  We study electron-acoustic phonon scattering and electron relaxation in
quantum rings in the absence and in the presence of external magnetic fields.
Electron-phonon interaction is accounted for both the deformation potential and
piezoelectric coupling. At zero magnetic field and small ring radius, the
deformation potential phonon scattering is orders of magnitude larger than the
piezoelectric one. However, the piezoelectric coupling is found to become
important when the ring radius and magnetic field increase. It can be the
dominant scattering mechanism at large ring radii and/or large magnetic fields.
In comparison with the quantum dot case, the acoustic phonon scattering is
stronger in quantum rings.
