Cross-sections and analyzing powers data obtained by inelastic scattering of 800 MeV polarized protons from several s-d shell nuclei have been analyzed using the Dirac coupled-channel (CC) formalism putting emphasis in the precise determination of higher order deformation in these nuclei. The superiority of the Dirac formalism compared to the classical Schr6dinger CC calculations in the analysis of these data was once more clearly established. The higher order deformations obtained through these calculations are compared to those obtained using the classical Schr6dinger equation. 25.40.Ep
PACS:The precise determination of the shape of a nucleus remains a difficult problem. This is particularly true for the determination of the nuclear deformation, a specific property of the shape of nuclei; such a determination has indeed been the subject of many experiments as well as theoretical investigations since several years [ 1,2]. A standard technique for investigating nuclear shape and therefore nuclear deformation is the measurement of inelastic cross-sections as was first suggested by Barret [3]. Indeed, analysis of inelastic cross-sections by means of the deformed optical model potential (DOMP) in the coupledchannel (CC) formalism has been proved to be a powerful tool for the determination of higher order deformation as was first demonstrated for rare earth nuclei by Hendrie et al.[4] using 50 MeV ~ particles.These experiments have for the first time clearly demonstrated the existence of some hexadecapole deformation (/?4) in the equilibrium shape of rare earth nuclei, whose value ranges from + 0.04 for 152Sm to -0.06 for [78Hf, deformation which is added to the usual quadrupole deformation /?2. Subsequently, inelastic scattering experiments with protons [5], alpha particles [6], electrons [7] or polarized low energy protons [8], analyzed through the DOMP indicated also the presence of a large /?4 term in the shape of several 2s-1 d shell nuclei.In particular, the analysis of 24.5 MeV polarized protons inelastic scattering from 2~ has revealed the existence in the equilibrium shape of this nucleus of a value of /84 which is the largest f14 deformation (fl4=0.28) found in the literature as well as the need for a large negative deformation B6 =-0.10 (called hexakontattetara deformation [1]) to match the magnitude of the measured cross-section for the 6 + state at 8.79 MeV [9]. However, this large/76 deformation found some time ago in 2~ was never confirmed until recently either by experiment or theoretical calculations based on Schr6dinger type calculations and no large/?6 was either reported for other s-d shell nuclei.In the actinide region, the first inelastic scattering experiment using 50 MeV 0~ particles [4] has clearly shown the need for a small/?6 term roughly constant form ~SaSm to 178Hf (I/761 G0.02) together with the /?4 term (I/741 G0.06) to reproduce the measured cross-section which includes the cross-section for the 6 + state.Recently, a large amount of inelastic polarized proton scattering data at Ep = 80...