Planar three-body problem with Calogero interactions and a magnetic field

Energy levels of three particles moving in two dimensions in the presence of an external magnetic field are computed by means of the 1/N-expansion, where N is roughly the angular momentum. The interparticle interaction is taken as the Calogero potential, r2/6+ β2/r2. The harmonic oscillator (β → 0) and Wigner (β → ∞) limits are reproduced exactly. Level ordering as a function of β and the magnetic field is studied. The results are in excellent qualitative agreement with numerical calculations for three electrons in a parabolic GaAs quantum dot. (author)