Angular momentum dependence of three fermions near unitarity

This study considers the unitary limit of three equal mass fermions interacting via Lennard-Jones potentials having various total orbital angular momenta and parity, $J^{\Pi}=0^{+}, 1^{+}, 1^{-}$ and $2^{-}$, specifically consisting of three spin-polarized fermions ($\uparrow \uparrow \uparrow $), or of two spin-up and one spin-down fermion ($\downarrow \uparrow \uparrow $). To explore alternative unitarity scenarios, we obtain numerical results for the regime where the p-wave scattering volume approaches infinity. Our study also considers different interactions between the atoms in different spin states, such as the case where the two spin-up fermions have a p-wave interaction and where a spin-up atom interacting with a spin-down atom has a strong s-wave interaction as well. Another case treated involves the different spin state fermions with strong p-wave interaction, while the two identical spin state fermions have a weak p-wave interaction. We also consider three spin-up fermions at the p-wave unitarity limit in different overall symmetries. Universal three-body channel properties are derived for the above cases. This study confirms that the p-wave Efimov effect does not occur for the two-component fermionic system with three equal mass particles, nor for three fermions in a single spin state at the p-wave unitary limit with total angular momentum $J^{\Pi}=1^{-}$.