The exact discontinuity of a partial wave along the left-hand cut and the exact N∕D method in non-relativistic scattering

Journal Article · Sun Dec 15 04:00:00 EST 2019 · Annals of Physics

DOI:https://doi.org/10.1016/J.AOP.2019.167965· OSTI ID:22852354

Entem, D. R. ^[1]

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1. Grupo de Física Nuclear and IUFFyM, Universidad de Salamanca, E-37008 Salamanca (Spain)

We first deduce the analytical continuation in the complex planes of the initial and final three-momenta of the Lippmann–Schwinger equation in coupled or uncoupled partial-wave amplitudes. This result allows us to deduce a master equation whose solution is the exact discontinuity of the on-shell partial-wave amplitudes along the left-hand cut. This equation is always a linear non-singular integral equation whose solution is fixed exclusively by the knowledge of the potential, applicable to either regular or singular potentials. The capability of calculating exactly this discontinuity allows one to settle the exact N∕D method in two-body non-relativistic scattering for coupled and uncoupled waves. We exemplify this new advance in scattering theory by explicitly checking the agreement between the Lippmann–Schwinger equation with the corresponding solutions of the exact N∕D method for some examples that involve regular and singular potentials, either attractive or repulsive.

• OSTI ID: 22852354
• Journal Information: Annals of Physics, Journal Name: Annals of Physics Vol. 411; ISSN 0003-4916; ISSN APNYA6
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
AMPLITUDES
INTEGRAL EQUATIONS
MATHEMATICAL SOLUTIONS
PARTIAL WAVES
POTENTIALS
SCATTERING
TWO-BODY PROBLEM