Role of anharmonicities of nuclear vibrations in fusion reactions at subbarrier energies

We discuss the effects of double octupole and quadrupole phonon excitations in $^{144}$Sm on fusion reactions between $^{16}$O and $^{144}$Sm at subbarrier 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 $^{144}$Sm. 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 subbarrier fusion reactions.