  Equal mass fermionic trimers with two different spin components near the
unitary limit are shown to possess a universal van der Waals bound or resonance
state near $s$-wave unitarity, when $p$-wave interactions are included between
the particles with equal spin. Our treatment uses a single-channel
Lennard-Jones interaction with long range two-body van der Waals potentials.
While it is well-known that there is no true Efimov effect that would produce
an infinite number of bound states in the unitary limit, we demonstrate that
another type of universality emerges for the symmetry $L^{\Pi}=1^{-}$. The
universality is a remnant of Efimov physics that exists in this system at
$p$-wave unitarity, and it leads to modified threshold and scaling laws in that
limit. Application of our model to the system of three lithium atoms studied
experimentally by Du, Zhang, and Thomas [Phys. Rev. Lett. {\bf 102}, 250402
(2009)] yields a detailed interpretation of their measured three-body
recombination loss rates.

Atomic Physics