Recombination rates from potential models close to the unitary limit

TL;DR

This paper explores the universal behavior of three-boson recombination rates near the unitary limit, using potential models and the hyperspherical adiabatic expansion to compare with universal formulas and analyze different systems.

Contribution

It demonstrates the applicability of universal recombination rate formulas to various systems, including the He-He and neutron-neutron-proton systems, with finite-range corrections improving the agreement.

Findings

Universal recombination rate formula fits well after finite-range corrections.

Good agreement between numerical results and universal theory for different potentials.

Universal behavior confirmed across different physical systems with large scattering lengths.

Abstract

We investigate universal behavior in the recombination rate of three bosons close to threshold. Using the He-He system as a reference, we solve the three-body Schr\"odinger equation above the dimer threshold for different potentials having large values of the two-body scattering length $a$. To this aim we use the hyperspherical adiabatic expansion and we extract the $S$-matrix through the integral relations recently derived. The results are compared to the universal form, $\alpha\approx 67.1\sin^2[s_0\ln(\kappa_*a)+\gamma]$, for different values of $a$ and selected values of the three-body parameter $\kappa_*$. A good agreement with the universal formula is obtained after introducing a particular type of finite-range corrections, which have been recently proposed by two of the authors in Ref.[1]. Furthermore, we analyze the validity of the above formula in the description of a very different system: neutron-neutron-proton recombination. Our analysis confirms the universal character of the process in systems of very different scales having a large two-body scattering length.