Transverse wobbling: A collective mode in odd-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>A</mml:mi></mml:math>triaxial nuclei

Abstract

The wobbling motion of a triaxial rotor coupled to a high-$j$ quasiparticle is treated semiclassically. Longitudinal and transverse coupling regimes can be distinguished depending on, respectively, whether the quasiparticle angular momentum is oriented parallel or perpendicular to the rotor axis with the largest moment of inertia. Simple analytical expressions for the wobbling frequency and the electromagnetic $E2$ and $M1$ transition probabilities are derived assuming rigid alignment of the quasiparticle with one of the rotor axes and harmonic oscillations (HFA). Transverse wobbling is characterized by a decrease of the wobbling frequency with increasing angular momentum. Two examples for transverse wobbling, ${}^{163}$Lu and ${}^{135}$Pr, are studied in the framework of the full triaxial particle-rotor model and the HFA. The signature of transverse wobbling, decreasing wobbling frequency, and enhanced $E2$ interband transitions, is found in agreement with experiment.