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Doubly odd Cs nuclei are of particular interest due to the bands built on low-$\Omega$ $h_{11/2}$proton and high-$\Omega$ $h_{11/2}$ neutron orbitals, which exhibit distinct shape-driving effects [1]. The nuclei $^{124,126,128,130,132}$Cs have been reported to display chiral symmetry in the positive parity band based on the $\pi h_{11/2} \otimes \nu h_{11/2}$ configuration [2,3]. In this work, lifetimes of both positive- and negative-parity bands are measured using the Doppler Shift Attenuation Method (DSAM). The extracted reduced transition probabilities, B(E2) and B(M1), are crucial observables for investigating the band structures in comparison with earlier results [4]. Furthermore, we applied the cranking model to estimate the deformation and crossing frequency of these bands.
The high-spin states of $^{130}$Cs were populated by using the $^{124}$Sn($^{11}$B, 5n)$^{130}$Cs fusion evaporation reaction at a beam energy of 70 MeV delivered by the Pelletron accelerator facility at the Tata Institute of Fundamental Research, Mumbai, India. A self-supporting target $^{124}$Sn of thickness ∼ 2.2 mg/cm$^2$ was used to stop most of the recoiling nuclei. The deexcited $\gamma$-rays were detected by the Indian National Gamma Array (INGA), comprising 21 Compton-suppressed HPGe Clover detectors [5]. The two-fold and higher fold data were stored in list mode by using the PIXIE-16-based digital data acquisition system. The decay scheme was confirmed by using the $\gamma-\gamma$ matrix. To extract the lifetime of the excited states, we fitted the Doppler shift attenuated lineshape using the LINESHAPE code [6] for detectors placed at angles 23$^\circ$, 90$^\circ$, and 157$^\circ$. Two distinct gating conditions were employed—GTA (gating on transitions above) and GTB (gating on transitions below)—to obtain accurate lifetime values, as described in Ref. [7].
The coupled band based on the $\pi h_{11/2} \otimes \nu h_{11/2}$ configuration has been reported in earlier studies [8]. A band crossing in this band was also observed around $\hbar \omega$ ≈ 0.46 MeV. Lifetime measurements of this coupled band were performed by WANG Lie-Lin et al., [4] up to spin 18$^+$, by using a 7.06 mg/cm$^2$ thick $^{124}$Sn backed on lead with 6.7 mg/cm$^2$ thickness [4]. Using such a target in DSAM analysis causes the recoiling nuclei to slow down in two different media (Sn and Pb), leading to increased uncertainties in stopping powers and questioning the reliability of the extracted lifetimes [4]. Nevertheless, it is worth mentioning their results – a near constant B(E2) of 28 W.u. and a staggering in B(M1) values. In the present work, we have extended the lifetime measurements of this band up to spin 22$^+$, revealing deviations from the previously reported lifetimes [4]. Our analysis shows pronounced staggering in both B(E2) and B(M1) values, with an average B(E2) value of approximately 20 W.u. and B(M1) around 0.21 μ$_N^2$. Similar staggering behavior in B(E2) and B(M1) values has also been reported in neighboring isotopes of $^{124,126,128}$Cs [2]. Beyond the band crossing ($\hbar\omega$ ≈ 0.46 MeV), we observed a gradual increase in B(E2) values. To investigate the underlying structure, Ultimate Cranking calculations [9] were performed. The deformation parameters ($\beta$ ≈ 0.17, $\gamma$ ≈ 31$^\circ$ in the Lund convention), determined from the minimum energy solution, show the triaxial nature. Moreover, using the Routhian diagrams, we identified the band crossing due to neutron alignment in the $h_{11/2}$ orbital at frequency 0.48 MeV. We also identified the backbend at a frequency of 0.6 MeV, which is experimentally observed at 0.56 MeV in the present work.
We also studied the alignment of the negative-parity band based on the $\pi g_{7/2} \otimes \nu h_{11/2}$ configuration [8], revealing a backbend around $\hbar\omega$ ≈ 0.46 MeV. We measured the lifetimes of this band for the first time, obtaining values in the range of 0.55–1.2 ps. The B(E2) values initially decrease with spin and then increase near the crossing. This band also exhibits a triaxial shape, with deformation parameters $\beta$ ≈ 0.18 and $\gamma$ ≈ 33.7$^\circ$.
In summary, the coupled band based on $\pi h_{11/2} \otimes \nu h_{11/2}$ configuration has been re-examined through lifetime measurements up to spin 22$\hbar$, and the results have been compared with earlier studies. The deformation parameters ($\beta$ ≈ 0.17, $\gamma$ ≈ 31$^\circ$) were extracted using the Ultimate Cranking model, which also explains the observed band crossing. In addition, the lifetime of the negative-parity band has been measured, and its detailed analysis is currently underway.
References
[1] Yunzuo Liu et al., Phys. Rev. C 54, 719 (1996) and references therein.
[2] K. Selvakumar et al., Phys. Rev. C 92, 064307 (2015) and references therein.
[3] G. H. Bhat, J. A. Sheikh, and R. Palit, Phys. Lett. B 707, 250 (2012).
[4] WANG Lie-Lin et al, Chinese Physics C 33, 2009.
[5] R. Palit et al., Nucl. Instrum. Methods A 680, 90 (2012).
[6] J. C. Wells and N. R. Johnson ORNL report 689, 44 (1991).
[7] U. Lamani et al., Nucl. Phys. A 1014, 122220 (2021).
[8] R. Kumar et al. Eur. Phys. J. A 11, 5 (2001) and references therein.
[9] T. Bengtsson and I. Ragnarsson, Nucl. Phys. A 436, 14 (1985) and references therein.