Measuring the surface thickness of the weak charge density of nuclei

The present PREX-II and CREX experiments are measuring the rms radius of the weak charge density of $^{208}\mathrm{Pb}$ and $^{48}\mathrm{Ca}$. We discuss the feasibility of a new parity violating electron scattering experiment to measure the surface thickness of the weak charge density of a heavy nucleus. Once PREX-II and CREX have constrained weak radii, an additional parity violating measurement at a momentum transfer near $0.76\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ for $^{208}\mathrm{Pb}$ or $1.28\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}1}$ for $^{48}\mathrm{Ca}$ can determine the surface thickness.