  Elastic electron scattering has been used to paint the most accurate picture
of the proton distribution in atomic nuclei. Spurred by new experimental
developments, it is now possible to gain valuable insights into the neutron
distribution using exclusively electroweak probes. Our goal is to assess the
information content and complementarity of the following three electroweak
experiments in constraining the neutron distribution of atomic nuclei: (a)
parity violating elastic electron scattering, (b) coherent elastic neutrino
nucleus scattering, and (c) elastic electron scattering of unstable nuclei.
Relativistic mean-field models informed by the properties of finite nuclei and
neutron stars are used to compute ground state densities and form factors of a
variety of nuclei. All the models follow the same fitting protocol, except for
the assumed and presently unknown value of the neutron skin thickness of 208Pb.
This enables one to tune the density dependence of the symmetry energy without
compromising the success in reproducing well known physical observables. We
found that the ongoing PREX-II and upcoming CREX campaigns at Jefferson Lab
will play a vital role in constraining the weak form factor of xenon and argon,
liquid noble gases that are used for the detection of both neutrinos and dark
matter particles. We concluded that remarkable new advances in experimental
physics have opened a new window into ground state densities of atomic nuclei
using solely electroweak probes. The diversity and versatility of these
experiments reveal powerful correlations that impose important nuclear
structure constraints. In turn, these constraints provide quantitative
theoretical uncertainties that are instrumental in searches for new physics and
insights into the behavior of dense matter.
