  Dirac phenomenological coupled channel analyses are performed using an
optical potential model for the high-lying excited vibrational states at 800
MeV unpolarized proton inelastic scatterings from $^{22}$Ne nucleus.
Lorentz-covariant scalar and time-like vector potentials are used as direct
optical potentials and the first-order vibrational collective model is used for
the transition optical potentials to describe the high-lying excited
vibrational collective states. The complicated Dirac coupled channel equations
are solved phenomenologically using a sequential iteration method by varying
the optical potential and the deformation parameters. Relativistic Dirac
coupled channel calculations are able to describe the high-lying excited states
of the vibrational bands in $^{22}$Ne clearly better than the nonrelativistic
coupled channel calculations. The channel-coupling effects of the multistep
process for the excited states of the vibrational bands are investigated. The
deformation parameters obtained from the Dirac phenomenological calculations
for the high-lying vibrational excited states in $^{22}$Ne are found to agree
well with those obtained from the nonrelativistic calculations using the same
Woods-Saxon potential shape.
