Hyperspherical asymptotics of a system of four charged particles

TL;DR

This paper analyzes the behavior of a four-charged-particle system using hyperspherical coordinates, providing detailed asymptotic expansions of the Hamiltonian in large hyperradius limits for various mass and charge configurations.

Contribution

It introduces a comprehensive hyperspherical asymptotic analysis of four charged particles, expanding the adiabatic Hamiltonian to third order in dimer-dimer and first order in particle-trimer limits.

Findings

Derived asymptotic expansions in powers of R^{-1} for the Hamiltonian

Extended analysis to arbitrary masses and charges

Provided detailed mathematical framework for large hyperradius behavior

Abstract

We present a detailed analysis of the charged four-body system in hyperspherical coordinates in the large hyperradial limit. In powers of $R^{-1}$ for any masses and charges, the adiabatic Hamiltonian is expanded to third order in the dimer-dimer limit and to first order in the particle-trimer limit.