Three-body recombination in a single-component Fermi gas with $p$-wave interaction

TL;DR

This paper analyzes three-body recombination in a single-component Fermi gas with p-wave interactions, deriving a new rate constant formula that includes temperature and interaction effects, improving understanding of fermionic atom collisions.

Contribution

The study introduces a novel expression for the three-body recombination rate in p-wave interacting fermions, incorporating temperature and effective range corrections, and validates it with a perturbative three-body calculation.

Findings

Derived a new rate constant formula with temperature and interaction dependence.

Identified the leading scaling law differs from previous v^{8/3} law.

Provided correction terms significant near resonance.

Abstract

We study the three-body recombination of identical fermionic atoms. Using a zero-range model for the $p$-wave interaction, we show that the rate constant of three-body recombination into weakly bound $p$-wave dimers can be written as $\alpha_{\rm rec} \propto v^{5/2}R^{1/2} k_T^4 (1+ C k_T^2 l_{\rm d}^2)$ for large and positive scattering volume $v$. Here $R$ is the $p$-wave effective range, $k_T^2$ gives the average thermal kinetic energy of the colliding atoms, and $l_{\rm d}$ is the size of the $p$-wave dimer. The leading term is different from the usually stated $v^{8/3}$-scaling law, but is consistent with an earlier two-channel calculation. For the subleading term, we compute the constant $C$ by solving the relevant three-body problem perturbatively when the parameter $\gamma\equiv R/v^{1/3}$ is small. The additional $C k_T^2 l_{\rm d}^2$ term provides important corrections for the temperature and interaction dependence of $\alpha_{\rm rec}$, especially close to resonance when $k_T l_{\rm d}$ is relatively large.