The cyclotron resonance line shape is dependent upon the current relaxation rate $\Gamma \mathrm{}\left(k\right)\mathrm{}$. We have numerically determined $\Gamma \mathrm{}\left(k\right)\mathrm{}$ and hence the cyclotron resonance linewidth $\gamma$ in the quantum limit for a nondegenerate semiconductor using a previously derived formula [J. Phys. Chem. Solids 41, 735 (1980)]. The electrons are assumed to interact with acoustic phonons via a deformation potential. For high temperatures we have found that the dependence of the linewidth $\gamma$ and peak absorption $P^{max}$ on the temperature and the resonance frequency ${\omega }_0$ is given approximately by $\gamma \propto T^{\frac{1}{2}}{\omega }_0$, $P^{max}\propto T^{\frac{-1\mathrm{}}{2}}{\omega }_0^{-1\mathrm{}}$, whereas for low temperatures $\gamma \propto T^{6.5}{\omega }_0^{-2\mathrm{}}$, $P^{max}\propto T^{-6.5\mathrm{}}{\omega }_0^2$. The line shape is found to be almost Lorentzian. We have compared our numerical results for $\Gamma \mathrm{}\left(k\right)\mathrm{}$ with the various approximations which are commonly employed.

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