Virtual and bound states in low-energy positron scattering by atoms and molecules via modified effective range theory

Modified effective range theory is applied as a tool to determine bound and virtual state energies in low-energy positron elastic scattering by atoms and molecules. This is achieved by the S-matrix continuation into the complex momentum plane, allowing to identify poles related to shallow energy states. The influence of the long-range polarization potential (∼ r −4 ) on the bound and virtual-state pole positions is analyzed for noble gases and nonpolar molecules such as H 2 , N 2 , and CH 4 . The quantitative relations between the S-matrix poles and the s -wave scattering length accounting for dipole polarization are introduced.