Physical consequences of anomalies in nonlocal potential problems

Journal Article · Wed Aug 01 04:00:00 EDT 1979 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.20.418· OSTI ID:6125006

Foldy, L L; Lock, J A

An s-wave two-body separable potential may give rise to several phenomena which are absent for nonsingular local potentials. We examine the physical implications of a well-known example of such phenomena, the continuum bound state, as well as of two lesser known anomalies, the so-called positive energy spurious state and negative-energy bound states with improper long-range behavior. By examining these anomalies in light of Levinson's theorem, Wigner's phase shift inequality, and the effect of a perturbation on the anomalous states by their insertion in a three-body scattering situation, we find in agreement with previous studies that the continuum bound state acts as a resonance of negligible width. However, we find it difficult to see how the presence of a spurious state can be detected experimentally.

• Research Organization: Physics Department, Case Western Reserve University, Cleveland, Ohio 44106
• OSTI ID: 6125006
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 20:2; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653000* -- Nuclear Theory
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BOUND STATE
DIFFERENTIAL EQUATIONS
EIGENVALUES
EQUATIONS
LEVINSON THEOREM
MANY-BODY PROBLEM
NONLOCAL POTENTIAL
PARTIAL WAVES
PERTURBATION THEORY
PHASE SHIFT
POTENTIALS
S WAVES
SCATTERING
SCHROEDINGER EQUATION
THREE-BODY PROBLEM
WAVE EQUATIONS