  Dirac coupled channel analyses are performed using optical potential model
for the high-lying excited states that belong to the 2$^-$ gamma vibrational
band at the 800 MeV unpolarized proton inelastic scatterings from $^{20}$Ne.
The first order vibrational collective models are used to obtain the transition
optical potentials to describe the high-lying excited vibrational collective
states and Lorentz-covariant scalar and time-like vector potentials are used as
direct optical potentials. The complicated Dirac coupled channel equations are
solved phenomenologically to reproduce the differential cross sections data by
varying the optical potential and deformation parameters using minimum
chi-square method. It is found that relativistic Dirac coupled channel
calculation could describe the excited states of the 2$^-$ gamma vibrational
band in $^{20}$Ne much better than the nonrelativistic coupled channel
calculation, especially for the 2$^-$ and 3$^-$ states of the band. It is shown
that the multistep excitation process via channel coupling with the $3^-$ state
is essential to describe the $2^-$ state excitation and pure direct transition
from the ground state is dominant for the 3$^-$ state excitation of the 2$^-$
gamma vibrational band in $^{20}$Ne.
