Phonon-assisted trapping by shallow impurity in quantum well

We have considered the capture of electron in a quantum well by shallow donor impurity due to the interaction with an acoustical phonon. Wave functions of the nine lowest bound states have been found by variational method. We have calculated the rates of transitions between the free states and bound states as well as between different bound states. In the case of phonon wavelength much smaller than the width of the well L the transition rates are proportional to ε^-5 (n_ε + 1 2± 1 2) L^-6, where ε is the transferred energy, n_ε is a phonon occupation number.