Radiative properties of multi-carrier bound excitons in GaAs

Excitons in semiconductors can have multiple lifetimes due to spin dependent oscillator strengths and interference between different recombination pathways. In addition, strain and symmetry effects can further modify lifetimes via the removal of degeneracies. We present a convenient formalism for predicting the optical properties of $k=0$ excitons with an arbitrary number of charge carriers in different symmetry environments. Using this formalism, we predict three distinct lifetimes for the neutral acceptor bound exciton in GaAs, and confirm this prediction through polarization dependent and time-resolved photoluminescence experiments. We find the acceptor bound-exciton lifetimes to be $T_o(1,3,3\mathrm{/}4)$ where $T_o=(0.61\pm 0.12)\text{ns}$. Furthermore, we provide an estimate of the intra-level and inter-level exciton spin-relaxation rates.