Abstract
The polaron Green function is calculated within the self-consistent random phase approximation for intermediate Fr\"ohlich coupling $(\ensuremath{\alpha}\ensuremath{\approx}1).$ The results are compared with perturbation theory where the motion of the poles on different Riemann sheets is analyzed in detail. The recently observed relaxation of holes in CdTe below the LO-phonon threshold is explained by the instability of the first polaron satellite.
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