Complex-coordinate calculation of1,3Presonances inPs−using Hylleraas functions

An accurate calculation for ${}_{}{}^{1,3}{}_{}{}^{}$P autodetaching resonances in ${\mathrm{Ps}}^{\mathrm{-}}$ has been carried out using the complex-rotation method, which has the advantage of giving resonance position and width at the same time. The wave function is of the Hylleraas type with an available number of terms up to 1140. We find one ${}_{}{}^1{}_{}{}^{}$P and two ${}_{}{}^3{}_{}{}^{}$P resonances below the n=2 threshold and two ${}_{}{}^1{}_{}{}^{}$P and two ${}_{}{}^3{}_{}{}^{}$P resonances below the n=3 threshold of the positronium atom. Resonance parameters are compared with those obtained from scattering and adiabatic calculations where available.