Pade approximants, NN scattering, and hard core repulsions

Journal Article · Wed Oct 01 04:00:00 EDT 1980 · Phys. Rev., C; (United States)

DOI:https://doi.org/10.1103/PhysRevC.22.1377· OSTI ID:5117767

Hartt, K

Pade approximants to the scattering function F=k cot(delta/sub 0/) are studied in terms of the variable x=k/sup 2/, using four examples of potential models which possess features of the np /sup 1/S/sub 0/ state. Strategies are thereby developed for analytically continuing F when only approximate partial knowledge of F is available. Results are characterized by high accuracy of interpolation. It is suggested that a physically realistic inverse scattering problem begins with such an analytically continued F. When it exists, the solution of this problem in terms of the Marchenko equation is a local potential of the Bargmann type. Some strategies for carrying out this program lead to a stably defined potential, while others do not. With hard core repulsions present, low-order Pade approximants accurately describe F for E/sub c.m./< or =300 MeV. However, since the condition ..delta..(infinity)-delta(0)=0 is not satisfied in any of our examples containing hard core repulsions, the Marchenko method does not have a solution for them. A possible physical consequence of this result is discussed. Another inverse scattering method is proposed for application to hard core problems.

• Research Organization: Physics Department, University of Rhode Island, Kingston, Rhode Island 02881
• OSTI ID: 5117767
• Journal Information: Phys. Rev., C; (United States), Journal Name: Phys. Rev., C; (United States) Vol. 22:4; ISSN PRVCA
• Country of Publication: United States
• Language: English

Related Subjects

653003* -- Nuclear Theory-- Nuclear Reactions &amp; Scattering
73 NUCLEAR PHYSICS AND RADIATION PHYSICS
ANALYTIC FUNCTIONS
BARYON-BARYON INTERACTIONS
BOUND STATE
EFFECTIVE RANGE THEORY
FUNCTIONS
HADRON-HADRON INTERACTIONS
HARD-CORE POTENTIAL
INTERACTIONS
INVERSE SCATTERING PROBLEM
NUCLEAR POTENTIAL
NUCLEON-NUCLEON INTERACTIONS
PADE APPROXIMATION
PARTICLE INTERACTIONS
PHASE SHIFT
POLYNOMIALS
POTENTIALS