Evolution of octupole deformation and collectivity in neutron-rich lanthanides

The onset of octupole deformation and its impact on related spectroscopic properties is studied in even-even neutron-rich lanthanide isotopes Xe, Ba, Ce, and Nd with neutron number $86⩽N⩽94$. Microscopic input comes from the Hartree-Fock-Bogoliubov approximation with constrains on the axially symmetric quadrupole and octupole operators using the Gogny-D1M interaction. At the mean-field level, reflection asymmetric ground states are predicted for isotopes with neutron number around $N=88$. Spectroscopic properties are studied by diagonalizing the interacting boson model Hamiltonian, with the parameters obtained via the mapping of the mean-field potential energy surface onto the expectation value of the Hamiltonian in the $s, d$, and $f$ boson condensate state. The results obtained for low-energy positive- and negative-parity excitation spectra as well as the electric dipole, quadrupole, and octupole transition probabilities indicate the onset of pronounced octupolarity for $Z\approx 56$ and $N\approx 88$ nuclei.

Figure 1

The SCMF-PESs obtained for ${}^{140-148}\mathrm{Xe}, {}^{142-150}\mathrm{Ba}, {}^{144-152}\mathrm{Ce}$, and ${}^{146-154}\mathrm{Nd}$ are plotted as functions of the quadrupole ${\beta }_2$ and octupole ${\beta }_3$ deformation parameters. 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

The strength parameters (a) ${\epsilon }_d$, (b) ${\epsilon }_f$, (c) ${\kappa }_2$, (d) ${\chi }_f$, (e) ${\chi }_d$, (f) ${\kappa }_3$, (g) $\rho$, and (h) ${\chi }_3$ of the $sdf$-IBM Hamiltonian (1), and the coefficients (i) $C_2$ and (j) $C_3$ are plotted as functions of the neutron number for the studied isotopic chains. The boson effective charges for the quadrupole $e_2$ and octupole $e_3$ transitions are also plotted in panels (k) and (l), respectively.

Figure 4

The low-energy excitation spectra of positive-parity even-spin yrast states in ${}^{140-148}\mathrm{Xe}, {}^{142-150}\mathrm{Ba}, {}^{144-152}\mathrm{Ce}$ and ${}^{146-154}\mathrm{Nd}$, computed by diagonalizing the mapped $sdf$-IBM Hamiltonian (1), are shown as functions of the neutron number. Experimental data have been taken from Ref. [76].

Figure 5

The same as in Fig. 4 but for odd-spin negative-parity yrast states.

Figure 6

The same as in Fig. 4 but for the $0_2^{+}, 2_2^{+}$, and $4_2^{+}$ states. The experimental data are taken from Refs. [76, 77].

Figure 7

The same as in Fig. 4 but for the $2_3^{+}, 3_1^{+}, 4_3^{+}$, and $5_1^{+}$ states. The experimental data are taken from Refs. [76, 77].

Figure 8

The expectation values of the $f$-boson number operator $\langle \widehat{n_f}\rangle$ in the IBM wave functions corresponding to the states (a) $0_1^{+}$, (b) $2_1^{+}$, (c) $0_2^{+}$, (d) $2_2^{+}$, (e) $1_1^{-}$, and (f) $3_1^{-}$ are plotted as functions of the neutron number.

Figure 9

The energy displacement $\delta E\left(I^{-}\right)$ (4) is plotted as a function of the neutron number. The theoretical values are connected by lines. Experimental values [76] for the $I^{\pi }=1^{-}, 3^{-}, 5^{-}, 7^{-}$, and $9^{-}$ yrast states are represented by open circles, squares, diamonds, and left- and right-pointing triangles, respectively. A broken horizontal line in each panel stands for the limit of stable octupole deformation $\delta E\left(I^{-}\right)=0$.

Figure 10

The energy ratio $E\left(I^{\pi }\right)/E\left(2_1^{+}\right)$ is depicted as a function of the spin $I^{\pi }$. For more details, see the main text.

Figure 11

The $B(E1;1_1^{-}\to 0_1^{+})$ (top), $B(E2;2_1^{+}\to 0_1^{+})$ (middle), and $B(E3;3_1^{-}\to 0_1^{+})$ (bottom) reduced transition probabilities (in Weisskopf units) are compared with the experimental data [5, 6, 76, 81].

Figure 12

The theoretical quadrupole $Q_2(I\to I-2)$ (top), octupole $Q_3(I\to I-3)$ (middle), and $Q_3(I\to I-1)$ (bottom) moments in $e{\mathrm{fm}}^{\lambda }$ units are plotted as as functions of the spin $I$. Even- (Odd-) $I$ values correspond to positive- (negative-) parity states.

Figure 13

Comparison of the theoretical and experimental low-energy level schemes of (a) ${}^{144}\mathrm{Ba}$, (b) ${}^{148}\mathrm{Nd}$, and (c) ${}^{150}\mathrm{Nd}$. The experimental data have been taken from Ref. [76].