  We present the first systematic nonlocal dispersive optical model analysis
using both bound-state and scattering data of $^{16,18}$O, $^{40,48}$Ca,
$^{58,64}$Ni, $^{112,124}$Sn, and $^{208}$Pb. In all systems, roughly half the
total nuclear binding energy is associated with the most-bound 10% of the total
nucleon density. The extracted neutron skins reveal the interplay of asymmetry,
Coulomb, and shell effects on the skin thickness. Our results indicate that
simultaneous optical model fits of inelastic scattering and structural data on
isotopic pairs are effective for constraining asymmetry-dependent nuclear
structural quantities otherwise difficult to observe experimentally.
