  Motivated by recent experiments on radiative recombination of two-dimensional
electrons in acceptor doped GaAs-AlGaAs heterojunctions as well as the success
of a harmonic solid model in describing tunneling between two-dimensional
electron systems, we calculate within the harmonic approximation and the time
dependent perturbation theory the line shape of the photoluminescence spectrum
corresponding to the recombination of an electron with a hole bound to an
acceptor atom. The recombination process is modeled as a sudden perturbation of
the Hamiltonian for the in-plane degrees of freedom of the electron. We include
in the perturbation, in addition to changes in the equilibrium positions of
electrons, changes in the curvatures of the harmonically approximated
potential. The computed spectra have line shapes similar to that seen in a
recent experiment. The spectral width, however, is roughly a factor of 3
smaller than that seen in experiment if one assumes a perfect Wigner crystal
for the initial state state of the system, whereas a simple random disorder
model yields a width a factor of 3 too large. We speculate on the possible
mechanisms that may lead to better quantitative agreement with experiment.
