Efimov physics implications at $p$-wave fermionic unitarity

TL;DR

This paper investigates how Efimov physics at p-wave unitarity influences long-range interactions among three fermions, revealing modifications without true Efimov states and extending previous results to new unitarity regimes.

Contribution

It extends the analysis of long-range interactions at p-wave unitarity for three fermions to small and intermediate hyperradii, including new unitarity scenarios and emphasizing the role of hyperradial corrections.

Findings

Agreement with previous work at s-wave unitarity

Extension to small and intermediate hyperradii

Identification of hyperradial adiabatic correction role

Abstract

Efimov physics at $p$-wave unitarity for three equal mass fermions in multiple symmetries interacting via Lennard-Jones potentials is predicted to modify the long range interaction potential energy, but without producing a true Efimov effect. This analysis treats the following total orbital angular momenta and parities, $J^{\Pi}=0^{+}, 1^{+}, 1^{-}$ and $2^{-}$, for either three spin-polarized fermions ($\uparrow \uparrow \uparrow $), or two spin-up and one spin-down fermion ($\downarrow \uparrow \uparrow $). Our results for the long range interaction in some of those cases agree with previous work by Werner and Castin and by Blume {\it et al.}, namely in cases where the $s$-wave scattering length goes to infinity. The present results extend those calculated interaction energies to small and intermediate hyperradii comparable to the van der Waals length, and we consider additional unitarity scenarios where the $p$-wave scattering volume approaches infinity. The crucial role of the diagonal hyperradial adiabatic correction term is identified and characterized.