Recoil distance method lifetime measurement of the $2_1^{+}$ state in ${}^{94}\mathrm{Sr}$ and implications for the structure of neutron-rich Sr isotopes

A high precision lifetime measurement of the $2_1^{+}$ state in ${}^{94}\mathrm{Sr}$ was performed at TRIUMF's ISAC-II facility by coupling the recoil distance method implemented via the TIGRESS integrated plunger with unsafe Coulomb excitation in inverse kinematics. Due to limited statistics imposed by the use of a radioactive ${}^{94}\mathrm{Sr}$ beam, a likelihood ratio ${\chi }^2$ method was derived and used to compare experimental data to Geant4 simulations. The $B(E2;2_1^{+}\to 0_1^{+})$ value extracted from the lifetime measurement of $7.{80}_{-0.40}^{+0.50}\text{(stat.)}\pm 0.07\text{(sys.)}$ ps is approximately 25% larger than previously reported while the relative error has been reduced by a factor of approximately 8. A baseline deformation has been established for Sr isotopes with $N\le 58$ which is a necessary condition for the quantum phase transition interpretation of the onset of deformation in this region. A comparison to existing theoretical models is presented.

Figure 1

A particle identification plot for a single CsI(Tl) detector. The PID scheme in the data analysis is performed on a detector-by-detector basis and can distinguish between (a) electrons from the ${\beta }^{-}$ decay of the implanted radioactive beam and (b) Al recoils arising from Coulomb excitation.

Figure 2

The distribution of total unreduced ${\chi }^2$ values as a function of input lifetime (black squares). The corresponding reduced ${\chi }^2$ value is given on the right axis. The cubic polynomial fit (red line) was used to determine the best fit lifetime and uncertainty.

Figure 3

Experimental data (gray) and the simulated line shape corresponding to the best fit lifetime ${\tau }_{\min .}=7.8$ ps (red) for groups 1 and 5; see Table 1 for details regarding the detector groups. The peak corresponding to the “fast component” decays is labeled with the $*$ symbol.

Figure 4

Systematics of $B(E2;2_1^{+}\to 0_1^{+})$ values in the Sr isotopes demonstrating the onset of deformation from $N=58$ to $N=60$. The uncertainties in the experimental data are given at $1\sigma$. For the current measurement, the size of the uncertainty is smaller than the data point. Experimental results are Mach (1991) [4], Pritychenko (2016) [10], and Clément (2016) [16]; the theory data are taken from Kumar (1985) [12], Skalski (1997) [13], Lalazissis (1995) [14], and Buchinger (1994) [15].