Momentum Transfer Dispersion Relations for Three-Particle Potential Scattering Amplitudes

1968 ◽  
Vol 169 (5) ◽  
pp. 1104-1114 ◽  
Author(s):  
J. B. Hartle ◽  
R. L. Sugar
Keyword(s):  
Scattering Amplitudes ◽  
Momentum Transfer ◽  
Potential Scattering ◽  
Dispersion Relations ◽  
Particle Potential

Dispersion relations for a two-channel scattering process: residues of the scattering amplitudes

1963 ◽  
Vol 59 (1) ◽  
pp. 161-166
Author(s):  
J. Underhill
Keyword(s):  
Scattering Amplitudes ◽  
Momentum Transfer ◽  
Integral Equations ◽  
Incident Energy ◽  
Dispersion Relations ◽  
Scattering Process ◽  
Image Position

1. This paper is a continuation of a previous one(1), in which dispersion relations satisfied by the scattering amplitudes for a non-relativistic two-channel scattering process were derived. It was shown that for the process described by the integral equationswiththe scattering amplitudes Mi(E, τ) (where E is the incident energy and τ is the momentum transfer), satisfy the relations

Dispersion Relations for Three-Particle Scattering Amplitudes. I

1966 ◽  
Vol 146 (4) ◽  
pp. 1130-1149 ◽  
Author(s):  
Morton Rubin ◽  
Robert Sugar ◽  
George Tiktopoulos
Keyword(s):  
Scattering Amplitudes ◽  
Dispersion Relations ◽  
Particle Scattering

Analyticity with respect to Momentum Transfer and Dispersion Relations

1990 ◽  
pp. 548-573
Author(s):  
N. N. Bogolubov ◽  
A. A. Logunov ◽  
A. I. Oksak ◽  
I. T. Todorov ◽  
G. G. Gould
Keyword(s):  
Momentum Transfer ◽  
Dispersion Relations

DIFFERENTIAL OPERATORS FOR SCATTERING AMPLITUDES

2007 ◽  
Vol 16 (09) ◽  
pp. 2910-2914
Author(s):  
MÁRCIO JOSÉ MENON ◽  
REGINA FONSECA ÁVILA
Keyword(s):  
Elastic Scattering ◽  
Scattering Amplitudes ◽  
Cross Section ◽  
Differential Form ◽  
Differential Operators ◽  
Dispersion Relations ◽  
Proton Scattering ◽  
Cross Section Data ◽  
Proton Proton ◽  
Section Data

We discuss novel dispersion relations in differential form, connecting real and imaginary parts of elastic scattering amplitudes and formally valid at any energy above the physical threshold. By means of fits to total cross section data from proton-proton and antiproton-proton scattering, we evaluate the corresponding ratio ρ between the real and imaginary parts of the forward amplitudes. We show that the results are exactly the same as those obtained through standard integral dispersion relations.

Existence of partial-wave two-cluster atomic scattering amplitudes

1979 ◽  
Vol 57 (3) ◽  
pp. 449-456 ◽  
Author(s):  
J. Nuttall ◽  
S. R. Singh
Keyword(s):  
Scattering Amplitudes ◽  
Partial Wave ◽  
Scattering Problem ◽  
Potential Scattering ◽  
Atomic Systems ◽  
Almost Everywhere ◽  
Cluster Threshold ◽  
Channel Potential ◽  
Atomic Scattering ◽  
Coupled Channel

It is shown, with some restrictions, that two-cluster partial wave scattering amplitudes for atomic systems whose particles interact via two-body Coulomb potentials exist almost everywhere in the energy range below any three-cluster threshold. The method of proof is to reduce the problem to a coupled channel potential scattering problem with pseudo-local potentials. Boost analyticity is used to derive the pseudo-locality.

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