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

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