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

14 pages, 1 figure

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Cited by in corpus (3)

• Transport in p-wave interacting Fermi gases
• Radio-Frequency Spectroscopy and the Dimensional Crossover in Interacting Spin-Polarized Fermi Gases
• Elastic collision rates of spin-polarized fermions in two dimensions