Three body dwell time

TL;DR

This paper extends the concept of dwell time from two-body to three-body systems, deriving relations that connect the lifetime of three-body resonances with substructure dwell times using the Kapur Peierls formalism.

Contribution

It introduces a novel extension of dwell time concepts to three-body systems and relates resonance lifetime to dwell times within this framework.

Findings

Derived relation between three-body and two-body dwell times.

Revisited and extended Kapur Peierls formalism for three-body systems.

Established that three-body resonance lifetime equals the three-body dwell time.

Abstract

The lifetime of an unstable state or resonance formed as an intermediate state in two body scattering is known to be related to the dwell time or the time spent within a given region of space by the two interacting particles. This concept is extended to the case of three body systems and a relation connecting the three body dwell time with the two body dwell times of the substructures of the three body system is derived for the case of separable wave functions. The Kapur Peierls formalism is revisited to discover one of the first definitions of dwell time in literature. An extension of the Kapur Peierls formalism to the three body case shows that the lifetime of a three body resonance can indeed be given by the three body dwell time.