Planar Three-Body Problem with Calogero Interactions and a Magnetic Field

摘要

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, r~2/6 + β~2/r~2. 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.