Average CsI neutron density distribution from COHERENT data

Using the coherent elastic neutrino-nucleus scattering data of the COHERENT experiment, we determine for the first time the average neutron rms radius of $^{133}\text{Cs}$ and $^{127}\text{I}$. We obtain the practically model-independent value $R_{n} = 5.5 {}^{+0.9}_{-1.1} \, \text{fm}$ using the symmetrized Fermi and Helm form factors. We also point out that the COHERENT data show a $2.3\sigma$ evidence of the nuclear structure suppression of the full coherence.