Potential splitting approach to multichannel Coulomb scattering: The driven Schroedinger equation formulation

Journal Article · Tue Mar 15 00:00:00 EDT 2011 · Physical Review. A

DOI:https://doi.org/10.1103/PHYSREVA.83.032722· OSTI ID:21541300

Volkov, M V ^[1]; Yakovlev, S L; Yarevsky, E A ^[2]; Elander, N ^[1]

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1. Department of Physics, AlbaNova University Center, Stockholm University, SE-106 91 Stockholm (Sweden)
2. Department of Computational Physics, St. Petersburg State University, RU-198504 St Petersburg (Russian Federation)

In this paper we suggest an approach for the multichannel Coulomb scattering problem. The Schroedinger equation for the problem is reformulated in the form of a set of inhomogeneous equations with a finite-range driving term. The boundary conditions at infinity for this set of equations have been proven to be purely outgoing waves. The formulation presented here is based on splitting the interaction potential into a finite-range core part and a long-range tail part. The conventional matching procedure coupled with the integral Lippmann-Schwinger equations technique is used in the formal theoretical basis of this approach. The reformulated scattering problem is suitable for application in the exterior complex scaling technique: the practical advantage is that after complex scaling, the problem is reduced to a boundary problem with zero boundary conditions. The Coulomb wave functions are used only at a single point; if this point is chosen to be at a sufficiently large distance, on using the asymptotic expansion of Coulomb functions, one may completely avoid the Coulomb functions in the calculations. The theoretical results are illustrated with numerical calculations for two models.

• OSTI ID: 21541300
• Journal Information: Physical Review. A, Vol. 83, Issue 3; Other Information: DOI: 10.1103/PhysRevA.83.032722; (c) 2011 American Institute of Physics; ISSN 1050-2947
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
74 ATOMIC AND MOLECULAR PHYSICS
ASYMPTOTIC SOLUTIONS
BOUNDARY CONDITIONS
COULOMB SCATTERING
LIPPMANN-SCHWINGER EQUATION
POTENTIALS
SCALING
SCHROEDINGER EQUATION
SERIES EXPANSION
WAVE FUNCTIONS
BASIC INTERACTIONS
DIFFERENTIAL EQUATIONS
ELASTIC SCATTERING
ELECTROMAGNETIC INTERACTIONS
EQUATIONS
FUNCTIONS
INTEGRAL EQUATIONS
INTERACTIONS
MATHEMATICAL SOLUTIONS
PARTIAL DIFFERENTIAL EQUATIONS
SCATTERING
WAVE EQUATIONS