Low-$Z$ boundary of the $N=88$–90 shape phase transition: ${}^{148}\mathrm{Ce}$ near the critical point

Excited states of the neutron-rich nucleus ${}^{148}\mathrm{Ce}$ have been populated by neutron-induced fission of a ${}^{235}\mathrm{U}$ target. Its electromagnetic decays were studied by means of $\gamma$-ray coincidence spectroscopy with fast-timing capabilities. Lifetimes of the $2_1^{+}$ and $4_1^{+}$ states of ${}^{148}\mathrm{Ce}$ were obtained and their $E2$ decay rates deduced. The $B_{4/2}=B(E2;4_1^{+}\to 2_1^{+})/B(E2;2_1^{+}\to 0_1^{+})$ ratio indicates that ${}^{148}\mathrm{Ce}$ is a transitional nucleus while the $N=88/90$ shape phase transition evolves into a gradual change of nuclear deformation for proton numbers $Z<60$.

Figure 1

(a) $R_{4/2}$ ratio for Gd, Sm, Nd, and Ce isotopic chains as a function of neutron number. The sharp transition of Gd and Sm from spherical nuclei ($R_{4/2}=2$) to deformed ones ($R_{4/2}=3.33$) is not present in Nd and Ce chains. (b) $B_{4/2}$ ratios for Gd, Sm, and Nd isotopic chains as a function of neutron number. The transition from $N=88$ to $N=90$ from near spherical symmetry to $\gamma$-rigid and $\gamma$-soft symmetry is sharp for Gd and Sm but not for Nd. Data taken from [12].

Figure 2

(a) Energy spectra from the EXILL&FATIMA array gated on the $6_1^{+}\to 4_1^{+}$ transition of ${}^{148}\mathrm{Ce}$ in EXILL, Ge [blue (lower)] and ${\mathrm{LaBr}}_3$ [red (upper)]. The gates in FATIMA detectors are marked with light gray. Combinations of those were set in order to get the time-difference spectra for the lifetime. The inset spectra (${\mathrm{LaBr}}_3$) is generated by setting an energy gate on the EXILL detectors on the $2_1^{+}\to 0_1^{+}$ transition and an energy gate on the FATIMA detectors on the $6_1^{+}\to 4_1^{+}$ transition. Three possible backgrounds under the full-energy peak are shown. (b) The black curve corresponds to the time-difference spectrum obtained from gates A and B, with the delayed and reflected antidelayed spectra summed in order to accommodate the full statistics. The red curve depicts the background-subtracted time-difference spectrum, with the delayed and the reflected antidelayed spectra summed up. Note that the black curve is multiplied by a factor of 10 for better visibility.

Figure 3

(a) The time-difference spectra (delayed and antidelayed) for the lifetimes of the $4_1^{+}$ states of ${}^{148}\mathrm{Ce}$. (b) The time-background under the full-energy peak of the $4_1^{+}\to 2_1^{+}$ transition was interpolated from background areas around the peak (see text).

Figure 4

(a) The ${\mathrm{B}}_{4/2}$ ratio for $N=90$ isotones. All isotopes lie near the QSPT with the exception of ${}^{152}\mathrm{Sm}$ which deviates towards the rigid rotor. Data taken from [12].${}^{*}$The CBS line is adjusted to the experimental ${\mathrm{R}}_{4/2}$ ratio of ${}^{152}\mathrm{Sm}$ with $r_{\beta }=0.14$ [4]. (b) Energy ratios of ${}^{148}\mathrm{Ce}$. Comparison of experimental data with vibrator, rigid rotor, X(5) and X(5)-${\beta }^8$ models.

Figure 5

PT lines for several boson numbers, 5–12, 50, and 250. For increasing boson number the PT line moves towards smaller values of $\zeta$ (from right to left for increasing boson number).

Figure 6

Placement of ${}^{148}\mathrm{Ce}$ into the IBM symmetry triangle of the IBM. The two contours ($R_{4/2}$ and $R_{0\gamma }$) fitting the experimental data are shown.

Figure 7

Trajectories of (a) cerium and (b) samarium isotopes in the IBM symmetry triangle. For ${}^{144}\mathrm{Ce}$ the observable $R_{\gamma }$ is unknown hence its $R_{4/2}$ contour is shown with a dashed line which is located entirely on the spherical side of the PT line. ${}^{144}\mathrm{Ce}$ is classified as spherical. The PT lines corresponding to the valence boson number of the isotopes are also plotted (from right to left for increasing boson number). (c) Comparison of the trajectories of the cerium, neodymium, and samarium isotopic chains inside the triangle as a function of neutron number.

Figure 8

Comparison of energy spectra of the adopted experimental data for $N=90$ isotones. The energies of the levels of each isotope are normalized to the energy of the $2_1^{+}$ state which is shifted to 100 keV. The $0_2^{+}$ states are plotted with light blue and the $2_{\gamma }^{+}$ states are plotted with green. The trend of the $2_{\gamma }^{+}$ shows an decreasing $\gamma$-softness around ${}^{152}\mathrm{Sm}$.

Figure 9

(a) Self-consistent triaxial quadrupole constrained energy surfaces in the $\beta \text{−}\gamma \mathrm{plane}(0\le \gamma \le {60}^{\circ }$). (b–f) Probability distributions in the $\beta \text{−}\gamma$ plane for the wave function of the lowest collective $0^{+}$ and $2^{+}$ states of ${}^{148}\mathrm{Ce}$.