Parity violation measurement of neutron density

Parity-violating electron scattering can measure neutron densities in a model independent fashion because the weak charge of a neutron is much larger than that of a proton. At Jefferson laboratory, the neutron radius of $^{208}$Pb has already been measured by PREX, and a future project CREX aims to measure the neutron radius of $^{48}$Ca. In this work, we propose to measure not only the neutron radius, but the full radial structure of the neutron density distribution in $^{48}$Ca, by measuring the parity violating asymmetry at a number of different momentum transforms and using a Fourier Bessel expansion to fit the neutron density directly. Finally, we estimate the statistical error in the Fourier Bessel coefficients that can be determined for a realistic experimental beam time.