Complex scaling calculation of phase shifts for positron collisions with positive ions

We present phase-shift calculations for positron collisions with positive ions using a complex scaling method (CSM). Based on the findings of this study [R. Suzuki, T. Myo, and K. Katō, Prog. Theor. Phys. 113, 1273 (2005).], we propose a modification of the phase shift in the CSM calculation, in which phase shifts are derived only from the complex eigenenergies of the CSM Hamiltonian. This modification is based on the fact that the contributions of high-lying complex eigenenergies can be approximated as a constant value in the case of a small collision energy, where neither target excitation nor positronium formation occurs. The proposed modification limits the contribution of the complex eigenenergies to the vicinity of the collision energy, which is also intuitively acceptable. We present a geometrical formulation of the modification and demonstrative calculations of positron scattering off positive ions. Our results agree well with those reported in the literature for the targets Ne, Ar, Kr, Xe, H, He, He^+, and Li^2+. The phase shifts of positron scattering off a Li^+ ion have also been reported.