Scattering length and effective range for charged-particle 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.32.1430· OSTI ID:5428391

Verhaar, B J; de Goey, L P.H.; Vredenbregt, E J.D.

The concepts of scattering length a and effective range r/sub e/ previously introduced for low-energy scattering from a potential V(r) in a plane and in higher dimensions are extended to include a 1/r potential (strength parameter ..gamma..). Both a and r/sub e/ have the physical significance of being equal to the radius of an equivalent hard sphere giving rise to the same O(k/sup 0/) and O(k/sup 2/) terms in the expression for the phase shift. The method used is based on the properties of the ''local scattering length'' a(r,..gamma..) for the potential V(r) cut off at radius r and an ''equivalent hard-sphere radius'' a(r,k,..gamma..) for wave number knot =0. It is shown that these quantities have a smooth behavior for ..gamma -->..0 and for dimension n..-->..2.

• Research Organization: Department of Physics, Eindhoven University of Technology, Postbus 513, 5600 MB, Eindhoven, The Netherlands
• OSTI ID: 5428391
• 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
POTENTIAL SCATTERING
EFFECTIVE RANGE THEORY
SCATTERING LENGTHS
HARD-SPHERE MODEL
INTERACTION RANGE
MANY-DIMENSIONAL CALCULATIONS
PHASE SHIFT
DIMENSIONS
DISTANCE
ELASTIC SCATTERING
LENGTH
SCATTERING
645500* - High Energy Physics- Scattering Theory- (-1987)