  To extract structure information from proton elastic scattering off S
isotopes at 320 MeV and Ni isotopes at $E_p=180$ MeV, this study proposes
isotopic analyses combining nuclear structure and reaction calculations. The
isotonic analysis was repeated on $^{48}$Ca and $^{50}$Ti. The structure
calculations were performed by using the spherical and deformed Relativistic
Hartree--Bogoliubov (RHB) calculations, and the spherical nonrelativistic
Skyrme Hartree--Fock--Bogoliubov calculations. The $(p,p)$ reactions were
calculated using the relativistic impulse approximation (RIA) assuming the
theoretical densities of target nuclei. The RIA calculations using the target
densities obtained by the RHB calculation, along with the density-dependent
point-coupling interactions reasonably reproduced the $(p,p)$ cross sections in
the studied mass number region. The nuclear structure and $(p,p)$ reactions
were analyzed in detail; especially, the effects of deformation on the isotopic
systematics of the surface densities and $(p,p)$ cross sections were clarified.
The deformation effects were found to be essential to describe the isotopic
systematics of the experimental $(p,p)$ cross sections. Overall, isotopic and
isotonic analyses are useful for extracting the nuclear structure information
such as nuclear deformations and single-particle features from proton
scattering, enabling sensitive probing of surface densities.
