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

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 ${\ensuremath{\alpha}}_{\mathrm{rec}}\ensuremath{\propto}{v}^{5/2}{R}^{1/2}{k}_{T}^{4}(1+C{k}_{T}^{2}{l}_{d}^{2})$ 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 ${l}_{d}$ 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 $\ensuremath{\gamma}\ensuremath{\equiv}R/{v}^{1/3}$ is small. The additional $C{k}_{T}^{2}{l}_{d}^{2}$ term provides important corrections for the temperature and interaction dependence of ${\ensuremath{\alpha}}_{\mathrm{rec}}$, especially close to resonance when ${k}_{T}{l}_{d}$ is relatively large.