Properties of Pseudopotentials for Higher Partial Waves

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.

Figure 1

Mass-scaled coordinates as introduced in Ref. 9 are shown here. Other sets of these coordinates are found by cyclic permutations.