Many-body scattering theory of electronic systems

TL;DR

This paper reviews analytical methods for understanding the continuum spectrum of correlated Coulomb systems, including three-body and N-body scattering, and introduces a Green function approach for thermodynamic properties of finite systems.

Contribution

It presents new analytical techniques for three- and N-body Coulomb scattering and extends Green function methods to finite interacting systems.

Findings

Derived three-body wave functions for long-range Coulomb interactions

Generalized methods to N-body scattering states

Developed Green function approach for thermodynamics of finite systems

Abstract

This work reviews recent advances in the analytical treatment of the continuum spectrum of correlated few-body non-relativistic Coulomb systems. The exactly solvable two-body problem serves as an introduction to the non-separable three-particle system. For the latter case we discuss the existence of an approximate separability of the long and the short-range dynamics which is exposed in an appropriately chosen curvilinear coordinates. The three-body wave functions of the long-ranged part of the Hamiltonian are derived and methods are presented to account approximately for the short-ranged dynamics. Furthermore, we present a generalization of the methods employed for the derivation of the three-body wave functions to the scattering states of $N$ charged particles. To deal with thermodynamic properties of finite systems we develop and discuss a recent Green function methodology designed for the non-perturbative regime. In addition, we give a brief account on how thermodynamic properties and critical phenomena can be exposed in finite interacting systems.