Sub-shell closure and shape coexistence in the transitional nucleus ${}^{98}\mathrm{Zr}$

In the rapid shape change from spherical to deformed nuclei in the $Z=40$ Zr isotopic chain, recent work has identified shape coexistence in ${}^{96}\mathrm{Zr}$. Between ${}^{96}\mathrm{Zr}$ and the strongly deformed ${}^{100}\mathrm{Zr}, {}^{98}\mathrm{Zr}$ is expected to also exhibit coexistence of nuclear shapes. The degree of mixing between different configurations is mainly determined by the nucleon-nucleon interactions. For nuclear model predictions, experimental constraints are needed, but they are barely available for ${}^{98}\mathrm{Zr}$. To study low-lying transitions in ${}^{98}\mathrm{Zr}$, a Coulomb excitation experiment was conducted at the Argonne Tandem-Linac Accelerator System (ATLAS) facility using a ${}^{98}\mathrm{Zr}$ beam extracted from the Californium Rare Ion Breeder Upgrade (CARIBU) ion source and Gamma-Ray Energy Tracking In-beam Nuclear Array (GRETINA) for $\gamma$-ray spectroscopy coupled to the compact heavy ion counter (CHICO2) for ion detection. This paper reports on the first decisive deduction of the $B(E2;2_1^{+}\to 0_1^{+})$ transition strength in ${}^{98}\mathrm{Zr}$ and on its interpretation.

Figure 1

Systematics of observables in the Zr isotopic chain: (a) Development of the low-lying level energies, (b) energy differences of $2^{+}$ and $0^{+}$ states, and (c) $R_{4/2}$ (blue, left-hand scale) and $B\left(E2\right)$ (red, right-hand scale) values of the ground states indicating a shape transition. Only a lower limit was available for the $B\left(E2\right)$ value for ${}^{98}\mathrm{Zr}$ prior to this work (shown by the arrow) and, hence, the (dashed) line linking ${}^{96}\mathrm{Zr}$ and ${}^{100}\mathrm{Zr}$ is simply to guide the eye.

Figure 2

Spectrum from GRETINA summed over all detector angles following Doppler correction for $A=98$ reaction products. The insert provides the difference in time of flight between the beam and the target nuclei over the scattering angle $\theta$. The selection of the $A=98$ ions is indicated by the dashed red line.

Figure 3

Doppler-corrected energy spectrum obtained with GRETINA summed over all detector angles. Shown in blue (lowest line at 1223 keV) is a fit to solely the $3_1^{-}\to 2_1^{+}$ transition peak of ${}^{98}\mathrm{Mo}$ at 1230 keV, in red (middle line at 1223 keV) and green (upper line at 1223 keV) hypothetical contributions of the $2_1^{+}\to 0_1^{+}$ transition of ${}^{98}\mathrm{Zr}$ at 1223 keV with 40 observed transition counts at the maximum possible FWHM (red, middle line) and best fitted value of the FWHM (green, upper line). See text for further details.

Figure 4

Experimental $B(E2;2_1^{+}\to 0_1^{+})$ values in the Zr chain and shell-model calculations (Sieja 2009 [30]) with standard (${\mathrm{e}}_{\mathrm{eff}}^{\nu }=0.5, {\mathrm{e}}_{\mathrm{eff}}^{\pi }=1.5$, shown by circles) and increased (${\mathrm{e}}_{\mathrm{eff}}^{\nu }=0.8, {\mathrm{e}}_{\mathrm{eff}}^{\pi }=1.8$, shown by stars) effective charges and recent Monte Carlo shell-model calculations (Togashi 2016 [14], shown by squares). The $B\left(E2\right)$ value of ${}^{98}\mathrm{Zr}$ is limited by previous work [18] (lower limit) and an upper limit was established in this work. Note the change of vertical scale above 20 W.u.