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

TL;DR

This paper analytically solves the D-dimensional three-body bound-state problem with zero-range interactions, revealing Efimov-like scaling and providing wave functions useful for probing effective dimensions in cold atomic systems.

Contribution

It derives analytical solutions for the mass-imbalanced three-body problem in arbitrary dimensions, extending Efimov physics to new dimensional regimes.

Findings

Reveals Efimov-like scaling dependence on dimension

Provides explicit wave functions for three-body bound states

Enables probing of effective dimensions in cold atomic traps

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 Schrodinger 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.