Experiment and previous calculations

It the present study, the HF solutions corresponding to chiral rotation were sought in four $N=75$ isotones, $^{130}$Cs, $^{132}$La, $^{134}$Pr, and $^{136}$Pm. These are the first nuclei in which candidate chiral bands were observed and systematically studied [2]. For the most recent experimental data refer to [10] for $^{130}$Cs, to [12,38,9] for $^{132}$La, to [2,39] for $^{134}$Pr, and to [40] for $^{136}$Pm. Absolute values of spins and reduced transition probabilities were measured only in $^{132}$La. The possible chiral bands known in this nucleus are shown in Fig. 1 with full symbols. The lowest one (circles) is the yrast in positive parity. Two closely-lying excited bands, B1 and B3 (squares and diamonds) are known [7,8,9], and it is unclear which one of them should be viewed as the chiral partner of the yrast band. The yrast and B1 bands are of positive-parity with known spins, while for band B3 the spin assignments are tentative.

Figure 1: (color online). Energies obtained from the HF TAC calculations, open circles and plus symbols, and from the classical model presented in Sec. III.D, dashed and solid lines, compared with the experimental data on the candidate chiral partner bands in $^{132}$La, full symbols. The HF results obtained for the SLy4 and SkM* forces are shown for the $N$, $G$, and $T$ time-odd fields included (see text).

For all the $N=75$ isotones in question, PRM calculations were performed [40,41,12,11], and generally a good agreement with experiment could be obtained for both the energies and the B(M1)/B(E2) ratios, with a proper adjustment of the model parameters. Lifetime measurements in $^{132}$La [7,8,9] revealed, however, that absolute values of the reduced transition probabilities significantly deviate from these earlier PRM predictions.

PQTAC/SCTAC calculations with pairing were carried out for all the considered nuclei as well [20,2,24], and are also quoted in Refs. [21,22,23]. The quadrupole deformations $\epsilon$ of $0.16$, $0.175$, $0.175$, $0.195$ and triaxialities $\gamma$ of $39^\circ$, $32^\circ$, $27^\circ$, $\approx26^\circ$ were found, respectively for $^{130}$Cs, $^{132}$La, $^{134}$Pr, $^{136}$Pm. Chiral solutions were obtained in a limited range of angular frequency. The lower limits corresponded to the critical frequency, $\omega_{\text{crit}}$, discussed in the present work. Only Refs. [20] and [24] quote their values, which are $\omega_{\text{crit}}=0.3\,\mathrm{MeV}/\hbar$ for $^{134}$Pr and $\omega_{\text{crit}}<0.2\,\mathrm{MeV}/\hbar$ for $^{136}$Pm. Comparison with experimental energies was given only for $^{134}$Pr in [2,20], where the behavior of the bands was reproduced, on the average.