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Background: The ground state neutron density of a medium mass nucleuscontains fundamental nuclear structure information and is at present relativelypoorly known.  Purpose: We explore if parity violating elastic electron scattering canprovide a feasible and model independent way to determine not just the neutronradius but the full radial shape of the neutron density $\rho_n(r)$ and theweak charge density $\rho_W(r)$ of a nucleus.  Methods: We expand the weak charge density of $^{48}$Ca in a modelindependent Fourier Bessel series and calculate the statistical errors in theindividual coefficients that might be obtainable in a model parity violatingelectron scattering experiment.  Results: We find that it is feasible to determine roughly six Fourier Besselcoefficients of the weak charge density of 48Ca within a reasonable amount ofbeam time. However, it would likely be much harder to determine the full weakdensity of a significantly heavier nucleus such as 208Pb.  Conclusions: Parity violating elastic electron scattering can determine thefull weak charge density of a medium mass nucleus in a model independent way.This weak density contains fundamental information on the size, surfacethickness, shell oscillations, and saturation density of the neutrondistribution in a nucleus. The measured $\rho_W(r)$, combined with thepreviously known charge density $\rho_{ch}(r)$, will literally provide adetailed textbook picture of where the neutrons and protons are located in anatomic nucleus.

The full weak charge density distribution of 48Ca from parity violating electron scattering