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

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

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