PLANAR 3-BODY PROBLEM WITH CALOGERO INTERACTIONS AND A MAGNETIC-FIELD

Energy levels of three particles moving in two dimensions in the prese nce of an external magnetic field are computed by means of the 1/N-exp ansion, where N is roughly the angular momentum. The interparticle int eraction is taken as the Calogero potential, r(2)/6 + beta(2)/r(2). Th e harmonic-oscillator (beta --> 0) and Wigner (beta --> infinity) limi ts are reproduced exactly. Level ordering as a function of beta and th e magnetic field is studied. The results are in excellent qualitative agreement with numerical calculations for three electrons in a parabol ic GaAs quantum dot.