Calculation of a Mirror Asymmetric Effect in Electron Scattering from Chiral Targets

Abstract

It is calculated that an unpolarized electron beam elastically scattered from a chiral molecule will acquire a net helicity of $H(s)\ensuremath{\sim}\ensuremath{\eta}{(\ensuremath{\alpha}Z)}^{2}$, where $\ensuremath{\alpha}=\frac{{e}^{2}}{\ensuremath{\hbar}c}$, $Z$ is the atomic number of the heaviest atom in an asymmetric environment in the molecule, and $\ensuremath{\eta}$ is a molecular asymmetry factor. For a carbon center ($Z=6$), $\ensuremath{\eta}$ is estimated to be ${10}^{\ensuremath{-}2}$ so that $H(s)\ensuremath{\sim}{10}^{\ensuremath{-}5}$, which would account for its lack of observation in a recent experiment sensitive to $H(s)>5\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}3}$. The calculation of other asymmetric electron (and positron)-chiral molecule interactions is discussed.