Nuclear structure of ${}^{126}\mathrm{Xe}$

Background: The $\left(N<82\right)\mathrm{Xe}$ isotopes with only four valence protons are known to be γ soft and to have the spectrum similar to the O(6) limiting symmetry.

Purpose: Study the validity of the $\mathrm{O}\left(6\right)\supset \mathrm{O}\left(5\right)$ symmetry in the various vibrational bands of the $N=72 {}^{126}\mathrm{Xe}$ isotope.

Methods: Comparison of the ${}^{126}\mathrm{Xe}$ spectrum with O(6) symmetry. Apply the microscopic theory of dynamic pairing plus quadrupole (DPPQ) model and the interacting boson model (IBM-1). The energy spectrum, absolute $B\left(\mathrm{E}2\right)$ values and E2 transition ratios are evaluated. The odd-even spin staggering in the γ band is displayed, and the potential-energy plot is used to determine the shape of the nucleus.

Results: The predictions of the eigenvalues and the $B\left(\mathrm{E}2\right)$ values and the interband $B\left(\mathrm{E}2\right)$ ratios extended over the five excited bands up to $\tau =5$ in the O(6) multiplet view. The O(5) symmetry is well preserved, and the O(6) symmetry is slightly broken.

Conclusions: The predictions in the DPPQ model provide an alternative framework to the fluctuations in the O(6) quantum numbers in the IBM framework. The DPPQ model predictions are in fair agreement with experiment. The IBM-1 predictions provide a complementary view.

Figure 1

Pattern of O(6) symmetry spectrum (partial), $({\nu }_{\mathrm{d}}={\nu }_{\mathrm{\Delta }})$.

Figure 2

The partial energy-level spectrum of ${}^{118–130}\mathrm{Xe}$.

Figure 3

Energy ratio $R_{I/2}$ of the ground band of ${}^{126}\mathrm{Xe}$ compared to O(5) symmetry.

Figure 4

Partial level energy spectrum of ${}^{126}\mathrm{Xe}$ in experiment.

Figure 5

Partial energy spectrum of ${}^{126}\mathrm{Xe}$ in IBM-1 (set 2).

Figure 6

Partial energy spectrum of ${}^{126}\mathrm{Xe}$ in the DPPQ model.

Figure 7

Plot of OES index $S$($I$) for ${}^{124,126}\mathrm{Xe}$.

Figure 8

Plot of $V(\beta ,\gamma =0^{\circ })$ for ${}^{126}\mathrm{Xe}$ from the DPPQ model.