Examination of nuclear chirality with a magnetic moment measurement of the $I=9$ isomeric state in ${}^{128}\mathrm{Cs}$

The $g$ factor of the isomeric $I=9^{+}$ bandhead of the yrast states in ${}^{128}\mathrm{Cs}$ is obtained from the time differential perturbed angular distribution measurement performed with the electromagnet at IPN Orsay. An external magnetic field of 2.146 T at the target position was attained with GAMIPE reaction chamber surrounded by four high-purity germanium detectors, of which two were low-energy photon spectrometer type. The results are in accordance with $\pi h_{11/2}\otimes \nu h_{11/2}^{-1}I=9^{+}$ bandhead assignment and are discussed in the context of chiral interpretation of the ${}^{128}\mathrm{Cs}$ nucleus as a composition of the odd proton, odd neutron, and even-even core with their angular momentum vectors. The obtained $g$-factor value was compared with predictions of the particle-rotor model. The experimental $g$ factor corresponds to the nonchiral geometry of the isomeric bandhead. This observation indicates the existence of the chiral critical frequency in ${}^{128}\mathrm{Cs}$ and may explain the absence of the chiral doublet members for $I<13\hslash$.

Figure 1

Relevant part of the level scheme of ${}^{128}\mathrm{Cs}$ obtained in Ref. [9]. The decay of the isomeric state is reconstructed from coincidences collected between beam pulses and from prompt-delayed gamma coincidences. The two transitions represented by dashed lines, 18 and 5 keV, are below the sensitivity threshold of the experiment due to high electron-conversion decay mode.

Figure 2

GAMIPE reaction chamber, the $B$ field uniformity, and the beam spot.

Figure 3

Experimental geometry and timing resolution.

Figure 4

Experimental setup arrangement.

Figure 5

Background subtraction from the time spectrum of 152 keV peak.

Figure 6

Intensity oscillation spectra registered by LEPS detectors. Black lines shows the intensity registered at $+{45}^{\circ }$ with respect to beam axis while red lines show the intensity seen at $-{45}^{\circ }$. The intensity curves were normalized by multiplying the $-{45}^{\circ }$ spectrum by factor of 2.4.

Figure 7

Observed oscillating ratios $R\left(t\right)$

Figure 8

Core angular momentum ${\mathbf{j}}_R$ may be coupled at different precession angles about the resultant ${\mathbf{j}}_{pn}$ of proton and neutron angular momentum to form the specified spin of the isomeric state. The planar geometry where ${\mathbf{j}}_R$ tends toward ${\mathbf{j}}_p$ gives the highest possible value of the $g$ factor. The second planar geometry where ${\mathbf{j}}_R$ tends toward ${\mathbf{j}}_n$ gives the lowest possible value of the $g$ factor. Aplanar geometry corresponding to chiral configuration gives the $g$-factor value in between.

Figure 9

The $g$-factor value expected for coupling of $\pi h_{11/2}\otimes \nu h_{11/2}^{-1}$ and core angular momenta $j_R=2\hslash$ (upper panel) and $j_R=4\hslash$ (lower panel) to the total spin $I=9\hslash$ of the isomeric state. Experimental values of $g_p$ and $g_n$ estimated from the $h_{11/2}$ orbital in single-odd neighboring nuclei were used.

Figure 10

(a) The energy spectra, (b) the intraband $B\left(E2\right)$, (c) the intraband $B\left(M1\right)$, and (d) the interband $B\left(M1\right)$ of the doublet bands in ${}^{128}\mathrm{Cs}$ calculated by the PRM approach in comparison with the experimental data available [3].

Figure 11

The $g$-factor values for the $9^{+}$ yrast bandhead as a function of triaxial deformation calculated by PRM with configurations $\pi h_{11/2}\otimes \nu h_{11/2}^{-5}, \pi h_{11/2}\otimes \nu h_{11/2}^{-3}$, and $\pi h_{11/2}\otimes \nu h_{11/2}^{-1}$.

Figure 12

The $g$-factor values as functions of spin expected for $\pi h_{11/2}\otimes \nu h_{11/2}^{-5}$ yrast band levels with triaxial deformation parameters $\gamma =0^{\circ }, {24}^{\circ }, {30}^{\circ }$, and ${38}^{\circ }$.

Figure 13

The absolute values of angular momentum of proton $j_p$, neutron $j_n$, and core $j_R$ as functions of spin expected for $\pi h_{11/2}\otimes \nu h_{11/2}^{-5}$ yrast band levels with triaxial deformation parameters $\gamma ={24}^{\circ }$.