  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 ${T_o (1,3,3/4)}$ 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.
