We derive a new optical conductivity formula for cyclotron transitions in the quantum limit in a 3-D system of electrons interacting with phonons utilizing a projection technique. The electron and phonon distribution functions are included in the line·shape factor, which differs from those in the theories of Badjou and Argyres [Phys. Rev. B35 (1987), 5964] and Cho and Choi [Phys. Rev. B47 (1993), 9273]. It thus becomes possible to explain, in an organized way, the phonon emissions and absorptions in all electron transition processes.at

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Utilizing the state-independent projection technique, we obtain a general formula for the cyclotron-transition linewidth for anisotropic deformation potential phonon scattering. The formula is applied to calculate the width in Ge at low temperatures. It is shown that the transition between the two lowest adjacent Landau levels makes the most contribution to the temperature and the magnetic field dependence of the width, and the result agrees better with the experiment as the higher-order contributions are included. The width increases with the magnetic field, implying that the interaction of electrons with acoustic phonons increases with the field.

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