Universal nature and finite-range corrections in elastic atom-dimer scattering below the dimer breakup threshold

TL;DR

This paper demonstrates that universal behavior in elastic atom-dimer scattering below the breakup threshold can be described with finite-range corrections, and this universality extends to nucleon-deuteron scattering, linking it to the three-body parameter.

Contribution

The study introduces finite-range corrections to the universal zero-range formula for atom-dimer scattering and shows its applicability to nucleon-deuteron scattering, confirming universality across different systems.

Findings

Good agreement with universal formula after finite-range corrections

Universal behavior observed in nucleon-deuteron scattering

Relation established between pole energy and three-body parameter

Abstract

We investigate universal behavior in elastic atom-dimer scattering below the dimer breakup threshold calculating the atom-dimer effective-range function $ak\cot\delta$. Using the He-He system as a reference, we solve the Schr\"odinger equation for a family of potentials having different values of the two-body scattering length $a$ and we compare our results to the universal zero-range form deduced by Efimov, $ak\cot\delta=c_1(ka)+c_2(ka)\cot[s_0\ln(\kappa_*a)+\phi(ka)]$, for selected values of the three-body parameter $\kappa_*$. Using the parametrization of the universal functions $c_1,c_2,\phi$ given in the literature, a good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections. Furthermore, we show that the same parametrization describes a very different system: nucleon-deuteron scattering below the deuteron breakup threshold. Our analysis confirms the universal character of the process, and relates the pole energy in the effective-range function of nucleon-deuteron scattering to the three-body parameter $\kappa_*$.