Inelastic scattering of 65-MeV polarized protons fromHf178,Hf180,W182, andW184and 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 $J^{\pi }$ ${=0\mathrm{}}^{+}$–$6^{+}$ 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.