Abstract
Solutions of Schroedinger's equation for systems interacting with long-range power-law potentials, [ital V][sub int]([ital r])[proportional to][ital r][sup [minus][ital n]] with [ital n][ge]2, are cast in the form of a power series in [ital V][sub int]. These perturbations lead to secular divergences that are eliminated by renormalizing the angular-momentum quantum number. Long-known perturbation techniques in classical mechanics and quantum-field theory yield modified effective-range formulas, quantum-defect functions, and solutions of close-coupling equations for wave propagation in long-range fields. As an example, we extract in first-order perturbation theory a modified effective-range expansion for the phase shift of an electron interacting with an atomic 1/[ital r][sup 4] polarization potential. Near thresholds, the method is applicable to all power-law potentials with [ital n][ge]2, and to their combinations, as well as to multichannel problems involving anisotropic potentials.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Physical review. A, Atomic, molecular, and optical physics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
