Complex-coordinate calculation of ${}_{}{}^1{}_{}{}^{}\mathrm{D}_{}^{\mathrm{e}}{}_{}{}^{}$ resonances using Hylleraas functions

The method of complex-coordinate rotation is used to calculate the lowest-lying ${}_{}{}^1{}_{}{}^{}\mathrm{D}_{}^{\mathrm{e}}{}_{}{}^{}$ resonances below the n=2 and 3 hydrogen thresholds. Hylleraas functions with up to N=1230 terms are used. Resonance parameters for the n=2 resonance are determined as E=-0.255 873 7±1×${10}^{\mathrm{-}6}$ Ry and Γ=0.000 633 4±2×${10}^{\mathrm{-}6}$ Ry. The resonance parameters for the n=3 resonance are determined as E=-0.131 906 6±1×${10}^{\mathrm{-}6}$ Ry and Γ=0.003 316±2×${10}^{\mathrm{-}6}$ Ry.