Finite Range Effects in Energies and Recombination Rates of Three Identical Bosons

TL;DR

This paper examines how finite-range effects influence energies and recombination rates in three-boson systems near Feshbach resonances, revealing deviations from zero-range Efimov physics predictions.

Contribution

It introduces and compares two finite-range models for three-boson systems, highlighting their impact on Efimov scaling and bound state thresholds.

Findings

Finite-range models predict variations in Efimov scaling factor 22.7.

Threshold for bound trimer formation shifts with effective range.

Large effective ranges significantly alter three-boson energy spectra.

Abstract

We investigate finite-range effects in systems with three identical bosons. We calculate recombination rates and bound state spectra using two different finite-range models that have been used recently to describe the physics of cold atomic gases near Feshbach resonances where the scattering length is large. The models are built on contact potentials which take into account finite range effects; one is a two-channel model and the other is an effective range expansion model implemented through the boundary condition on the three-body wave function when two of the particles are at the same point in space. We compare the results with the results of the ubiquitous single-parameter zero-range model where only the scattering length is taken into account. Both finite range models predict variations of the well-known geometric scaling factor 22.7 that arises in Efimov physics. The threshold value at negative scattering length for creation of a bound trimer moves to higher or lower values depending on the sign of the effective range compared to the location of the threshold for the single-parameter zero-range model. Large effective ranges, corresponding to narrow resonances, are needed for the reduction to have any noticeable effect.