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A pair of transverse wobbling bands has been observed in the nucleus $^{135}$Pr. The wobbling is characterized by $Delta I$ =1, E2 transitions between the bands, and a decrease in the wobbling energy confirms its transverse nature. Additionally, a transition from transverse wobbling to a three-quasiparticle band comprised of strong magnetic dipole transitions is observed. These observations conform well to results from calculations with the Tilted Axis Cranking (TAC) model and the Quasiparticle Triaxial Rotor (QTR) Model.
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In [J. T. Matta et al., Phys. Rev. Lett. 114, 082501 (2015)] a transverse wobbling band was reported in $^{135}$Pr. The critical experimental proof for this assignment is the E2 dominated linking transitions between the wobbling and normal bands, which are supported by two experiments performed with Gammasphere and INGA. However, the M1 dominated character cannot be excluded based on the reported experimental information, indicating that the wobbling assignment is still questionable.
The electromagnetic character of the $Delta I=1$ transitions connecting the one- to zero-phonon and the two- to one-phonon wobbling bands should be dominated by an $E2$ component, due to the collective motion of the entire nuclear charge. In the present work it is shown, based on combined angular correlation and linear polarization measurements, that the mixing ratios of all analyzed connecting transitions between low-lying bands in $^{135}$Pr interpreted as zero-, one-, and two-phonon wobbling bands, have absolute values smaller than one. This indicates predominant $M1$ magnetic character, which is incompatible with the proposed wobbling nature. All experimental observables are instead in good agreement with quasiparticle-plus-triaxial-rotor model calculations, which describe the bands as resulting from a rapid re-alignment of the total angular momentum from the short to the intermediate nuclear axis.
New rotational bands built on the $ u$$(h_{11/2})$ configuration have been identified in $^{105}$Pd. Two bands built on this configuration show the characteristics of transverse wobbling: the $Delta$$I$=1 transitions between them have a predominant E2 component and the wobbling energy decreases with increasing spin. The properties of the observed wobbling bands are in good agreement with theoretical results obtained using constrained triaxial covariant density functional theory and quantum particle rotor model calculations. This provides the first experimental evidence for transverse wobbling bands based on a one-neutron configuration, and also represents the first observation of wobbling motion in the $A$$sim$100 mass region.
The $g$-factor and static quadrupole moment of the nuclides $^{135}$Pr, $^{105}$Pd, and $^{187}$Au in the wobbling motion are investigated in the particle-rotor model as functions of the total spin $I$. The $g$-factor of $^{105}mathrm{Pd}$ increases with increasing $I$, due to the negative gyromagnetic ratio of a neutron valence-neutron. This behavior is in contrast to the decreasing $g$-factor of the other two nuclides, $^{135}$Pr and $^{187}$Au, which feature a valence-proton. The static quadrupole moment $Q$ depends on all three expectation values of the total angular momentum. It is smaller in the yrast band than in the wobbling band for the transverse wobblers $^{135}$Pr and $^{105}$Pd, while larger for the longitudinal wobbler $^{187}$Au.
Excited states of $^{133}$La have been investigated to search for the wobbling excitation mode in the low-spin regime. Wobbling bands with $n_omega$ = 0 and 1 are identified along with the interconnecting $Delta I$ = 1, $E2$ transitions, which are regarded as one of the characteristic features of the wobbling motion. An increase in wobbling frequency with spin implies longitudinal wobbling for $^{133}$La, in contrast with the case of transverse wobbling observed in $^{135}$Pr. This is the first observation of a longitudinal wobbling band in nuclei. The experimental observations are accounted for by calculations using the quasiparticle-triaxial-rotor (QTR) model, which attribute the appearance of longitudinal wobbling to the early alignment of a $pi=+$ proton pair.
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