Reliability of the Born-Oppenheimer approximation in noninteger dimensions

TL;DR

This paper investigates the accuracy of the Born-Oppenheimer approximation in a three-body quantum system with mass imbalance in noninteger dimensions, comparing it with exact methods for a specific experimental system.

Contribution

It provides a novel analysis of the Born-Oppenheimer approximation's reliability in noninteger dimensions for a resonant three-body system, specifically for $^7$Li-$^{87}$Rb$_2$.

Findings

BO approximation closely matches Bethe-Peierls results in certain regimes

Differences observed in Efimov scale parameter and wave functions

Insights into the validity of BO in noninteger dimensions for experimental systems

Abstract

We address the question of the reliability of the Born-Oppenheimer (BO) approximation for a mass-imbalanced resonant three-body system embedded in noninteger dimensions. We address this question within the problem of a system of currently experimental interest, namely $^7$Li$-^{87}$Rb$_2$. We compare the Efimov scale parameter as well as the wave functions obtained using the BO approximation with those obtained using the Bethe-Peierls boundary condition.