Magnetic field dependence of the hopping transitions in germanium and silicon

The influence of magnetic field on the phonon-induced hopping transitions leads to some galvanomagnetic effects in germanium and silicon crystals, e.g., magnetoresistivity in the impurity conduction. Here the probability of the hopping transitions between two donor centers in the presence of a weak magnetic field is calculated on the basis of the previous results of Myszkowski and Rogala. Only the adiabatic processes accompanied by emission or absorption of one phonon are considered. The exact form of the deformation potential is used, and both LA and TA phonons are taken into account. The theory is valid for donor centers situated on arbitrary substitutional sites in the crystal.