Three-Body Bound States in Atomic Mixtures With Resonant $p$-Wave Interaction

We employ the Born-Oppenheimer approximation to find the effective potential in a three-body system consisting of a light particle and two heavy ones when the heavy-light short-range interaction potential has a resonance corresponding to a nonzero orbital angular momentum. In the case of an exact resonance in the $p$-wave scattering amplitude, the effective potential is attractive and long range; namely, it decreases as the third power of the interatomic distance. Moreover, we show that the range and power of the potential, as well as the number of bound states, are determined by the mass ratio of the particles and the parameters of the heavy-light short-range potential.