Two-Variable Galilei-Group Expansions of Nonrelativistic Scattering Amplitudes

Journal Article · Mon Oct 01 04:00:00 EDT 1973 · Physical Review. D, Particles Fields

DOI:https://doi.org/10.1103/PhysRevD.8.2552· OSTI ID:4327901

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

Two-variable Galilei-group expansions are derived for the two-particle nonrelativistic scattering amplitude. These expansions contain the usual partial- wave and eikonal expansions and supplement them by further expansions in the remaining kinematic variable. The expansions are written both for square- integrable and for asymptotically increasing amplitudes and are shown to correspond to the nonrelativistic limit of previously considered relativistic two- variable expansions. Dynamical singularities (Breit-Wigner resonances, bound states, poles in the impact-parameter plane, etc,) are investigated and related to the asymptotic behavior of the expansion coefficients (or Galilei amplitudes). The threshold and high-energy limits of the expansions are discussed. As a mathematical by-product we give a classification of the subgroups of E(3) and also some results on the representation theory of this group; in particular we study the Clebach-Gordan coefficients.

• Research Organization: Centre de Recherches Mathematiques, Universite de Montreal, Case Postale 6128, Montreal, P. Q., Canada
• Sponsoring Organization: USDOE
• NSA Number: NSA-29-025385
• OSTI ID: 4327901
• Journal Information: Physical Review. D, Particles Fields, Journal Name: Physical Review. D, Particles Fields Journal Issue: 8 Vol. 8; ISSN 0556-2821
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

*SCATTERING AMPLITUDES-- GALILEI TRANSFORMATIONS
CLEBSCH-GORDAN COEFFICIENTS
LORENTZ GROUPS
N64310 - -Physics (High Energy)--Particle Invariance Principles & Symmetry--General
N64500* --Physics (High Energy)--Scattering Theory
O GROUPS
PARTIAL WAVES