High-lying resonances in Ps-H scattering below the H$^{- }$- e$^{+}$ threshold

In this work, we carry out an investigation of high-lying $S$-wave resonances in Ps-H scattering below the (H$^{-}$ - e$^{+})$ threshold. The method of complex-coordinate-rotation [1] is used together with employing highly correlated wave functions containing all six inter-particle coordinates. Using such Hylleraas-type bases [2] up to 6412 terms, the energy positions and widths up to the 7$S$ state in the Rydberg series converging to the H$^{-}$ threshold are calculated. The high-lying resonances from our present calculations are fitted to a quantum defect formula, and from which the energies of even higher members of the Rydberg series can be deduced. [1].Y. K. Ho, \textit{Phys. Rept}. \textbf{99}, 1 (1983). [2]. Z.-C. Yan and G. W. F. Drake\textit{, J. Phys. B} \textbf{30}, 4723 (1997).