Representations for the Three-Body T-Matrix, Scattering Matrices and Resolvent in Unphysical Energy Sheets

TL;DR

This paper develops explicit formulas for the three-body T-matrix, scattering matrices, and resolvent in unphysical energy sheets, enabling better analysis of three-body resonances through analytic continuation.

Contribution

It introduces explicit representations for the three-body T-matrix and related operators in unphysical sheets, facilitating resonance analysis in three-body quantum systems.

Findings

Explicit formulas for T-matrix in unphysical sheets

Representation of scattering matrices and resolvent

Method for identifying three-body resonances

Abstract

Explicit representations for the Faddeev components of the three-body T-matrix continued analytically into unphysical sheets of the energy Riemann surface are formulated. According to the representations, the T-matrix in unphysical sheets is explicitly expressed in terms of its components taken in the physical sheet only. The representations for the T-matrix are then used to construct similar representations for the analytic continuation of the three-body scattering matrices and the resolvent. Domains on unphysical sheets are described where the representations obtained can be applied. A method for finding three-body resonances based on the Faddeev differential equations is proposed.