New Calculations of Recombination Rates for Cold $^4$He Atoms and Determination of Universal Scaling Functions

TL;DR

This paper introduces a new method for calculating three-body recombination rates in cold helium-4 atoms, leveraging the relationship between phase shifts and the S-matrix, and determines universal scaling functions relevant to Efimov physics.

Contribution

A novel computational approach for recombination rates using phase shift and S-matrix relationships, enabling the first determination of universal scaling functions for helium-4.

Findings

Recombination rates computed with the new method match previous results for HFD-B3-FCII.

Universal functions for Efimov physics are determined for the first time.

Recombination coefficients vary with different atom-atom potentials.

Abstract

Three-body recombination rates for cold $^4$He are calculated with a new method which exploits the simple relationship between the imaginary part of the atom-dimer elastic scattering phase shift and the $S$-matrix for recombination. The elastic phase shifts are computed above breakup threshold by solving a three-body Faddeev equation in momentum space with inputs based on a variety of modern atom-atom potentials. Recombination coefficients for the HFD-B3-FCII potential agree very well with the only previously published results. Since the elastic scattering and recombination processes for $^4$He are governed by "Efimov physics", they depend on universal functions of a scaling variable. The newly computed recombination coefficients for potentials other than HFD-B3-FCII make it possible to determine these universal functions for the first time.