Abstract
It is shown that when long-range potentials are present the wave functions for each channel are the solutions of certain homogeneous integral equations. These equations imply that the wave functions do not satisfy the Lippmann-Schwinger equations. However, the same wave functions also satisfy inhomogeneous integral equations involving an operator Z (a). This operator guarantees the existence of channel wave operators as strong limits of modified time evolution operators. An explicit integral representation for this operator is presented and it is shown that it displays ultraviolet divergencies at large relative velocities of the fragments whenever these fragments interact via Coulomb-like potentials. In case that long-range forces are absent Z (a) = 1 and the inhomogeneous integral equations reduce to the Lippmann-Schwinger equations for the wave function. We also present a general method for relating the wave functions for Coulomb-like potentials to the solutions of the Lippmann-Schwinger equations for screened Coulomb-like 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 callDisclaimer: 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.
