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

Abstract

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.

Keywords

• positron elastic scattering
• S-matrix poles
• scattering length
• bound states
• virtual states