Variational calculation of Fano linewidth: Application to excitons in quantum wells

A procedure for calculating the resonance width of a state degenerate with a continuum is proposed. It is based on a diagonalization of the Hamiltonian on a finite variational basis followed by application of the Fano theory on the resulting eigenstates. The method is first tested on a one-dimensional model that admits an exact solution, and then applied to the problem of the light-hole (LH) exciton in narrow GaAs-${\mathrm{Ga}}_{1\mathrm{-}\mathit{x}}$${\mathrm{Al}}_{\mathit{x}}$As quantum wells. The resonance width of the LH exciton is found to be of the order of a meV, and to increase as the well width is reduced.