The experimental $E1$ strength distribution below 4 MeV in rare-earth nuclei suggests a local breaking of isospin symmetry. In addition to the octupole states, additional $1^-$ states with enhanced E1 strength have been observed in rare-earth nuclei
by means of ($gamma,gamma$) experiments. By reproducing the experimental results, the spdf interacting boson model calculations provide further evidence for the formation of an $alpha$ cluster in medium-mass nuclei and might provide a new understanding of the origin of low-lying E1 strength.
Background: Excitations with mixed proton-neutron symmetry have been previously observed in the $N=52$ isotones. Besides the well established quadrupole mixed-symmetry states (MSS), octupole and hexadecapole MSS have been recently proposed for the nu
clei $^{92}$Zr and $^{94}$Mo. Purpose: The heaviest stable $N=52$ isotone $^{96}$Ru was investigated to study the evolution of octupole and hexadecapole MSS with increasing proton number. Methods: Two inelastic proton-scattering experiments on $^{96}$Ru were performed to extract branching ratios, multipole mixing ratios, and level lifetimes. From the combined data, absolute transition strengths were calculated. Results: Strong $M1$ transitions between the lowest-lying $3^-$ and $4^+$ states were observed, providing evidence for a one-phonon mixed-symmetry character of the $3^{(-)}_2$ and $4^+_2$ states. Conclusions: $sdg$-IBM-2 calculations were performed for $^{96}$Ru. The results are in excellent agreement with the experimental data, pointing out a one-phonon hexadecapole mixed-symmetry character of the $4^+_2$ state. The $big< 3^-_1||M1||3^{(-)}_2big>$ matrix element is found to scale with the $<2^+_{mathrm{s}}||M1||2^+_{mathrm{ms}}>$ matrix element.
