Reliability of the Born-Oppenheimer Approximation in Noninteger Dimensions

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 \(^7\) $_{}^7$ Li \(-^{87}\) ${-}^{87}$ Rb \(_2\) $_2^{}$ . 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.