Tests of collectivity in ${}^{98}\mathrm{Zr}$ by absolute transition rates

Lifetimes of low-spin excited states in ${}^{98}\mathrm{Zr}$ were measured using the recoil-distance Doppler-shift technique and the Doppler-shift attenuation method. The nucleus of interest was populated in a ${}^{96}\mathrm{Zr}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{98}\mathrm{Zr}$ two-neutron transfer reaction at the Cologne FN Tandem accelerator. Lifetimes of six low-spin excited states, of which four are unknown, were measured. The deduced $B\left(E2\right)$ values were compared with Monte Carlo shell model and interacting boson model with configuration mixing calculations. Both approaches reproduce well most of the data but leave challenging questions regarding the structure of some low-lying states.

Figure 1

The energies of the first excited $2^{+}$ states for Zr and Sr isotopes with $N=52\text{–}62$ (symbols connected by a solid line), together with the $B(E2;2_1^{+}\to 0_1^{+})$ (symbols connected by a dashed line). Data are taken from the nuclear data sheets [7, 8, 9, 10, 11, 12, 13]. The $B(E2;2_1^{+}\to 0_1^{+})$ value for ${}^{98}\mathrm{Zr}$ is taken from Ref. [14].

Figure 2

Particle-gated $\gamma$-ray singles spectrum of both detector rings for plunger distance of $22\mu \mathrm{m}$. (a) and (b) show different cutouts of the spectrum. The transitions belonging to ${}^{98}\mathrm{Zr}$ are indicated and colored in red. The peaks belonging to the Coulomb excitation in the ${}^{181}\mathrm{Ta}$ stopper are indicated with an asterisk.

Figure 3

Level scheme of ${}^{98}\mathrm{Zr}$ populated in the ${}^{96}\mathrm{Zr}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{98}\mathrm{Zr}$ two-neutron transfer reaction at beam energy of 50 MeV. The width of the lines are proportional to the transition intensities given in Table 1.

Figure 4

Particle-$\gamma$ gated $\gamma$-ray spectrum of both detector rings for a plunger distance of $22\mu \mathrm{m}$. The transitions belonging to ${}^{98}\mathrm{Zr}$ are indicated and colored in red.

Figure 5

Particle-gated spectra of the backward detector ring for all distances (indicated in the top-right corner) of the $4_2^{+}\to 3_1^{-}$ (left), the $3^{-}\to 2_1^{+}$, the $4_1^{+}\to 2_1^{+}$ (middle), and the $2_1^{+}\to 0_1^{+}$ (right) transitions used to obtain the shifted (dashed red) and the unshifted (blue) intensities. The horizontal dashed lines represent the level of the background used for the determination of the peak areas were obtained.

Figure 6

Fitted decay curve together with the data points for the $4_2^{+}$ state using the $4_2^{+}\to 3_1^{-}$ transition observed at backwards angle. The obtained lifetime is given as well.

Figure 7

Same as Fig. 6 but for the $2_2^{+}\to 0_1^{+}$ transition.

Figure 8

Fitted decay curve together with the data points: (a) and (b) for the $4_1^{+}$ state, (c) and (d) for the $3_1^{-}$, and (e) and (f) for $2_1^{+}$. The upper panel is for the backward detector ring, and the lower panel is for the forward detector ring.

Figure 9

DDCM analysis (see text) of the backward-detector ring for the $4_1^{+}$ state (a)–(c), for the $3_1^{-}$ state (d)–(f), and for the $2_1^{+}$ state (g)–(i). The individual lifetimes obtained in the analysis are displayed in the upper panel. The middle panel shows the evolution of the shifted component and the fit to it used to obtain the derivative $d\left[S_i\left(x\right)\right]/dx$. The lower panel shows the evolution of the unshifted component and the fit to it used to obtain the individual lifetimes.

Figure 10

DSA fits to the Doppler-broadened line shapes of the $2_3^{+}\to 2_1^{+}$ transition for the (a) $22\text{−}\mu \mathrm{m}$ and the (b) $41\text{−}\mu \mathrm{m}$ distances of the forward detector ring used to obtain the lifetime of the $2_3^{+}$ state.

Figure 11

(a) Experimental and (b) calculated [25, 26] energy levels in MeV and $E2$ rates in W.u. for ${}^{98}\mathrm{Zr}$. Levels marked in blue (black) indicate states assigned to the $A$-normal ($B$-intruder) configuration. $E2$ transitions strengths marked in red are from the current paper.

Figure 12

$E2$ transition rates in W.u. for $2^{+}\to 0^{+}$ transitions within the intruder-$B$ configuration for the Zr isotopes. The symbols ($•$, $\blacksquare ,▴$, and $♦$) denote experimental rates. The dashed line depicts the IBM-CM-1 calculation of Ref. [25]. The data for ${}^{94}\mathrm{Zr},{}^{96}\mathrm{Zr},{}^{100}\mathrm{Zr},{}^{102}\mathrm{Zr}$, and (${}^{104}\mathrm{Zr},{}^{106}\mathrm{Zr}$) are taken from Refs. [3, 4, 13, 42, 46], respectively. For ${}^{98}\mathrm{Zr}$, the experimental values are from the current paper ($♦$), from Ref. [14] ($▴$), and the black upper and lower limits are from Refs. [42, 45]. Note that the explicit experimental values in ${}^{98}\mathrm{Zr}$ deviate from one another as well as from the calculated values of the IBM-CM-1 (43.39 W.u.) and of the MCSM (70 W.u.).