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Dirac coupled channel calculations are performed phenomenologically for thehigh-lying excited states that belong to the 2$^+$ gamma vibrational band atthe 800-MeV polarized proton inelastic scatterings from the s-d shell nuclei,$^{24}$Mg and $^{26}$Mg. Optical potential model is used and scalar andtime-like vector potentials are considered as direct potentials. First-ordervibrational collective models are used to obtain the transition opticalpotentials in order to accommodate the high-lying excited vibrationalcollective states. The complicated Dirac coupled channel equations are solvedphenomenologically to reproduce the differential cross section and analyzingpower data by varying the optical potential and deformation parameters.  It is found that the relativistic Dirac coupled channel calculation coulddescribe the high-lying excited states of the 2$^+$ gamma vibrational band atthe 800-MeV polarized proton inelastic scatterings from s-d shell nuclei$^{24}$Mg and $^{26}$Mg reasonably well, showing better agreement with theexperimental data compared to the results obtained from the nonrelativisticcalculations. Calculated deformation parameters for the excited states areanalyzed and compared with those of nonrelativistic calculations.

Dirac Coupled-channel Analyses of Polarized Proton Scatterings to the 2$^+$ Gamma Vibrational Band in $^{24}$Mg and $^{26}$Mg