Distribution of oscillator strength in Gaussian quantum dots: An energy flow from center-of-mass mode to internal modes

Abstract

The energy spectra and oscillator strengths of two, three, and four electrons confined by a quasi-two-dimensional attractive Gaussian-type potential have been calculated for different strength of confinement $\ensuremath{\omega}$ and potential depth $D$ by using the quantum chemical configuration interaction (CI) method employing a Cartesian anisotropic Gaussian basis set. A substantial redshift has been observed for the transitions corresponding to the excitation into the center-of-mass mode. The oscillator strengths, concentrated exclusively in the center-of-mass excitation in the harmonic limit, are distributed among the near-lying transitions as a result of the breakdown of the generalized Kohn theorem. The distribution of the oscillator strengths is limited to the transitions located in the lower-energy region when $\ensuremath{\omega}$ is large but it extends towards the higher-energy region when $\ensuremath{\omega}$ becomes small. The analysis of the CI wave functions shows that all states in the energy range covered by the present study can be classified according to the polyad quantum nnumber ${v}_{p}$. It is shown that the distribution of the oscillator strengths for large $\ensuremath{\omega}$ occurs among transitions involving excited states with the same value of ${v}_{p}$ as the center-of-mass excited state, ${v}_{p,\mathit{cm}}$, while it occurs among transitions involving the excited states with ${v}_{p}={v}_{p,\mathit{cm}}$ and ${v}_{p}={v}_{p,\mathit{cm}}+2$ for small $\ensuremath{\omega}$.