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Proton elastic scattering off Sn isotopes at $E_p=295$ MeV in the mass numberrange of $A=$116--124 was investigated using calculation employing relativisticimpulse approximation (RIA) with theoretical densities obtained for the Snisotopes from relativistic Hartree-Bogoliubov (RHB) and nonrelativistic SkyrmeHartree-Fock-Bogoliubov (SHFB) calculations of spherical nuclei. In the RIAcalculations, a modified version of the Murdock and Horowitz model thatincludes a density dependence in the effective nucleon-nucleon ($NN$)interaction was used. A calculation using the theoretical density obtained froma relativistic calculation employing the DD-ME2 interaction successfullyreproduced the experimental data for $^{122}$Sn$(p,p)$, but it overestimatedthe $^{116}$Sn$(p,p)$ and $^{118}$Sn$(p,p)$ cross sections at backward angles.Isotopic analyses of the $(p,p)$ reactions combined with nuclear structureproperties were performed based on reaction calculations that used a modeldensity modified from the DD-ME2 density to optimize the neutron density of theSn isotopes by fitting the isotopic cross section ratios. The resultingoptimized density reproduced the experimental $(p,p)$ data for the series of Snisotopes from $^{116}$Sn to $^{124}$Sn. The neutron root-mean-square(rms) radiiand the skin thickness of the Sn isotopes obtained in the present analysisexhibited smooth $A$ dependences in the range of $A=$116--124, which areconsistent with the theoretical predictions obtained using the DD-ME2interaction but seem to contradict the experimental results determined from the$(p,p)$ data. In a detailed analysis of the surface neutron density probed byproton elastic scattering, a signal of the shell effect at $N=66$ in Snisotopes was found.

Shell effect in $A=$116--124 Tin isotopes investigated using isotopic analysis of proton scattering at 295 MeV