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

Dirac Coupled Channel Analyses of the 2$^-$ Gamma Vibrational band excitation in $^{20}$Ne