Extracting the hexadecapole deformation from backward quasi-elastic scattering

Background: The hexadecapole deformation beta(4) is usually difficult to determine experimentally, especially its sign. The rapidly accumulated knowledge of beta(2) inspires the desire of beta(4) for radioactive nuclei, but the current low-quality beam is a severe experimental challenge. Therefore, a simple but sensitive method to extract beta(4) in such a condition is urgently called for. Purpose: To study the feasibility of extracting beta(4) from the lower-energy backward quasi-elastic (QEL) scattering. Methods: The QEL scattering at sub-barrier energy region is sensitive to the coupled-channels (CC) effect and consequently may be used to extract beta(4). The QEL scattering excitation functions for O-16 + Sm-152, Er-170, and Yb-174 were measured at a backward angle with small energy intervals at energies near the Coulomb barrier. Experimental fusion barrier distributions were also derived. The lower-energy data were analyzed to extract beta(4) with the help of the CC calculations. Results: The obtained beta(4) agrees with the available results reasonably well. Conclusions: We have demonstrated that the QEL scattering at sub-barrier energies provides a feasible and sensitive method to extract the value of beta(4), which is essentially meaningful for the radioactive nucleus because of its low beam intensity.