Efimov Effect for P-wave Interactions

Lucas Platter

C. Luciuk, Scott Smale, Stefan Trotzky +3 more

Yusuke Nishida

Whether the Efimov effect is possible, in principle, for $p$-wave or higher partial-wave interactions is a fundamental question. Recently, there has been a claim that three nonrelativistic particles with resonant $p$-wave interactions exhibit the Efimov effect. We point out that the assumed $p$-wave scattering amplitude inevitably causes a negative probability. This indicates that the Efimov states found there cannot be realized in physical situations. We also restate our previous argument that the Efimov effect, defined as an infinite tower of universal bound states characterized by discrete scale invariance, is impossible for $p$-wave or higher partial-wave interactions.

J. H. Macek, James Sternberg

Contact psuedopotentials for relative angular momentum greater than zero are of interest for the study of cold atomic gases. For bosons, it is known that when the s-wave scattering length becomes infinite, an infinite number of three-body bound states, called Efimov states, are predicted by such potentials. Realistic potentials also exhibit the such states, thus a study of the Efimov effect for contact psuedopotentials for higher partial waves and fermions is important for the study of cold atoms. In this Letter we analyze three-body states of three particles interacting via psuedopotentials for higher partial waves and show that there is an Efimov effect for three fermions interacting via p-wave psuedopotentials.

Yvan Castin, Christophe Mora, Ludovic Pricoupenko

We study three same-spin-state fermions of mass M interacting with a distinguishable particle of mass m in the unitary limit where the interaction has a zero range and an infinite s-wave scattering length. We predict an interval of mass ratio 13.384<M/m<13.607 where there exists a purely four-body Efimov effect, leading to the occurrence of weakly bound tetramers without Efimov trimers.

Yusuke Nishida