Microscopic description of octupole collective excitations near $N=56$ and $N=88$

Octupole deformations and related collective excitations are analyzed using the framework of nuclear density functional theory. Axially symmetric quadrupole-octupole constrained self-consistent mean-field (SCMF) calculations with a choice of universal energy density functional and a pairing interaction are performed for Xe, Ba, and Ce isotopes from proton-rich to neutron-rich regions, and neutron-rich Se, Kr, and Sr isotopes, in which enhanced octupole correlations are expected to occur. Low-energy positive- and negative-parity spectra and transition strengths are computed by solving the quadrupole-octupole collective Hamiltonian, with the inertia parameters and collective potential determined by the constrained SCMF calculations. Octupole-deformed equilibrium states are found in the potential energy surfaces of the Ba and Ce isotopes with $N\approx 56$ and 88. The evolution of spectroscopic properties indicates enhanced octupole correlations in the regions corresponding to $N\approx Z\approx 56$, $Z\approx 88$ and $Z\approx 56$, and $N\approx 56$ and $Z\approx 34$. The average ${\beta }_{30}$ deformation parameter and its fluctuation exhibit signatures of octupole shape-phase transition around $N=56$ and 88.

Figure 1

SCMF $({\beta }_2,{\beta }_3)$ PESs for ${}^{108–118}\mathrm{Xe}$, ${}^{110–120}\mathrm{Ba}$, and ${}^{112–122}\mathrm{Ce}$. Global minima are identified by the red dots. Contours join points on the surface with the same energy, and the difference between neighboring contours is 1 MeV.

Figure 2

Same as in the caption to Fig. 1 but for ${}^{140–150}\mathrm{Xe}$, ${}^{142–152}\mathrm{Ba}$, and ${}^{144–154}\mathrm{Ce}$.

Figure 3

Same as in the caption to Fig. 1 but for the neutron-rich nuclei ${}^{86–96}\mathrm{Se}$, ${}^{88–98}\mathrm{Kr}$, and ${}^{90–100}\mathrm{Sr}$.

Figure 4

Same as in the caption to Fig. 1 but for the $N=56$ isotones from ${}^{90}\mathrm{Se}$ ($Z=34$) to ${}^{112}\mathrm{Ba}$ ($Z=56$).

Figure 5

Comparison of the QOCH and experimental low-energy excitation spectra for the positive- and negative-parity yrast states of ${}^{144}\mathrm{Ba}$ and ${}^{112}\mathrm{Xe}$. Solid and dashed arrows denote $E2$ and $E3$ transitions, respectively, and the corresponding $B\left(E2\right)$ and $B\left(E3\right)$ values are given in Weisskopf units. Experimental results are from Refs. [6, 51].

Figure 6

Probability density distributions for the lowest positive-parity ($0_1^{+}$) and negative-parity ($1_1^{-}$) states of ${}^{144}\mathrm{Ba}$ (upper) and ${}^{112}\mathrm{Xe}$ (lower) in the ${\beta }_2\text{−}{\beta }_3$ plane.

Figure 7

Evolution of QOCH excitation spectra for the positive-parity yrast states along the chains of Xe, Ba, and Ce isotopes. Experimental values are from the ENSDF database [51].

Figure 8

Same as in the caption to Fig. 7 but for the negative-parity states.

Figure 9

Same as in the caption to Fig. 7 but for the positive-parity states in Se, Kr, and Sr isotopes.

Figure 10

Same as in the caption to Fig. 7 but for the negative-parity states in Se, Kr, and Sr isotopes.

Figure 11

$B(\mathrm{E}2;2_1^{+}\to 0_1^{+})$ (top), $B(\mathrm{E}3;3_1^{-}\to 0_1^{+})$ (middle), and $B(\mathrm{E}1;1_1^{-}\to 0_1^{+})$ (bottom) reduced transition probabilities for the Xe, Ba, and Ce isotopes. Solid symbols connected by lines denote the QOCH results. Experimental values (open symbols) are taken from the ENSDF database [51].

Figure 12

Excitation spectra of the low-lying positive- (top row) and negative-parity (bottom row) yrast states of the $N=56$ isotones as functions of the proton number $Z$. The excitation spectra computed with the QOCH are plotted on the left-hand side of the figure, and are compared with the available experimental data [51] on the right.

Figure 13

Average values of the (a) ${\beta }_2$ and (b) ${\beta }_3$ deformation parameters in the $0_1^{+}$ ground state, $\overline{{\beta }_{\lambda }}=\sqrt{\langle {\beta }_{\lambda }^2\rangle }$, and the fluctuations (c) $\delta {\beta }_2/\overline{{\beta }_2}$ and (d) $\delta {\beta }_3/\overline{{\beta }_3}$, for the Xe, Ba, Ce, Se, Kr, and Sr isotopes as functions of the neutron number $N$. The variance $\delta {\beta }_{\lambda }$ is defined as $\delta {\beta }_{\lambda }=\sqrt{\langle {\beta }_{\lambda }^4\rangle -{\langle {\beta }_{\lambda }^2\rangle }^2}/2\overline{{\beta }_{\lambda }}$.