We study theoretically how we can determine the neutron density distributio
ns of unstable nuclei from proton elastic scattering. We apply the relativi
stic impulse model to study the sensitivities of the observables to the den
sity distributions which are expressed in Woods-Saxon form. We find that bo
th the radius and diffuseness of densities can be determined from restricte
d elastic scattering data in principle. We think this result is helpful to
design future experiments.