D -dimensional three-body bound-state problem with zero-range interactions

Abstract

We solved analytically the three-body mass-imbalanced problem embedded in $D$ dimensions for zero-range resonantly interacting particles. We derived the negative energy eigenstates of the three-body Schr\"odinger equation by imposing the Bethe-Peierls boundary conditions in $D$ dimensions for zero-energy two-body bound states. The solution retrieves the Efimov-like discrete scaling factor dependence with dimension. The analytical form of the mass-imbalanced three-body bound-state wave function can be used to probe the effective dimension of asymmetric cold atomic traps for Feshbach resonances tuned close to the Efimov limit.