Electron-electron interaction in quantum dots

A convergent renormalized perturbation series in powers of the electron-electron coupling constant lambda is proposed for calculating the energy of a quantum dot with hard wall confining potential. The renormalization procedure is based on the standard perturbation series, the scaling properties of the system and the asymptotic energy expansion valid in the lambda-->infinity region. To obtain that asymptotic expansion the vibration excitations of the electron ring are considered. As the asymptotic expansion shows non-analytical behavior a special procedure for matching the perturbation series with an arbitrary asymptotic function is developed. The method is illustrated by calculating the ground and some excited states of 2, 3 and 4 electrons in the dot. The comparison of the obtained results with the available exact numerical results shows the great accuracy of the proposed method over the whole range of lambda values.