First Measurement of the $g$ Factor in the Chiral Band: The Case of the ${}^{128}\mathrm{Cs}$ Isomeric State

The $g$ factor of the 56 ns half-life isomeric state in ${}^{128}\mathrm{Cs}$ has been measured using the time-differential perturbed angular distribution method. This state is the bandhead of the positive-parity chiral rotational band, which emerges when an unpaired proton, an unpaired neutron hole, and an even-even core are coupled such that their angular momentum vectors are aplanar (chiral configuration). $g$-factor measurements can give important information on the relative orientation of the three angular momentum vectors. The measured $g$ factor $g=+0.59(1)$ shows that there is an important contribution of the core rotation in the total angular momentum of the isomeric state. Moreover, a quantitative theoretical analysis supports the conclusion that the three angular momentum vectors lie almost in one plane, which suggests that the chiral configuration in ${}^{128}\mathrm{Cs}$ demonstrated in previous works by characteristic patterns of electromagnetic transitions appears only above some value of the total nuclear spin.

Figure 1

Relevant part of the level scheme of ${}^{128}\mathrm{Cs}$ obtained in Ref. [9]. The assigned value of spin $I^{\pi }=9^{+}$ of the $T_{1/2}=56\mathrm{ns}$ isomeric state is compatible with the systematics of levels in the neighboring nuclei. Dashed arrows correspond to unobserved, highly converted transitions. The arrows with energy labels in parentheses indicate unobserved transitions included in the level scheme based on experimental arguments.

Figure 2

Experimental modulation ratios for the transitions involved in the isomeric decay and least-squares fits (red lines).

Figure 3

Core angular momentum ${\mathit{j}}_R$ may be coupled at different precession angles about the resultant ${\mathit{j}}_{pn}$ of proton and neutron angular momenta to form the specified spin of the isomeric state. The planar geometry where ${\mathit{j}}_R$ tends toward ${\mathit{j}}_p$ gives the highest possible value of the $g$ factor (0.6 for $j_p=j_n=11/2,j_R=2$). A second planar geometry where ${\mathit{j}}_R$ tends toward ${\mathit{j}}_n$ gives the lowest possible value of the $g$ factor (0.4 for $j_p=j_n=11/2,j_R=2$). Aplanar geometry corresponding to chiral configuration gives the $g$-factor value in between.

Figure 4

The normalized orientation parameter, Eq. (3), versus $g$-factor values for the three configurations $A$ (purple line), $B$ (blue line), and $C$ (red line) at $I=9\hslash$ calculated by PRM with varying triaxial deformation parameters from 0° to 60°. The experimental value is also shown for comparison (black solid line). See text for details.