Hyperspherical approach to the three-bosons problem in 2D with a magnetic field

We examine a system of three-bosons confined to two dimensions in the presence of a perpendicular magnetic field within the framework of the adiabatic hyperspherical method. For the case of zero-range, regularized pseudo-potential interactions, we find that the system is nearly separable in hyperspherical coordinates and that, away from a set of narrow avoided crossings, the full energy eigenspectrum as a function of the 2D s-wave scattering length is well described by ignoring coupling between adiabatic hyperradial potentials. In the case of weak attractive or repulsive interactions, we find the lowest three-body energy states exhibit even/odd parity oscillations as a function of total internal 2D angular momentum and that for weak repulsive interactions, the universal lowest energy interacting state has an internal angular momentum of $M=3$. With the inclusion of repulsive higher angular momentum we surmise that the origin of a set of ``magic number'' states (states with anomalously low energy) might emerge as the result of a combination of even/odd parity oscillations and the pattern of degeneracy in the non-interacting lowest Landau level states.