Exact spectra of photon emission and absorption are given for the Mahan–Nozières–De Dominicis (MND) Hamiltonian in the finite-temperature case. Besides infrared divergence, existence of a bound state and relaxation shift of the threshold energy are rigorously taken into account. We discuss in detail the interplay between the infrared divergence and thermal broadening and examine how the results in the ladder approximation are improved by the exact treatment. Based on the numerical results, quantitative comparison with recent experiments for quantum wells with ${\varepsilon }_F$=200 K and 4.2 K<T<60 K is attempted. In the case of absorption it is found that if an appropriate value for the lifetime of a core hole is assumed, the MND Hamiltonian is capable of yielding a line shape in fairly good agreement with the experiments. For the emission spectra, however, the agreement is worse and it seems that some dissipative mechanism operating prior to photon emission has to be included.

• Received 7 September 1988

DOI:https://doi.org/10.1103/PhysRevB.39.3054