Radii for most stable
nuclei have been deduced from electron scattering form
factors and/or from the x-ray transition energies of muonic atoms.
The relative radii for a
series of isotopes can be extracted from the isotope shifts of atomic x-ray transitions.
The rms radius for the nuclear point-proton density, \( R_p \) is obtained from the rms charge radius by:
$$
R_p = \sqrt{R^2_{\mathrm{ch}}- R^2_{\mathrm{corr}}},
$$
where
$$
R^2_{\mathrm{corr}}= R^2_{\mathrm{op}}+(N/Z)R^2_{\mathrm{on}}+R^2_{\mathrm{rel}},
$$
where
$$
R_{\mathrm{op}}= 0.875(7) \mathrm{fm}.
$$
is the rms radius of the proton, \( R^2_{\mathrm{on}} = 0.116(2) \) $\mbox{fm}^{2}$ is the
mean-square radius of the neutron and \( R^2_{\mathrm{rel}} = 0.033 \) $\mbox{fm}^{2}$ is the relativistic Darwin-Foldy correction. There are additional smaller nucleus-dependent corrections.