Investigation of screening effects on the shape resonances in the electron-hydrogen system using the complex-scaling method

In the present work we study the effects of screened Coulomb potentials on shape resonances in the electron-hydrogen system. Here we concentrate on the $^{1}S^{\mathrm{e}}$ and $^{1}P^{\mathrm{o}}$ shape resonances associated with and lying above, respectively, the H ($N=$2), (N$=$3), (N$=$4), and ($N=$5) thresholds. The complex-scaling method [1] is used to extract resonance poles, together with employing correlated Hylleraas-type wave functions up to 1078 and 1771 terms for the $S$- and $P$-wave states, respectively, to represent the two-electron system. To model the screening effect we replace the pure Coulomb interaction term for any pair of charged particles by a screened Coulomb (or Yukawa-type) interaction term. Our un-screened shape resonances agree well with those in the literature [2, 3]. We will present our latest results for the screened cases at the meeting.\\[4pt] [1] Y. K. Ho,\textit{ Phys. Rept. }\textbf{99}, 1 (1983) and references therein.\\[0pt] [2] A. B\"urgers and E. Lindroth, \textit{Eur. Phys. J. D }\textbf{10}, 327 (2000).\\[0pt] [3] S. Kar and Y. K. Ho, \textit{Phys. Rev. A }\textbf{86}, 014501 (2012).