  We consider the effects of single impurities on polarons in three-dimensions
(3D) using a continuous time quantum Monte-Carlo algorithm. An exact treatment
of the phonon degrees of freedom leads to a very efficient algorithm and we are
able to compute the polaron dynamics on an infinite lattice using an auxiliary
weighting scheme. The magnitude of the impurity potential, the electron-phonon
coupling and the phonon frequency are varied. We determine the magnitude of the
impurity potential required for polaron trapping. For small electron-phonon
coupling the number of phonons increases dramatically on trapping. The polaron
binding diagram is computed, showing that intermediate-coupling
low-phonon-frequency polarons are localized by exceptionally small impurities.
