Nonuniversal bound states of two identical heavy fermions and one light particle

Abstract

We study the behavior of the bound-state energy of a system consisting of two identical heavy fermions of mass $M$ and a light particle of mass $m$. The heavy fermions interact with the light particle through a short-range two-body potential with positive $s$-wave scattering length ${a}_{s}$. We impose a short-range boundary condition on the logarithmic derivative of the hyperradial wave function and show that, in the regime where Efimov states are absent, a nonuniversal three-body state cuts through the universal three-body states previously described by Kartavtsev and Malykh [O. I. Kartavtsev and A. V. Malykh, J. Phys. B 40, 1429 (2007)]. The presence of the nonuniversal state alters the behavior of the universal states in certain regions of the parameter space. We show that the existence of the nonuniversal state is predicted accurately by a simple quantum defect theory model that utilizes hyperspherical coordinates. An empirical two-state model is employed to quantify the coupling of the nonuniversal state to the universal states.