Structure of the ${11/2}^{-}$ isomeric state in ${}^{133}\mathrm{La}$

We report measurement of the $g$-factor for the ${11/2}^{-}$ isomeric state at 535 keV in ${}^{133}\mathrm{La}$, employing the time differential perturbed angular distribution technique (TDPAD). This isomer was populated in the reaction ${}^{126}\mathrm{Te}({}^{11}\mathrm{B}$, $4n){}^{133}\mathrm{La}$ at beam energy of 52 MeV. From the observed nuclear spin precession, analysed through combined, magnetic dipole and electric quadrupole hyperfine interactions, we obtain the $g$ factor for the $11/2^{-}$ state as $g=1.16\pm 0.07$. In addition, this analysis provides the spectroscopic quadrupole moment $\left|Q\right|=1.71\pm 0.34b$, yielding the deformation parameter $\beta =0.28\pm 0.10$. Further, we have performed theoretical calculations using the large-scale shell model and the Monte Carlo shell model. The results successfully describe the low-lying levels and the band structures of ${}^{133}\mathrm{La}$, and the calculated $g$ factor compares well with the values obtained from our experiment. The dominant configuration of $11/2^{-}$ isomeric state in ${}^{133}\mathrm{La}$ is inferred to be $\pi \left(h_{11/2}\right)\otimes {}^{132}\mathrm{Ba}\left(0^{+}\right)$.

Figure 1

Schematic drawing of the experimental arrangement of the TDPAD setup.

Figure 2

Partial level scheme of ${}^{133}\mathrm{La}$ showing the isomer at 535 keV (adopted from Ref. [10]).

Figure 3

Lifetime decay spectrum obtained with energy gate on the 477 keV $\gamma$ line.

Figure 4

Spin rotation spectrum of $11/2^{-}$ isomeric state of ${}^{133}\mathrm{La}$ with $B_{\mathrm{ext}}=2\mathrm{T}$.

Figure 5

Level schemes of ${}^{133}\mathrm{La}$ by the experiments (left) and by the present LSSM calculation (right). The arrows denote the $B\left(E2\right)$ transition between the negative parity states, and their widths are proportional to the $B\left(E2\right)$ strengths with with the effective charges $(e_p,e_n)=(1.6,0.8)e$.

Figure 6

$T$ plot of the $11/2_1^{-}$ state in ${}^{133}\mathrm{La}$ coordinated by the intrinsic mass quadrupole moments, $Q_0$ and $Q_2$. The contour line shows the energy surface obtained by the $Q$-constrained Hartree-Fock method with the variation after parity projection. The locations of the circles indicate the intrinsic shape of the MCSM basis states. The size of each circle denotes the overlap probability of the MCSM basis state and the total wave function, namely its importance in the total wave function.