Mixed-symmetry octupole and hexadecapole excitations in the N=52 isotones

Abstract

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 nuclei ${}^{92}$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 $⟨3_1^{-}||M1||3_2^{(-)}⟩$ matrix element is found to scale with the $<2_{\mathrm{s}}^{+}||M1||2_{\mathrm{ms}}^{+}>$ matrix element.