Measuring the Neutron Distribution from Coherent Elastic Neutrino Nucleus Scattering

Last year the COHERENT collaboration was able to measure for the first time the Coherent Elastic Neutrino Nucleus Scattering (CE\(\nu\)NS). Neutrinos within the right energy range can be produced in large quantities at accelerator facilities via pion Decay At Rest (\(\pi\)DAR) and used to measure CE\(\nu\)NS. This new channel opens several, interesting possibilities: studying the CE\(\nu\)NS spectrum it will be possible, for example, to search for Physics Beyond the Standard Model, looking for deviations from the predictions of the electroweak theory; it can also give important inputs for the understanding of core collapse supernovas, where neutrino-nucleus interactions and, more generally, collective neutrino behavior play a crucial role. Using CE\(\nu\)NS it is also possible to measure precisely the electroweak form factor for a large number of different nuclei, extracting information on the neutron distribution inside the nucleus as well. In this presentation I will focus on the last aspect: I will calculated the precision that can be achieved in such kind of experiment, investigating in particular the effects of the low-energy threshold and the systematic errors on the quenching factor. The expected precision will be calculated using the Helm model and also with a model-independent approach.