Role of Levinson's theorem in neutron-deuteron quartet S -wave scattering

Journal Article · Wed Aug 01 04:00:00 EDT 1990 · Physical Review, C (Nuclear Physics); (USA)

DOI:https://doi.org/10.1103/PhysRevC.42.R506· OSTI ID:6603068

Sofianos, S A; Papastylianos, A; Fiedeldey, H ^[1]; Alt, E O ^[2]

---

1. Department of Physics, University of South Africa, P.O. Box 392, Pretoria (South Africa)
2. Department of Physics, University of South Africa, P.O. Box 392, Pretoria (South Africa) Institute fuer Physik, Universitaet Mainz, P.O. Box 3980, Mainz (West Germany)

The real part of the phase shift for elastic neutron-deuteron scattering in the quartet {ital S} wave channel, as calculated with the exact three-body theory, assumes at threshold the value {pi} if normalized to zero at infinity; that is, it does not comply with the expectations raised by a naive application of Levinson's theorem since no bound state exists in this channel. A description of this situation on an equivalent two-body level via a potential, constructed by means of the Marchenko inverse scattering theory, necessitates the introduction of a fictitious bound state. This predominantly attractive, equivalent local potential can be related via supersymmetry to a strictly phase equivalent partner potential. The latter is unique and purely repulsive, a behavior already exhibited by the underlying exact effective neutron-deuteron interaction. At the origin it possesses a singularity of the centrifugal barrier-type which admits of the required zero-energy phase shift value of {pi} by means of a modified version of Levinson's theorem. Hence, the unphysical bound state of the attractive equivalent local potential plays a role in three-body scattering theory analogous to the one of a Pauli-forbidden state in the context of the resonating group method.

• OSTI ID: 6603068
• Journal Information: Physical Review, C (Nuclear Physics); (USA), Journal Name: Physical Review, C (Nuclear Physics); (USA) Vol. 42:2; ISSN 0556-2813; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions & Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
BARYON-BARYON INTERACTIONS
BOUND STATE
ELASTIC SCATTERING
HADRON-HADRON INTERACTIONS
INTERACTIONS
LEVINSON THEOREM
MANY-BODY PROBLEM
NEUTRON-DEUTERON INTERACTIONS
NUCLEON-DEUTERON INTERACTIONS
PARTIAL WAVES
PARTICLE INTERACTIONS
PHASE SHIFT
S WAVES
SCATTERING
THREE-BODY PROBLEM