N electrons in a quantum dot: Two-point Pade approximants

We present analytic estimates for the energy levels of N electrons (N = 2-5) in a two-dimensional parabolic quantum dot. A magnetic field is applied perpendicularly to the confinement plane. The relevant scaled energy is shown to be a smooth function of the parameter beta = (effective rydberg/effective dot energy)(1/6). Two-point Pade approximants are obtained from the series expansions of the energy near the oscillator (beta --> 0) and Wigner (beta --> infinity) limits. The approximants are expected to work with an error not greater than 2.5% over the entire interval 0 less than or equal to beta < infinity.