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 ${}^7$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.