Hyperspherical approach to the four-body problem

TL;DR

This paper develops a hyperspherical method to solve the quantum four-body problem, providing potential curves for ultracold fermionic gases, which could enhance understanding of molecular lifetimes and the BCS-BEC crossover.

Contribution

It introduces a hyperspherical approach to the four-body problem, enabling calculation of potential curves for ultracold fermionic systems.

Findings

Potential curves for four-body systems are obtained.

Rates for elastic and inelastic processes are calculated.

Insights into molecular lifetimes in ultracold gases are provided.

Abstract

The four-particle system is the simplest few-body system containing the fundamental physics involved in ultracold fermionic gases. We have made recent efforts to solve the quantum four-body problem in the adiabatic hyperspherical representation. Our approach yields a set of coupled potential curves that can in turn be solved for all elastic and inelastic processes. These rates may play an important role in the lifetime of molecules in ultracold fermi gases. We believe this will lead to a deeper understanding of ultracold fermi systems and the physics of the BCS-BEC crossover.