Role of Anharmonicities of Nuclear Vibrations in Fusion Reactions at Sub-barrier Energies

We discuss the effects of double octupole and quadrupole phonon excitations in ¹⁴⁴Sm on fusion reactions between ¹⁶O and ¹⁴⁴Sm at sub-barrier energies. The effects of anharmonicities of the vibrational states are taken into account by using the sdf-interacting boson model. We compare the results with those in the harmonic limit to show that anharmonicities play an essential role in reproducing the experimental fusion barrier distribution. From the analysis of the high quality fusion data available for this system, we deduce negative static quadrupole moments for both the first 2⁺ and 3^- states in ¹⁴⁴Sm. This is the first time that the sign of static quadrupole moments of phonon states in a spherical nucleus is determined from the data of sub-barrier fusion reactions.