Quasi-Coulomb series in a two-dimensional three-body system

We show that the bound states in a three-body system display a Coulomb series with a Gaussian cut-off provided: (i) the system consists of a light particle and two heavy bosonic ones, (ii) the heavy-light short-range potential has a resonance in the $p$-wave scattering amplitude, and (iii) all three particles move in two space dimensions. For a decreasing mass ratio this quasi-Coulomb series merges into a pure Coulombic one.