  The isotopic systematics of Sn isotopes in the range A=116--124 were
investigated by combining the nuclear structure and reaction calculations for
the analysis of Sn(p,p) reactions at 295 MeV. The Sn(p,p) reactions were
calculated employing relativistic impulse approximation (RIA) with theoretical
densities obtained for the Sn isotopes from relativistic Hartree-Bogoliubov
(RHB) calculations with the DD-ME2 interaction and nonrelativistic Skyrme
Hartree-Fock-Bogoliubov (SHFB) calculations with the SKM* interaction.
Calculation using the DD-ME2 density reproduced the experimental data for
$^{122}$Sn(p,p) but overestimated the $^{116}$Sn(p,p) and $^{118}$Sn(p,p) cross
sections at backward angles. In the isotopic analysis of the cross section
ratio $R(\sigma)$ of $^{122}$Sn to $^{116}$Sn, a calculation using the SKM*
density reproduced the peak amplitudes of $R(\sigma)$ obtained from the
experimental cross sections, whereas a calculation using the DD-ME2 density did
not. The ratio $R(\sigma)$ was found to be sensitive to the isotopic change of
the neutron $3s_{1/2}$ occupation through the isotopic difference of the
surface neutron density around r=4--5 fm. Isotopic analysis indicated that a
rapid increase of the $3s_{1/2}$ occupation from $^{116}$Sn to $^{122}$Sn
obtained by the DD-ME2 calculation is unlikely. This result derived from the
295 MeV Sn(p,p) cross section data is consistent with the direct measurement of
the neutron occupations in Sn isotopes by neutron transfer and pick-up
reactions.
