Abstract
We derive a general formula for a modified effective-range function (MERF), , for all partial waves, . This is a generalization of the effective-range function associated with a short-range potential, . Here is the energy variable and the phase shift. The MERF can be associated with a potential that allows a decomposition into a long-range and a short-range component. It is a complex real-meromorphic function of in the complex plane in a domain containing the origin. This (large) domain is determined by the short-range part of the potential. We give a simple formula for , valid for all . It can be used if the long-range part of the potential is analytic at . For we have the simple expression Here and are the Jost function and Jost solution, respectively, associated with the long-range part of the potential, and is the difference between the -wave phase shift associated with the total potential and that of the long-range potential. The prime in denotes differentiation with respect to . The extension to the case of the Coulomb potential which violates the condition of analyticity at is briefly discussed.
- Received 19 December 1980
DOI:https://doi.org/10.1103/PhysRevA.26.1218
©1982 American Physical Society