ELECTRON-ELECTRON INTERACTION IN QUANTUM DOTS

A convergent renormalized perturbation series in powers of the electro n-electron coupling constant lambda is proposed for calculating the en ergy of a quantum dot with hard wall confining potential. The renormal ization procedure is based on the standard perturbation series, the sc aling properties of the system and the asymptotic energy expansion val id in the lambda-->infinity region. To obtain that asymptotic expansio n the vibration excitations of the electron ring are considered. As th e asymptotic expansion shows non-analytical behavior a special procedu re for matching the perturbation series with an arbitrary asymptotic f unction is developed. The method is illustrated by calculating the gro und and some excited states of 2, 3 and 4 electrons in the dot. The co mparison of the obtained results with the available exact numerical re sults shows the great accuracy of the proposed method over the whole r ange of lambda values.