(e,3e)process on a quantum dot

Abstract

The exact initial state wave function of an interacting electron pair in a quantum dot under parabolic confinement and neutralization of the dot by the substrate after ejection of electrons is exploited to obtain the fivefold differential cross section $(X)$ of the $(e,3e)$ process on the dot. The reflections of the center-of-mass (c.m.) motion and relative motion on $X$ are decoupled if the incident and scattered electrons are energetic and the ejected electrons are slow. The results are studied in fixed mutual angle (with zero c.m. momentum $K$) and Bethe ridge modes which allow the ``cleanest'' analysis of the contribution of the relative motion. The Coulomb interaction between the emitted electrons is found to qualitatively change the angular distribution of $X$. In the mode in which the magnitude of $K$ is equal to the momentum transfer $q$, the angular distribution of $X$ with respect to ${\ensuremath{\theta}}_{Kq}={\mathrm{cos}}^{\ensuremath{-}1}(\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{K}∙\stackrel{\ifmmode \hat{}\else \^{}\fi{}}{q})$ leads to a mapping of the initial c.m. wave function of the ejected pair. However, the c.m. motion is found to be best studied in the kinematics where the relative momentum $\stackrel{P\vec}{k}$ of the ejected pair is equal to $\stackrel{P\vec}{q}$.