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

• URL: http://arxiv.org/abs/2201.00962v2
• Date: Mon, 26 Dec 2022 07:50:56 GMT
• Title: Three-body recombination in a single-component Fermi gas with $p$-wave interaction
• Authors: Shangguo Zhu, Zhenhua Yu, Shizhong Zhang
• Abstract summary: We study the three-body recombination of identical fermionic atoms. We show that the rate constant of three-body recombination into weakly bound $p$-wave dimers can be written as $alpha_rm rec propto v5/2R1/2 k_T4.
• Score: 2.6641834518599308
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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