Rotational predissociation of extremely weakly bound atom-molecule complexes produced by Feshbach resonance association

TL;DR

This paper investigates the rotational predissociation of ultracold atom-molecule complexes with extremely weak binding energies, deriving accurate lifetime expressions based on scattering parameters, especially near the threshold energy.

Contribution

It introduces new analytical formulas for predissociation lifetimes that remain accurate at very small binding energies, improving upon numerical methods.

Findings

Predissociation lifetimes are maximized when the binding energy is positive.

The derived formulas accurately predict lifetimes near the threshold energy.

Predissociation is longest when the state is just above the excited state threshold.

Abstract

We study the rotational predissociation of atom - molecule complexes with very small binding energy. Such complexes can be produced by Feshbach resonance association of ultracold molecules with ultracold atoms. Numerical calculations of the predissociation lifetimes based on the computation of the energy dependence of the scattering matrix elements become inaccurate when the binding energy is smaller than the energy width of the predissociating state. We derive expressions that represent accurately the predissociation lifetimes in terms of the real and imaginary parts of the scattering length and effective range for molecules in an excited rotational state. Our results show that the predissociation lifetimes are the longest when the binding energy is positive, i.e. when the predissociating state is just above the excited state threshold.