High-lying resonances in positron scattering by the helium ion below the Ps($n$=3) threshold*

Ever since Bhatia and Drachman [1] reported two $S$-wave resonances in positron scattering by a helium ion, there has been considerable interest in and sometimes controversial on the investigation of the resonances in such a system [2]. In the present work, we apply the method of complex-coordinate rotation to investigate resonances in positron scattering by helium ions. Highly correlated Hylleraas functions are used to calculate resonances for high-angular-momentum states up to $L=9$. We will report the results for high-lying resonances below Ps($n$=3) threshold. A comparison will be made with the available results in the literature. \\ \ \\ \noindent [1] A. K. Bhatia and R. J. Drachman, Phys. Rev. A {\bf 42}, 5117 (1990) \\ \noindent [2] Y. K. Ho, Phys. Rev. A {\bf 53}, 3165 (1996); A. Igarashi and I. Shimamura, Phys. Rev. A {\bf 56}, 4733 (1997); Y. K. Ho and Z.-C. Yan, Phys. Rev. A {\bf 66}, 062705 (2002); A. Igarashi and I. Shimamura, Phys. Rev. A {\bf 70}, 012706 (2004); N. Yamanaka, et al. Phys. Rev. A {\bf 70}, 062701 (2004)