Dirac Coupled Channel Analyses of the 2$^-$ Gamma Vibrational band   excitation in $^{20}$Ne
  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. 
Sugie Shim
nucl-th