Charge and transition densities for the samarium isotopes by electron scattering

We analyzed 251.5 and 401.4 MeV electron scattering data on ${}_{}{}^{144,148,150,152}{}_{}{}^{}\mathrm{Sm}$. The momentum transfer ranged from 0.6 to 2.5 ${\mathrm{fm}}^{-1\mathrm{}}$. These isotopes span the transition region from the spherical ${}_{}{}^{144}{}_{}{}^{}\mathrm{Sm}$ to the deformed ${}_{}{}^{152}{}_{}{}^{}\mathrm{Sm}$. Ground state charge distributions and lowest $2^{+}$ state transition charge densities were determined via a phase shift analysis for elastic scattering and distorted-wave Born approximation calculations for inelastic scattering. Our analysis used charge densities described as a sum of spherical Bessel functions over a radius interval from zero to a cutoff of $R$, with densities zero at larger radii. The fitting for the ground and $2^{+}$ states included constraints in the form of measured Barrett moments from muonic experiments and measured $B\left(E2\mathrm{}\right)\mathrm{}$ transition rates from muonic and other experiments. Error bands were determined for the densities including statistical and normalization uncertainties, and model dependent uncertainties associated with contributions from higher terms in the spherical Bessel function form. We find that as neutrons are added from isotope to isotope, the charge is displaced from the region of 4.0 fm to the region of 7.5 fm. The rms radii of ${}_{}{}^{144,148,150,152}{}_{}{}^{}\mathrm{Sm}$ were deduced with uncertainties of about 0.006 to 0.009 fm.