t)\,dtd\vec{k}^{'}.$$ (2.48)

Here it is inferred that the final states are not occupied, that is, the definition of the function $S(\vec{k},\vec{k}^{'},\vec{r},t)$ does not include the quantum mechanical Pauli exclusion principle. The form of this function depends on the type of a scattering mechanism. It can have a rather complex structure. In general it can depend on the distribution function itself. S. Smirnov: