Efimov Physics and Beyond

TL;DR

This paper investigates Efimov physics in three-boson systems with large scattering lengths, emphasizing the effects of finite effective range on binding energies and angular dependence, extending understanding beyond idealized zero-range models.

Contribution

It introduces a method to calculate three-boson binding energies considering finite effective range, showing how energies converge with cut-off and differ from traditional Efimov predictions.

Findings

Binding energies depend on effective range r and converge at L~10/r

Energies for r>0 differ significantly from Efimov's universal ratios

Angular dependence remains consistent for deeper states regardless of effective range

Abstract

Efimov physics relates to 3-body systems with large 2-body scattering lengths a and small effective ranges r. For many systems in nature the assumption of a small effective range is not valid. The present report shows binding energies E of three identical bosons calculated with 2-body potentials that are fitted to scattering data and momentum cut-offs (L) by inverse scattering. Results agree with previous works in the case of r<<a. While energies diverge with momentum cut-off L for r=0, they converge for r>0 when L=~10/r. With 1/a=0 the converged energies are given by E(n) =C(n)/r*r with n labeling the energy-branch and calculated values C(0)=0.77, C(1)=.0028. This gives a ratio ~278 thus differing from the value ~515 in the Efimov case. Efimov's angular dependent function is calculated. Good agreement with previous works is obtained when r<< a. With the increased values of effective range the shallow states still appear Efimov-like. For deeper states the angular dependence differs but is independent of the effective range.