Potential scattering and Galilei-invariant expansions of scattering amplitudes

Journal Article · Thu Nov 15 04:00:00 EST 1973 · Phys. Rev., D, v. 8, no. 10, pp. 3527-3538

DOI:https://doi.org/10.1103/PhysRevD.8.3527· OSTI ID:4340870

Kalnins, E G; Patera, J; Sharp, R T; Winternitz, P

Previously derived Galilei-group expansions for the four-particle nonelativistic scattering amplitude are applied to potential scattering and the expansion coefficients (or Galilei amplitudes) are related in the first Born approximation to the potential. For the spherical partial-wave expansion the coefficients require a knowledge of the Clebsch-Gordan coefficients of E(3), and for the cylindrical eikonal expansion they are simply related to the usual eikonal function. A model amplitude containing BreitWigner resonances and other k-plane singularities, having correct threshold and reasonable asymptotic behavior, is analyzed in detail. It is shown that poles of partial-wave amplitudes a/sub 1/(k) in the k plane correspond to exponential-type asymptotics in the Galilei amplitudes. Specific models, in particular the Bargmann and separable potentials, are examined and their Galilei amplitudes calculated. A Schwinger-type variational principle is given for the Galilei amplitudes. (auth)

• Research Organization: Univ. of Montreal
• Sponsoring Organization: USDOE
• NSA Number: NSA-29-028079
• OSTI ID: 4340870
• Journal Information: Phys. Rev., D, v. 8, no. 10, pp. 3527-3538, Journal Name: Phys. Rev., D, v. 8, no. 10, pp. 3527-3538; ISSN PRVDA
• Country of Publication: Country unknown/Code not available
• Language: English

Related Subjects

*POTENTIAL SCATTERING-- SCATTERING AMPLITUDES
BORN APPROXIMATION
BOUNDARY CONDITIONS
BREIT-WIGNER FORMULA
CLEBSCH-GORDAN COEFFICIENTS
EIKONAL APPROXIMATION
GALILEI TRANSFORMATIONS
GROUP THEORY
N64500* --Physics (High Energy)--Scattering Theory
PARTIAL WAVES
RESONANCE
SERIES EXPANSION
SINGULARITY
VARIATIONAL METHODS