Abstract
We present main features of a surface-integral approach to the Coulomb few-body scattering problem. This approach is valid for both short-range and Coulombic longe-range interactions. We give new general definitions for the potential scattering amplitude. For the Coulombic potentials the generalized amplitude gives the physical on-shell amplitude without recourse to a renormalization procedure. New post and prior forms for the amplitudes of breakup, direct and rearrangement scattering in a Coulomb three-body system are also presented. The Green’s functions and formal solutions of the Schrödinger equation in integral form are not used. Therefore, for the purpose of defining the scattering amplitudes the knowledge of a complicated analytic structure of the Green’s function in the complex-energy plane is not required.
Highlights
Atomic and subatomic many-particle systems with the long-range Coulomb interactions and cosmological many-body systems with the gravitational interactions are of fundamental importance for our understanding of the universe
First we investigate the limit on the left-hand side (LHS) which can be written as LHS = lim − 1 r2 dr r0→∞ 2μ
We have given a brief account of a formalism of scattering theory which is applicable to two-body and three-body systems with both short-range and Coulombic long-range potentials
Summary
Atomic and subatomic many-particle systems with the long-range Coulomb interactions and cosmological many-body systems with the gravitational interactions are of fundamental importance for our understanding of the universe. The conventional theory fails to provide a formal post-form definition of the breakup amplitude for three charged particles in terms of the total wavefunction with outgoing scattered waves describing the process. Despite the success of the computational methods in describing the measured cross sections, the traditional formal theory of scattering was unable to provide a definition for the breakup amplitude in terms of the scattered wave. This has been a long-standing problem [11]. In the present work we outline a surface-integral approach to formulating scattering theory This represents an extension of the general formalism of scattering theory to systems of two and three charged particles with long-range Coulombic interactions. Further details of the present formalism can be found in Ref. [12]
Sign-in/Register to view highlights & summary 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.
