Medium-spin γ-ray spectroscopy of the transitional nucleus ${}^{160}\mathrm{Er}$

The nucleus ${}^{160}\mathrm{Er}$, with the structural parameter $R_{4/2}=E(4_1^{+})/E(2_1^{+})=3.10$, falls on the transition path between the critical point of the vibrator-rotor shape phase transition and the rigid rotor limit, thus serving as a critical test of the CBS rotor model, which describes this transition region. Medium-spin states of ${}^{160}\mathrm{Er}$ have been populated via the reaction ${}^{159}\mathrm{Tb}$(${}^6\mathrm{Li}$,5n) and new levels have been identified and interpreted as the even-spin members of the γ band and members of the β vibrational band. Level energies and branching ratios are compared to the CBS rotor model predictions.

Figure 1

(Color online) Schematic structural triangle for the nuclear collective model [9] where the vertices represent idealized limits of structure and the legs transition regions. The CBS model describes the transition region from X(5) to the symmetric rigid rotor (dashed line). Nuclides with $R_{4/2}=3.1$ (e.g.,${}^{164}\mathrm{Yb}$, ${}^{168}\mathrm{Hf}$, and ${}^{160}\mathrm{Er}$, on which this paper focuses) might be intermediate between X(5) and the rigid rotor.

Figure 2

$\gamma \gamma$-coincidence projection from the ${}^{159}\mathrm{Tb}$(${}^6\mathrm{Li}$,5$n){}^{160}\mathrm{Er}$ experiment with the ground band transitions in ${}^{160}\mathrm{Er}$ labeled.

Figure 3

(Color online) Coincidence relationship between the $6^{+}\to 4^{+}$ (upper spectrum) and $8^{+}\to 6^{+}$ (lower spectrum) ground band transitions showing the placement of the $8_{\beta }^{+}\to 6^{+}$ (1156-keV) and the $8_{\gamma }^{+}\to 6^{+}$ (1185-keV) transitions.

Figure 4

Partial level scheme of ${}^{160}\mathrm{Er}$ observed in this experiment. The observation of the 439- and 312-keV transitions (labels in parentheses) are uncertain owing to contaminants in the reaction. The dashed levels were not identified in this experiment but seen in prior β-decay experiments [13].

Figure 5

(Color online) Angular correlation analysis of two known (pure $E2$ and pure $E1$) transitions showing the quality of data produced at SUNY Stony Brook's Stony Cube setup. The coincidence groups are labeled by three integers, which denote in units of $\pi /4$ the two angles between the observational directions and the beam and between the planes defined by the beam and the γ-decay directions.

Figure 6

(Color online) Assignment of spin quantum number $J=14$ for the 3373.5-keV level from the $\gamma \gamma$ angular correlation analysis. The solid squares show the relative intensities of the 1031.5-keV γ ray in coincidence with a member of the ground band. All of the $\gamma \gamma$ coincidences between the 1031.5-keV transition and any member of the ground band were summed to reduce the background. The multipole mixing ratio δ was treated as a free parameter in the case of the $J=13$ hypothesis.

Figure 7

(Color online) Measurement of spin quantum number $J=6$ for the 1499.3-keV level from the $\gamma \gamma$ angular correlation analysis. Also shown for comparison is the simulation for a $J=5$ hypothesis. In both cases the multipole mixing ratio δ was treated as a free parameter.

Figure 8

Systematics of γ, yrast, and β bands (left to right) of erbium isotopes showing the smooth variation in energy levels of the newly found excited states in ${}^{160}\mathrm{Er}$ as a function of neutron number. Data for neighboring isotopes are taken from [15].

Figure 9

(Color online) Evolution of the relative moment of inertia [${\theta }_K(J)/{\theta }_K(K\hspace{1em}+\hspace{1em}$2) as defined in Eq. (7)] as a function of spin for the ground band (upper graph) β vibrational band (center graph) and γ vibrational band (lower graph) with the CBS rotor model predictions (solid curve). The curve in middle graph is normalized to the lowest transition observed in our data [i.e., ${\theta }_0(J)/{\theta }_0(6)$ is what is plotted].

Figure 10

(Color online) Measured interband to intraband branching ratios for transitions of known pure E2 character in the β band. IBM predictions (parameters for ${}^{160}\mathrm{Er}$ taken from [10]) are given by the dotted blue curve. The solid green curve shows the CBS rotor model's predictions. The dashed green curve shows the CBS model's predictions with inclusion of a higher order term in β for the E2 operator with expansion parameter χ [see Ref. 6 for the definition of $T(E2)$ to second order], which was found from a fit to the known absolute $B(E2)$ values [25] in the ground band. Therefore, we should stress that both curves are parameter-free predictions of these branching ratios.