An investigation of resonances in $e^{+}$-H scattering embedded in Debye plasmas

We have carried out calculations for $S$-wave and $P$-wave resonances in $e^{\mathrm{+}}$-H scattering in weakly coupled Debye plasmas in which the interacting potential between two charge particles is represented by a screened Coulomb potential. We have employed the complex-scaling method [1] with Hylleraas-type wave functions to take into account of the correlation effects. In the complex-scaling treatment of the screened Coulomb potential, we first performed a Taylor series expansion for the exponential function that contains the ``$r_{\mathrm{ij}}$'' factor into a polynomial with various powers ($r_{\mathrm{ij}})^{\mathrm{n}}$. Then complex transformation with $r_{\mathrm{ij}}\to r_{\mathrm{ij}}$ \textit{exp}(i$\theta$) for such a series was subsequently carried out, and resonance complex eigenvalues were deduced from their stabilization with respect to the changes of rotational angles $\theta $, and with respect to the changes of some parameters in the wave functions (see [2] for more details). For $S$-wave resonances, reasonably good agreement has been found with earlier calculations using different methods [3, 4]. Some new results for the $P$-wave resonances will be presented at the meeting.\\[4pt] [1] Y. K. Ho\textit{, Phys. Rept.} \textbf{99}, 1, (1983), and references therein;\\[0pt] [2] L.-G. Jiao and Y. K. Ho, \textit{Phys. Plasmas} \textbf{20}, 083303 (2013);\\[0pt] [3] S. Kar and Y. K. Ho, \textit{J. Phys. B} \textbf{38}, 3299 (2005);\\[0pt] [4] S. Chakraborty and Y. K. Ho, \textit{Phys. Rev. A }\textbf{77}, 014502 (2008).