Shape coexistence and evolution in ${}^{98}\mathrm{Sr}$

Shape coexistence between the strongly deformed ground state and the weakly deformed $0_2^{+}$ state in ${}^{98}\mathrm{Sr}$ has been a major topic of interest due to the energy difference of 215 keV, which is the smallest in all even-even nuclei. The electric monopole transition strength ${\rho }^2\left(E0\right)$ is an important quantity that can relate the deformation difference and the shape mixing between the two $0^{+}$ states, which are admixtures of the vibrational (S) and the rotational (D) states in a simple mixing model. In a $\beta$-decay spectroscopy experiment, the experimental ${\rho }^2\left(E0\right)$ was measured. A value of 0.053(5) is consistent with the previous measurement and was combined with known electric quadrupole transition strengths $B\left(E2\right)$ in calculations of a two-state mixing model. Based on a systematic study on neighboring Kr, Zr, and Mo isotopes, the mixing of the $0^{+}$ and $2^{+}$ states in ${}^{98}\mathrm{Sr}$ was determined to be 8.6% and 1.3%, respectively, corresponding to deformation parameters ${\beta }_{\text{D}}=0.38\left(1\right)$ and ${\beta }_{\text{S}}=-0.23\left(2\right)$. These parameters reproduce experimental transition strengths well except for the $4_1^{+}\to 2_1^{+}$ transition, which suggests a smaller D-band deformation for $J\ge 4$.

Figure 1

Systematic of low-lying $0^{+}$ and $2^{+}$ states in Sr isotopes around $N=60$. A sudden deformation in the ground state of ${}^{98}\mathrm{Sr}$ occurs as the two $0^{+}$ states with very different shapes undergo order inversion at $N=60$. The data for these nuclei are taken from Refs. [7, 8, 9, 10, 11, 12].

Figure 2

Energy spectrum of PACES after gating on the 656-keV $\gamma$ ray detected in the $8\pi$ spectrometer. The insert shows a partial level scheme of ${}^{98}\mathrm{Sr}$.

Figure 3

Deformation parameters obtained from experimental $B(E2;2_1^{+}\to 0_1^{+})$ of nuclei around ${}^{98}\mathrm{Sr}$, assuming zero shape mixing. A quadratic fit of $\beta$ was performed on Sr isotopes with $N<60$ to estimate the root-mean-square value of the S-band deformation. The data are taken from Refs. [7, 10, 11, 12, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39].

Figure 4

Experimental $R_{42}$ of well-deformed $N\ge 60$ isotopes of Sr, Zr, and Mo. A quadratic fit on $R_{42}$ of Zr isotopes was applied, and the trend was shifted by the $R_{42}$ difference at $N=62$ to estimate the unperturbed $R_{42}$ for ${}^{98}\mathrm{Sr}$ to be used in the bandhead $E\left(0_{\text{D}}\right)$ and $\mathrm{\Delta }{E}_2$ estimation. The data are taken from Refs. [10, 11, 12, 35, 36, 37, 38, 39, 41, 42, 43].

Figure 5

$1\sigma$ confidence interval bands of the four experimental quantities as functions of ${\beta }_{\text{D}}$ and ${\beta }_{\text{S}}$, at given mixing energies and amplitudes. A ${\chi }^2$ minimization was applied to obtain ${\beta }_{\text{D}}=0.381\left(6\right)$ and ${\beta }_{\text{S}}=-0.233\left(17\right)$, whose uncertainties are bounds of the $1\sigma$ contour from the fit. The large discrepancy in ${\beta }_{\text{D}}$ with the experimental $B(E2;4_1^{+}\to 2_1^{+})$ value suggests a shape reconfiguration into a smaller deformation of the D-band at higher spins.