Scattering length and effective range for scattering in a plane and in higher dimensions

Journal Article · Sun Sep 01 00:00:00 EDT 1985 · Phys. Rev. A; (United States)

DOI:https://doi.org/10.1103/PhysRevA.32.1424· OSTI ID:5295687

Verhaar, B J; de Goey, L P.H.; van den Eijnde, J P.H.W.; Vredenbregt, E J.D.

It is shown how the concepts of scattering length and effective range, previously introduced for low-energy scattering from a potential V(r) in a plane, correspond to the well-known parameters in three dimensions. This is done by considering low-energy scattering in a general dimension n> or =2 and subsequently showing that both the n = 2 and n = 3 cases fit naturally in such a generalized treatment. Furthermore, our previous work is extended to long-range potentials, decreasing faster than 1/r/sup n/+1. The method used is based on the properties of a local scattering length a(r) for the potential V(r) cut off at radius r and an equivalent hard-sphere radius a(r,k) for knot =0. Some applications and illustrative examples are given.

• Research Organization: Department of Physics, Eindhoven University of Technology, Postbus 513, 5600 MB, Eindhoven, The Netherlands
• OSTI ID: 5295687
• Journal Information: Phys. Rev. A; (United States), Vol. 32:3
• Country of Publication: United States
• Language: English

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
SCATTERING LENGTHS
INTERACTION RANGE
MANY-DIMENSIONAL CALCULATIONS
ELECTRON-ELECTRON INTERACTIONS
POTENTIALS
QUANTUM MECHANICS
SCHROEDINGER EQUATION
USES
DIFFERENTIAL EQUATIONS
DIMENSIONS
DISTANCE
EQUATIONS
INTERACTIONS
LENGTH
LEPTON-LEPTON INTERACTIONS
MECHANICS
PARTIAL DIFFERENTIAL EQUATIONS
PARTICLE INTERACTIONS
WAVE EQUATIONS
645500* - High Energy Physics- Scattering Theory- (-1987)