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

Abstract

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 β=(effective Rydberg/effective dot energy)^{1/6}. Two-point Pade approximants are obtained from the series expansions of the energy near the oscillator ($\beta \to 0$) and Wigner ($\beta \to \infty$) limits. The approximants are expected to work with an error not greater than 2.5% in the entire interval $0\le \beta <\infty$.

27 pages. LaTeX. 6 figures not included

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