Quadrupole-octupole coupling and the evolution of collectivity in neutron-deficient Xe, Ba, Ce, and Nd isotopes

The evolution of quadrupole and octupole collectivity in neutron-deficient Xe, Ba, Ce, and Nd nuclei near the “octupole magic” neutron number $N=56$ is investigated within the mapped $sdf$-IBM framework. Microscopic input is obtained via quadrupole and octupole constrained Hartree-Fock-Bogoliubov calculations, based on the parametrization D1M of the Gogny energy density functional. Octupole-deformed mean-field ground states are predicted for Ba and Ce isotopes near $N=56$. Excitation energies of positive- and negative-parity states as well as electric transition rates are computed with wave functions resulting from the diagonalization of the mapped IBM Hamiltonian. The parameters of the Hamiltonian are determined via the mapping of the mean-field potential energy surfaces onto the expectation value of the Hamiltonian in the condensate state of the $s$, $d$, and $f$ bosons. Enhanced octupolarity is predicted for Xe, Ba, and Ce isotopes near $N=56$. The shape/phase transition from octupole-deformed to strongly quadrupole-deformed near $N=60$ is analyzed in detail.

Figure 1

SCMF-PESs, as functions of the quadrupole ${\beta }_2$ and octupole ${\beta }_3$ deformations, for ${}^{108\text{–}118}\mathrm{Xe}$, ${}^{110\text{–}120}\mathrm{Ba}$, ${}^{112\text{–}122}\mathrm{Ce}$, and ${}^{114\text{–}124}\mathrm{Nd}$. The color code indicates the total HFB energies (in MeV) plotted up to 5 MeV with respect to the global minimum. The energy difference between neighboring contours is 0.2 MeV. For each nucleus, the global minimum is indicated by a red solid circle. Results have been obtained with the Gogny-D1M EDF.

Figure 2

The same as in Fig. 1, but for the mapped IBM-PESs.

Figure 3

Strength parameters (a) ${\epsilon }_d$, (b) ${\epsilon }_f$, (c) ${\kappa }_2$, (d) ${\chi }_d$, (e) ${\chi }_f$, (f) $\rho$, and (g) ${\kappa }_3$, of the $sdf$-IBM Hamiltonian (1), and the coefficients (h) $C_2$ and (i) $C_3$. for the studied isotopic chains. For more details, see the main text.

Figure 4

The low-energy excitation spectra of positive-parity ($\pi =+1$) even-spin yrast states obtained for ${}^{108\text{–}118}\mathrm{Xe}$, ${}^{110\text{–}120}\mathrm{Ba}$, ${}^{112\text{–}122}\mathrm{Ce}$, and ${}^{114\text{–}124}\mathrm{Nd}$ are compared with the available experimental data [86]. Theoretical (experimental) values are represented by filled (open) symbols connected by solid (dotted) lines.

Figure 5

The same as in Fig. 4, but for the negative-parity ($\pi =-1$) odd-spin states.

Figure 6

The same as in Fig. 4, but for the quasi-$\beta$ band states.

Figure 7

The same as in Fig. 4, but for the quasi-$\gamma$ band states.

Figure 8

The expectation values of the $f$-boson number operator $\langle \widehat{n_f}\rangle$ in the IBM wave functions corresponding to the $K=0_1^{+}$(a) and $K=0_1^{-}$ (b) states, the quasi-$\beta$ (c) and quasi-$\gamma$ (d) bands of Xe isotopes.

Figure 9

Experimental and predicted band structures in ${}^{114}\mathrm{Xe}$, ${}^{116}\mathrm{Xe}$, and ${}^{118}\mathrm{Xe}$.

Figure 10

The calculated $B(E1;1_1^{-}\to 0_1^{+})$ (a), $B(E2;2_1^{+}\to 0_1^{+})$ (c), and $B(E3;3_1^{-}\to 0_1^{+})$ (e) reduced transition probabilities in Weisskopf units (W.u.), represented by the solid symbols connected by lines. Experimental data for the Xe nuclei are taken from [12, 16, 86, 87], and are represented by the open symbols. Note that the error bars for the experimental $B\left(E2\right)$ rates of ${}^{114,116,118}\mathrm{Xe}$ are not shown, as they are smaller than the marker size.

Figure 11

The energy displacement $\delta E_{I^{-}}$ (4) is plotted as a function of the neutron number. Theoretical values are connected by lines. Experimental values [86] for the $I^{\pi }=3^{-}$, $5^{-}$, $7^{-}$, and $9^{-}$ yrast states are represented by open squares, diamonds, and left- and right-pointing triangles, respectively. A broken horizontal line in each panel stands for the limit of stable octupole deformation $\delta E_{I^{-}}=0$.

Figure 12

The energy ratio $E\left(I^{\pi }\right)/E\left(2_1^{+}\right)$ is plotted as a function of spin $I^{\pi }$, with $\pi =+1$ for even-$I$ and $\pi =-1$ for odd-$I$ yrast states. The available experimental data for the Xe, Ba, and Ce isotopes are taken from [86].

Figure 13

Effective quadrupole (a) and octupole (b) deformations $\langle {\beta }_{\lambda }\rangle$ and fluctuations $\sigma \left({\beta }_{\lambda }\right)$ in the ${\beta }_2$ (c) and ${\beta }_3$ (d) deformations. For more details, see the main text.