Exotic low-energy vibrational modes

Nuclei near closed shells or subshells are often interpreted as exhibiting vibrational structures. Mixed-symmetry (MS) states are collective vibrational modes in which neutron and proton intrinsic g-factors are additive in the isovector part of the M1 magnetic dipole operator and may lead to large B(M1) values of $\sim$1$\mu_N^2$. The fundamental MS mode in nearly-spherical nuclei is a 2$^+$ excitation (2$_{1,MS}^+$) with a strong M1 transition to the one-phonon 2$^+_1$ level and, typically, a rather weak E2 transition to the ground state. Exotic cases of MS states have recently been identified in $^{93}$Nb and $^{94}$Zr. The former, the first case of a MS state in a nearly spherical odd-mass nucleus, arises from the weak coupling between the bosonic core, (2$^+_{1,MS}$, $^{94}$Mo), and the fermionic $\pi$ 2p$^{-1}_{1/2}$ proton hole. The latter presents an anomalous case of quadrupole vibrations, where the MS state, 2$_{1,MS}^+$, lies below the strongly anharmonic 2$^+$ two-phonon state (isoscalar), and the 2$^+_{1,MS}$ $\rightarrow$ 0$^+_1$ transition is observed to have a larger E2 transition strength than the 2$^+_1$ $\rightarrow$ 0$^+_1$ decay. This material is based upon work supported by the U.S. National Science Foundation under Grant No. PHY-0354656.