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In [S. Biswas et al., Eur. Phys. J. A 55, 159 (2019)] a longitudinal wobbling band was reported in $^{133}$La. The critical experimental proof for this assignment is the E2 dominated linking transitions between the wobbling and normal bands, which are supported by angular distribution and linear polarization measurements. However, severe problems are found in the reported experimental information, indicating that the assignment of wobbling band was not firmly established.
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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.
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 rare phenomenon of nuclear wobbling motion has been investigated for the nucleus $^{187}$Au. A longitudinal wobbling-bands pair has been identified and clearly distinguished from the associated signature-partner band on the basis of angular distribution measurements. Theoretical calculations in the framework of the Particle Rotor Model (PRM) are found to agree well with the experimental observations. This is the first experimental evidence for longitudinal wobbling bands where the expected signature partner band has also been identified, and establishes this exotic collective mode as a general phenomenon over the nuclear chart.
The $g$-factor and static quadrupole moment for the wobbling mode in the nuclide $^{133}$La are investigated as functions of the spin $I$by employing the particle rotor model. The model can reproduce the available experimental data of $g$-factor and static quadrupole moment. The properties of the $g$-factor and static quadrupole moment as functions of $I$ are interpreted by analyzing the angular momentum geometry of the collective rotor, proton-particle, and total nuclear system. It is demonstrated that the experimental value of the $g$-factor at the bandhead of the yrast band leads to the conclusion that the rotor angular momentum is $Rsimeq 2$. Furthermore, the variation of the $g$-factor with the spin $I$ yields the information that the angular momenta of the proton-particle and total nuclear system are oriented parallel to each other. The negative values of the static quadrupole moment over the entire spin region are caused by an alignment of the total angular momentum mainly along the short axis. Static quadrupole moment differences between the wobbling and yrast band originate from a wobbling excitation with respect to the short axis.
In [S. Nandi et al., Phys. Rev. Lett. 125, 132501 (2020)] two transverse wobbling bands were reported in $^{183}$Au. The critical experimental proof for this assignment is the E2 dominated linking transitions between the wobbling and normal bands, which are supported by fitting the measured DCO ratio and polarization results. However, the uncertainties are significantly underestimated according to an analysis on the statistical error. With reasonable error, the mixing ratios cannot be exclusively decided, and the M1 dominated character cannot be excluded, indicating that the wobbling assignment is still questionable.
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