(e,3e) process on a quantum dot

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 θ_Kq=cos⁻¹(K̂∙q̂) 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 k⃗ of the ejected pair is equal to q⃗.