Triaxial-band structures, chirality, and magnetic rotation in ${}^{133}\text{La}$

The structure of ${}^{133}\text{La}$ has been investigated using the ${}^{116}\text{Cd}({}^{22}\text{Ne},4pn)$ reaction and the Gammasphere array. Three new bands of quadrupole transitions and one band of dipole transitions are identified and the previously reported level scheme is revised and extended to higher spins. The observed structures are discussed using the cranked Nilsson-Strutinsky formalism, covariant density functional theory, and the particle-rotor model. Triaxial configurations are assigned to all observed bands. For the high-spin bands it is found that rotations around different axes can occur, depending on the configuration. The orientation of the angular momenta of the core and of the active particles is investigated, suggesting chiral rotation for two nearly degenerate dipole bands and magnetic rotation for one dipole band. It is shown that the $h_{11/2}$ neutron holes present in the configuration of the nearly degenerate dipole bands have significant angular momentum components not only along the long axis but also along the short axis, contributing to the balance of the angular momentum components along the short and long axes and thus giving rise to a chiral geometry.

Figure 1

Partial level scheme of ${}^{133}\text{La}$ showing the low- and medium-spin states. Arrow widths are proportional to $\gamma \text{-ray}$ intensities.

Figure 2

Partial level scheme of ${}^{133}\text{La}$ with the high-spin bands (see text for details).

Figure 3

Double-gated coincidence spectra for the newly identified bands $Q8, Q9$, and $Q10$ of ${}^{133}\text{La}$. The spectrum of band $Q8$ is obtained by summing the spectra with a gate on the 135-, 179-, 209- and 331-keV transitions of band $D1$ and a second gate on the in-band transitions. The spectrum of band $Q9$ is obtained by summing the spectra double-gated on all combinations of the in-band transitions (except 963 and 871 keV), and the 179-keV $\gamma$ ray of band $D1$. The spectrum of band $Q10$ is obtained by summing the spectra double-gated on combinations of all in-band transitions (except 1591 and 1694 keV). Transitions marked with asterisks represent the band members, while those marked with # are identified contaminants from other bands.

Figure 4

The $B\left(M1\right)/B\left(E2\right)$ ratios of bands $D1$ and $D2$ of ${}^{133}\text{La}$. The solid lines linking the experimental values are meant to guide the eye.

Figure 5

Quasiparticle alignment as a function of rotational frequency for bands $Q1, Q2, Q8, Q9, Q10, D1, D2$, and $D4$ in ${}^{133}\text{La}$. The Harris parameters used are ${\mathcal{J}}_0=10{\hslash }^2/\mathrm{MeV}$ and ${\mathcal{J}}_1=20{\hslash }^4/{\mathrm{MeV}}^3$, and the projection of the total angular momentum on the $z$ axis is $K=0$ in all cases. The parity of the bands is also indicated in the legend. For band $D4$, the solid line with full symbols denotes the $\alpha =+1/2$ sequences, while the dashed line with empty symbols denotes the $\alpha =-1/2$ sequences.

Figure 6

Energies relative to a standard rotating liquid drop reference calculated for the experimental bands observed in ${}^{133}\text{La}$. The labeling of the configurations is explained in the text. With an odd number of $h_{11/2}$ neutron holes, two signature-degenerate bands are formed, which are shown by the same color and symbols. For the dipole bands, the closed symbols denote the $\alpha =+1/2$ sequences, while the open symbols denote the $\alpha =-1/2$ sequences.

Figure 7

The observed bands of ${}^{133}\text{La}$ are presented relative to a rotating liquid drop reference in the upper panel, while the calculated configurations assigned to these bands are given relative to the same reference in the middle panel. The lower panel provides the difference between calculations and experiment.

Figure 8

Potential-energy surface in the ${\beta }_2-\gamma$ plane $(0\le {\beta }_2\le 0.4,0\le \gamma \le {60}^{\circ })$ for the ground-state configuration of ${}^{133}\text{La}$ in constrained triaxial RMF calculations with the PC-PK1 effective interaction. All energies are normalized with respect to the energy of the absolute minimum (in MeV) indicated by the star. The energy separation between each contour line is 0.5 MeV.

Figure 9

The potential energy as a function of ${\beta }_2$ in adiabatic (open circles) and configuration-fixed (lines) constrained triaxial RMF calculations with the PC-PK1 effective interaction for ${}^{133}\text{La}$.

Figure 10

The results of PRM calculations in comparison with experimental data: (a) the energies $E\left(I\right)$, less than a reference $\varepsilon$, for bands $D1, D2$ and $Q8, Q9$ for the configurations assigned in the present work; (b) the $B\left(M1\right)/B\left(E2\right)$ ratios for bands $D1$ and $D2$ for the proposed configurations.

Figure 11

The root mean square components along the intermediate ($i$, squares), short ($s$, circles), and long ($l$, triangles) axes of the core $R_k=\sqrt{\langle {\widehat{R}}_k^2\rangle \phantom{0}}$, the active neutron $J_{nk}=\sqrt{\langle {\widehat{j}}_{nk}^2\rangle \phantom{0}}$, and the active proton $J_{pk}=\sqrt{\langle {\widehat{j}}_{pk}^2\rangle \phantom{0}}$ calculated as a function of spin by means of the PRM for bands $D1, D2$, and $Q8, Q9$ in ${}^{133}\text{La}$.

Figure 12

The energies $E\left(I\right)$ for band $D4$ calculated by the PRM (solid and dashed lines) in comparison with the experimental data (solid squares).

Figure 13

The reduced transition probabilities $B\left(M1\right)$ and $B\left(E2\right)$ of band D4 calculated with the PRM.

Figure 14

The root mean square components along the intermediate ($i$, squares), short ($s$, circles), and long ($l$, triangles) axis of the core $R_k=\sqrt{\langle {\widehat{R}}_k^2\rangle }$, the active neutron $J_{nk}=\sqrt{\langle {\widehat{j}}_{nk}^2\rangle }$, and the active proton $J_{pk}=\sqrt{\langle {\widehat{j}}_{pk}^2\rangle }$ calculated as a function of spin by means of the PRM for band $D4$.