The luminescence line shapes of an electron-hole plasma in Ga-Al-As have been calculated within the random-phase approximation (RPA). Different models have been tested for the spectral weight function. The fully self-consistent RPA is found to overestimate the weight of the plasmon sideband and to underestimate the energy-gap narrowing. An approach which neglects plasmon replicas instead yields luminescence spectra in excellent agreement with experiment over a wide range of plasma densities and temperatures. A further model is also introduced to estimate an upper bound for the weight of plasmon sidebands in the experimental spectra. We used both static and dynamical phonon screening. We found that the former screening correctly describes luminescence up to densities such that the plasmon energy is of the order of the longitudinal-optical-phonon energy
