Inelastic scattering of 65-MeV polarized protons from 178Hf, 180Hf, 182W, and 184W and multipole moments of the optical potential.

Abstract

Differential cross sections and analyzing powers of polarized proton elastic and inelastic scattering from $^{178}\mathrm{Hf}$, $^{180}\mathrm{Hf}$, $^{182}\mathrm{W}$, and $^{184}\mathrm{W}$ have been measured at 65 MeV. Analysis has been performed in the framework of the coupled channel formalism of the deformed optical potential for ${J}^{\ensuremath{\pi}}$${=0}^{+}$--${6}^{+}$ members of the ground state rotational band. In this analysis, all the deformation parameters of the real central, volume imaginary, surface imaginary, and spin-orbit parts of the deformed optical potential were searched independently. Up to the ${6}^{+}$ state, excellent fits have been obtained. It is found that the quadrupole moment of the real central part is 6--9 % larger than that of the charge density for all the measured nuclei, but the quadrupole moment of the Woods-Saxon form factor of the spin-orbit part agrees with the charge quadrupole moment within the fitting error. These results are consistent with the difference between the effects of the density dependence of the effective nucleon-nucleon interaction on the real central part and the spin-orbit part of the optical potential. Similar trends are also found for the hexadecapole moments of the real central part and the spin-orbit part. A folding model calculation using a realistic effective interaction has been carried out and its results are compared to those of the coupled channel analysis.