TITLE:
The Khuri-Jones Threshold Factor as an Automorphic Function
AUTHORS:
B. H. Lavenda
KEYWORDS:
Threshold Factor; Automorphic Function; Elliptic and Loxodromic Elements
JOURNAL NAME:
Journal of Modern Physics,
Vol.4 No.7,
July
8,
2013
ABSTRACT: The Khuri-Jones correction to the partial wave scattering amplitude
at threshold is an automorphic function for a dihedron. An expression for the
partial wave amplitude is obtained at the pole which the upper half-plane maps
on to the interior of semi-infinite strip. The Lehmann ellipse exists below
threshold for bound states. As the system goes from below to above threshold,
the discrete dihedral (elliptic) group of Type 1 transforms into a Type 3
group, whose loxodromic elements leave the fixed points 0 and ∞ invariant. The
transformation of the indifferent fixed points from -1 and +1 to the
source-sink fixed points 0 and ∞ is the result of a finite resonance width in
the imaginary component of the angular momentum. The change in symmetry of the
groups, and consequently their tessellations, can be used to distinguish bound
states from resonances.