  Unpolarized 800 MeV proton inelastic scatterings from an s-d shell nucleus
$^{22}$Ne are analyzed using phenomenological optical potentials in the Dirac
coupled channel formalism. The first-order rotational collective model is used
to obtain the transition optical potentials for the low lying excited
collective states that belong to the ground state rotational band of the
nucleus. The optical potential parameters of Woods-Saxon shape and the
deformation parameters of the excited states are varied phenomenologically
using the sequential iteration method to reproduce the experimental
differential cross section data. The effective central and spin-orbit optical
potentials are obtained by reducing the Dirac equations to the
Schr\"odinger-like second-order differential equations and the surface-peaked
phenomena are observed at the real effective central potentials when the
scattering from $^{22}$Ne is considered. The obtained deformation parameters of
the excited states are compared with those of the nonrelativistic calculations
and another s-d shell nucleus $^{20}$Ne. The deformation parameters for the
$2^+$ and the $4^+$ states of the ground state rotational band at the nucleus
$^{22}$Ne are found to be smaller than those of $^{20}$Ne, indicating that the
couplings of those states to the ground state are weaker at the nucleus
$^{22}$Ne compared to those at the nucleus $^{20}$Ne. The multistep channel
coupling effect is confirmed to be important for the $4^+$ state excitation of
the ground state rotational band at the proton inelastic scattering from the
s-d shell nucleus $^{22}$Ne.
