Solutions of the radial equation for scattering by a nonlocal potential

Journal Article · Tue Jun 01 04:00:00 EDT 1976 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.13.2131· OSTI ID:7192728

Mulligan, B; Arnold, L G; Bagchi, B; Krause, T O

Nonlocality is characteristic of potentials describing processes in which degrees of freedom are eliminated, and provides for a description of a much wider variety of phenomena than that encountered with short range local potentials. In this paper, properties of the radial equation for symmetric nonlocal potentials are investigated, using a configuration space approach and restricting the analysis to real k. Emphasis is placed on identifying those constraints associated with a local potential which are relaxed in going from a local to a nonlocal potential. The Fredholm determinants associated with the integral equations for the physical, regular, and Jost solutions are central to the development. Unlike the case for a short range local potential, for a nonlocal potential these Fredholm determinants can vanish for real knot-equal0. It is shown that when D/sup plus-or-minus/(k) =0 all other Fredholm determinants are zero as well. The properties of the solutions at the zeroes of the Fredholm determinants are discussed in this context, and the concepts ''spurious state'' and ''continuum bound state'' are clarified. The behavior of solutions is illustrated with examples. (AIP)

• Research Organization: Department of Physics, The Ohio State University, Columbus, Ohio 43210
• OSTI ID: 7192728
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 13:6; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

645500* -- High Energy Physics-- Scattering Theory-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BARYON-BARYON INTERACTIONS
BOUND STATE
DIFFERENTIAL EQUATIONS
ELASTIC SCATTERING
EQUATIONS
FREDHOLM EQUATION
FUNCTIONS
HADRON-HADRON INTERACTIONS
INTEGRAL EQUATIONS
INTERACTIONS
NONLOCAL POTENTIAL
NUCLEON-NUCLEON INTERACTIONS
PARTICLE INTERACTIONS
POTENTIAL SCATTERING
SCATTERING
SCHROEDINGER EQUATION
SYMMETRY
WAVE EQUATIONS
WAVE FUNCTIONS