Quasi-three body systems - properties and scattering

TL;DR

This paper analytically studies quasi-three body systems with hierarchical masses, deriving properties like scattering cross-sections and decay rates as expansions in the small mass ratio, simplifying complex three-body interactions.

Contribution

It introduces an analytical approach to quasi-three body systems with hierarchical masses, reducing the problem to two-body interactions and deriving key properties as power series expansions.

Findings

Derived scattering cross-sections as mass ratio expansions

Calculated hyperfine splitting and Lamb shifts analytically

Analyzed Auger decay of excited states in hierarchical systems

Abstract

We investigate systems of three mutually interacting particles with masses of which the inner is much bigger than the intermediate and the latter is much bigger than the outer. Then the three-body problem reduces to the two-body scattering or structure of the light one in the field of the pseudo-nucleus formed by two others. We calculate analytically the properties of considered systems, such as the scattering cross-sections, hyperfine splitting, Auger decay of exited states and Lamb shits, presenting them as expansions in powers of the ratio of light to intermediate particle masses. This ratio is the small parameter of the studied problems.