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

Nuclear Theory;Nuclear Experiment