Resonances in three-body scattering theory
type: Item
instance of: scholarly article
title: Resonances in three-body scattering theory
zbMATH Open document ID: 0617.47008
DOI: 10.1016/0196-8858(84)90010-1
author: Erik Balslev
published in: Advances in Applied Mathematics
publication date: 1984-01-01T00:00:00Z
review text: In this paper resonances in multichannel scattering theory associated with the three body problem for negative energies, assuming exponential decay of the two-body interactions, is discussed. These resonances are characterized as (1) poles of an analytically continued resolvent acting between certain exponentially weighted spaces, (2) eigenvalues of a Schrödinger operator acting in a suitable space, (3) singular points of the Faddeev matrix, (4) singular points of the Lippman-Schwinger operator, (5) poles of the S-matrix, (6) poles of the analytic families of the exponentially growing eigenfunctions. The analysis is restricted to the analytic continuation of the resolvent, the S-matrix etc., across the spectrum to the second sheet in the lower and upper half-planes and the resonances in this region. Further how the various operator- and vector-valued functions can be analytically continued on a Riemann surface determined by two sheeted parabolic regions focused at thresholds as \(\sqrt{z}\)-type branch points is indicated.
Mathematics Subject Classification ID: 47A40
Mathematics Subject Classification ID: 47L90
Mathematics Subject Classification ID: 81U10
Mathematics Subject Classification ID: 81U20
zbMATH DE Number: 4000795
zbMATH Keywords: resonances in multichannel scattering theory
zbMATH Keywords: three body problem for negative energies
zbMATH Keywords: exponential decay of the two-body interactions
zbMATH Keywords: poles of an analytically continued resolvent
zbMATH Keywords: eigenvalues of a Schrödinger operator
zbMATH Keywords: singular points of the Faddeev matrix
zbMATH Keywords: singular points of the Lippman-Schwinger operator
zbMATH Keywords: S-matrix
MaRDI profile type: Publication
full work available at URL: 0196-8858(84)90010-1
OpenAlex ID: W2078102211
cites work: Q4191142
cites work: Q3865044
cites work: Analytic scattering theory for many-body systems below the smallest three-body threshold
cites work: A link between scattering resonances and dilation analytic resonances in few body quantum mechanics
cites work: Abstract stationary theory of multichannel scattering
cites work: Local distortion technique, resonances, and poles of the S-matrix
cites work: Q3913314
cites work: Q4178095
cites work: Eigenfunction expansions and scattering theory for perturbations of - \(\Delta\)
cites work: Resonant states and poles of the scattering matrix for perturbations of - \(\Delta\)
cites work: Resonances, scattering theory, and rigged Hilbert spaces
cites work: Q4183133
cites work: Q3866506
description: scientific article; zbMATH DE number 4000795