Utilizing the state-independent projection technique, we obtain a gene
ral formula for the cyclotron-transition linewidth for anisotropic def
ormation potential phonon scattering. The formula is applied to calcul
ate the width in Ge at low temperatures. It is shown that the transiti
on between the two lowest adjacent Landau levels makes the most contri
bution to the temperature and the magnetic field dependence of the wid
th, and the result agrees better with the experiment as the higher-ord
er contributions are included. The width increases with the magnetic f
ield, implying that the interaction of electrons with acoustic phonons
increases with the field.