Positron-hydrogen resonances associated with the positroniumN=3and hydrogenN=4thresholds

Some lower-lying S-wave resonances in positron-hydrogen scattering associated with the N=3 positronium (Ps) and N=4 hydrogen thresholds are investigated by using the method of complex-coordinate rotation. Using Hylleraas-type wave functions with M=969 terms, several resonances in these energy regions are calculated for the first time. In particular, the lowest resonance associated with the Ps(N=3) threshold is found to lie at E=-0.077 063 Ry, and the lowest resonance associated with the H(N=4) threshold is found to lie at E=-0.067 867 Ry. In addition, we also locate a shape resonance lying just above the Ps(N=3) threshold at E=-0.055 44 Ry.