Transverse Wobbling in ${}^{135}\mathrm{Pr}$

A pair of transverse wobbling bands is observed in the nucleus ${}^{135}\mathrm{Pr}$. The wobbling is characterized by $\mathrm{\Delta }I=1$, $E2$ 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 model and the quasiparticle rotor model.

Figure 1

Partial level scheme of ${}^{135}\mathrm{Pr}$ showing the previously known yrast band ($n_{\omega }=0$), the “signature partner band,” the wobbling band ($n_{\omega }=1$), and the dipole band. The lowest level shown is an ${\frac{11}{2}}^{-}$ isomeric level with $E_x=358\mathrm{keV}$ [22].

Figure 2

(Left panels) Angular distributions for the first three transitions between the $n_{\omega }=1$ and $n_{\omega }=0$ bands, as also the best fits (the solid red lines) from which the mixing ratios, $\delta$, presented in Table 1, were extracted (see text). The expected angular distributions for pure $M1$ transitions (the dashed blue lines) are provided for comparison. Angular distribution data and fits are presented also for the 593.9 keV transition linking the signature partner and yrast bands (see text) and for the 1075.5 keV pure $E2$ transition from the yrast band (right panels).

Figure 3

The asymmetries (the filled squares) for the first two transitions (747.0 and 812.8 keV) from the $n_{\omega }=1$ band to the $n_{\omega }=0$ band, as extracted from polarization data. The filled circles represent known $E2$ transitions from the yrast band and the black triangle a known 412.3 keV $M1$ transition from a level sequence in ${}^{135}\mathrm{Pr}$ not displayed in Fig. 1. Also shown is the measured polarization asymmetry for the 593.9 keV transition linking the signature partner and yrast bands (see text).

Figure 4

Level energies for the three bands featured in Fig. 1; the filled and open diamonds represent the wobbling band pair and the filled squares represent the three-quasiparticle dipole band. The results from the TAC model are presented as lines.

Figure 5

Experimental and QTR level energies minus a rotor contribution for the yrast, wobbling, and signature partner bands. Inset: Wobbling energies (filled circles) associated with the wobbler-band pair observed in the nucleus ${}^{135}\mathrm{Pr}$ plotted as a function of spin $I$. Predicted values from the QTR model are also shown (see text). The lines through the experimental points are drawn to guide the eye.