Positron annihilation in the doubly excited states of positronium negative ions

The two-photon-annihilation rates for some ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$ doubly excited states of positronium negative ions are calculated. Hylleraas-type wave functions are used to represent the system. The doubly excited wave functions are obtained by use of a stabilization method. In comparing the annihilation lifetimes with the autoionization lifetimes (related to the inverse of the resonance widths that were obtained previously by using the method of complex-coordinate rotation), it is concluded that the decay mode of these lower-lying doubly excited ${}_{}{}^1{}_{}{}^{}\mathrm{S}_{}^{\mathrm{e}}{}_{}{}^{}$ states is dominated by autoionization processes.