Summary: | Wobbling motion as an exotic collective mode in nuclei without axial symmetry, was intensively discussed during the last few years. The observation of the newly proposed transverse wobbling, first reported in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>135</mn></msup></semantics></math></inline-formula>Pr and soon after in nuclei from other mass regions, was considered as a significant discovery in low-spin nuclear structure. However, both the reported experimental results and the proposed theoretical models were actively questioned in work devoted to the study of the low-spin wobbling mode in the same nuclei. We recently re-measured the electromagnetic character of the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>Δ</mo><mi>I</mi><mo>=</mo><mn>1</mn></mrow></semantics></math></inline-formula> transitions connecting the one- to zero-phonon and the two- to one-phonon wobbling bands in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>135</mn></msup></semantics></math></inline-formula>Pr, showing their predominant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>M</mi><mn>1</mn></mrow></semantics></math></inline-formula> magnetic character, which is in contradiction with the wobbling interpretation. These new experimental results, which were reproduced by either the quasiparticle-plus-triaxial-rotor model and interacting boson-fermion model calculations, are against the previously proposed wobbling nature of the low-spin bands in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>135</mn></msup></semantics></math></inline-formula>Pr. On the other hand, we obtained conclusive experimental evidence for the theoretically proposed transverse wobbling bands at medium spin in <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>136</mn></msup></semantics></math></inline-formula>Nd. The comparison of the experimental data with calculations using the triaxial projected shell model as well as a new particle-rotor model with frozen orthogonal geometry of the active nucleons, supports the description in terms of transverse wobbling of medium-spin bands in triaxial even-even nuclei.
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