  The microscopic coupled-channel calculation of inelastic proton scattering is
performed for the study of neutron excitations in $2^+_1$ states of $^{18}$O,
$^{10}$Be, $^{12}$Be, and $^{16}$C. Proton-nucleus potentials in the
coupled-channel calculation are microscopically derived by folding the
Melbourne $g$-matrix $NN$ interaction with matter and transition densities of
target nuclei obtained by the structure model calculation of antisymmetrized
molecular dynamics. The calculated result reasonably reproduces the elastic and
inelastic proton scattering cross sections, and supports the dominant
contribution of neutron in the $2^+_1$ excitation of $^{12}$Be and $^{16}$C as
well as $^{18}$O. Sensitivity of the inelastic scattering cross sections to the
neutron transition density is discussed. The exotic feature of the neutron
transition density with the amplitude in the outer region in $^{12}$Be and
$^{16}$C is focused.
