Weak Nuclear Form Factor

The weak nuclear form factor is the final missing piece to complete our understanding of the nuclear structure and the Coherent Elastic Neutrino Nucleus Scattering (CEvNS) cross section. The weak form factor is dominated by the neutron distributions of the atomic nucleus, which are poorly known. The complex scalar and vector potentials within the nucleus are provided using a Relativistic Mean Field (RMF) approach. These potentials are used to calculate the point neutron and proton distributions, and in conjunction with single-nucleon electric Sachs form factors---obtained from data---are used to predict the weak form factor. It is determined that the radius of the proton distributions agree within 1% to the experimental values. The agreement of the proton distributions gives confidence that the predicted neutron distributions are computed correctly. It is also determined that to constrain the weak form factor, next-generation measurements need to be at 1% error. The correction due to the weak form factor for CEvNS is determined to be approximately between 10-40% for neutron number, N, ranging from 20 to 126. The findings show that the precise measurement of the weak form factor is necessary for the accurate determination of the CEvNS cross section and our comprehension of the nuclear structure as a whole. Most importantly, the predicted quantities and estimated errors give guidance to experiments measuring the weak form factor.