Evolution of chirality from transverse wobbling in $^{135}$Pr

TL;DR

The paper reports the first observation of chirality in $^{135}$Pr, identifying two nearly degenerate chiral-partner bands built on the configuration $\pi(1h_{11/2})^1\otimes\nu(1h_{11/2})^{-2}$. Through high-statistics Gammasphere data and detailed angular-distribution analyses, the authors extract mixing ratios and establish predominantly $E2$ interband transitions between the bands, consistent with chiral geometry. Quasiparticle triaxial rotor (QTR) calculations, complemented by TPSM comparisons, reproduce many features of the observed spectra, including energy differences at band crossings and transition-probability trends, while also highlighting discrepancies such as energy staggering and interband/intraband ratio variations. The study also refutes criticisms by Lv et al., reinforcing the coexistence of transverse wobbling and chirality in $^{135}$Pr and marking the first instance of both hallmarks of triaxiality in a single nucleus.

Abstract

Chirality is a distinct signature that characterizes triaxial shapes in nuclei. We report the first observation of chirality in the nucleus $^{135}$Pr using a high-statistics Gammasphere experiment with the $^{123}$Sb($^{16}$O,4n)$^{135}$Pr reaction. Two chiral-partner bands with the configuration $π(1h_{11/2})^1\otimesν(1h_{11/2})^{-2}$ have been identified in this nucleus. Angular distribution analyses of the $ΔI = 1$ transitions connecting the two bands reveal a dominant dipole character, and quasiparticle triaxial rotor model calculations show good agreement with the data. Since the simultaneous observation of chirality and transverse wobbling in $^{135}$Pr relies critically on these angular distribution results, we also address and refute the experimental and theoretical criticisms raised in a recent work by Lv et al., presenting additional evidence that further strengthens our interpretation. This marks the first observation of both hallmarks of triaxiality-chirality and wobbling-in the same nucleus.

Figures (13)

• Figure 1: (Color online) Angular momentum geometry for (a) transverse wobbling (TW), (b) transverse chiral vibration (TCV), and (c) chiral rotation (CR) mode in the body fixed frame, where $l$, $m$, and $s$ correspond to the long, medium, and short axis, respectively, and $\bm{J}$ is the total angular momentum vector. The TW orbit is centered around the $s$-axis while the TCV orbit around the black axis in the $l$-$s$ plane is the total quasiparticle angular momentum. In the CR mode $\bm{J}$ is localized out of the three principal planes and oscillates between the equivalent octants of opposite chirality of the principal axes (only two are shown). The quasineutron and quasiproton angular momenta are shown as the violet and blue arrows aligned with the $l$- and $s$- axes, respectively. With increasing $J$, the quasiparticle arrows start following the motion of $\bm{J}$.
• Figure 2: Partial level scheme of $^{135}$Pr developed in the present work. The lowest level shown is an 11/2$^{-}$ isomeric level with $E_{x}$ = 358.0 keV. The five connecting transitions between dipole bands DB2 and DB1 have been newly identified in this work. The tentative $\gamma$-ray transitions are given as dotted lines.
• Figure 3: (Color online) The observed coincidence spectrum resulting from the (a) double gate on the yrast in-band 1000- and 1075-keV transitions, (b) sum of gates on E$_\gamma$ = 642, 573, and 477 keV, (c) sum of all possible double gates on the $\Delta I$ = 1, M1 transitions within DB1 and DB2, and (d) double gate on 373- and 660-keV transitions. An inset is included in the bottom panel to magnify and clearly display the three lowest DB2 $\to$ DB1 transitions. The coincident $\gamma$-ray energies are marked against the respective energy peaks. The peaks marked in red correspond to the $\Delta$I = 1 in-band transitions of DB1 and DB2. Yrast in-band transitions are marked in black. All other transitions arising from the deexcitation of $^{135}$Pr are marked in blue and an (*) is marked on the transitions that were observed, but are not displayed, in the level scheme of Fig. \ref{['f:level_scheme']}.
• Figure 4: The observed coincidence spectrum resulting from a double gate on (a) 373- and 746-keV transitions, (b) 498- and 459-keV transitions, and (c) 520- and 554-keV transitions. The spectra are zoomed in to present the DB2 $\to$ DB1 transitions. All the other peaks observed in these spectra have been identified and placed in the level scheme.
• Figure 6: (Color online) Angular distribution plots for the three lowest $\Delta I = 1$ transitions connecting the DB1 and DB2 bands. (Left) The experimental points are given as black circles, and the solid red lines are fits to the angular distributions. (Center) A plot of the a$_4$ coefficient versus the a$_2$ coefficient for various initial and final spin combinations. The experimental a$_4$-a$_2$ values, obtained from the fits in the left panel, are displayed in black and align with the most probable spin sequence. (Right) The calculated $\chi^2$ values comparing theoretical and experimental angular distributions from the left panel. The minimum $\chi^2$ values in these plots correspond to the $\delta$ values extracted from the angular distribution fits. For completeness, $\chi^2$ values for other possible spin sequences are also included.