Variational bounds from matrix Pade approximants in potential scattering. [Phase shifts, coupling]

Journal Article · Fri Apr 15 04:00:00 EST 1977 · Phys. Rev., D; (United States)

DOI:https://doi.org/10.1103/PhysRevD.15.2345· OSTI ID:7115735

Bessis, D; Mery, P; Turchetti, G

We fully develop the content of the Schwinger variational principle for the phase shifts in potential scattering. We introduce matrix Pade approximations built up from the perturbation expansion of the Green's function. They appear to lead to a new type of (Pade) approximation when optimized through the variational principle. These new approximations, which are no longer rational fractions in the expansion parameter, appears to have the full analytical richness of the exact solution. For the case of a nonchanging-sign potential these new types of approximations provide the best bounds to the phase shifts and bound states. The extension to arbitrarily singular potentials is also discussed. A numerical example confirms the extreme efficiency of the method. Typically, values of the coupling giving rise to one or two bound states are obtained within 10/sup -3/ of their exact values, and this on the full range of energy, by including only the first and second Born terms of the perturbation series.

• Research Organization: Service de Physique Theorique, Centre d'Etudes Nucleaires de Saclay, BP N/sup o/ 2-91190 Gif-sur-Yvette, France
• OSTI ID: 7115735
• Journal Information: Phys. Rev., D; (United States), Journal Name: Phys. Rev., D; (United States) Vol. 15:8; ISSN PRVDA
• Country of Publication: United States
• Language: English

Related Subjects

645500* -- High Energy Physics-- Scattering Theory-- (-1987)
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
BOUND STATE
ELASTIC SCATTERING
FUNCTIONS
GREEN FUNCTION
K MATRIX
MATRICES
PADE APPROXIMATION
PERTURBATION THEORY
PHASE SHIFT
POTENTIAL SCATTERING
SCATTERING
SCHWINGER VARIATIONAL METHOD
VARIATIONAL METHODS