Lifetime measurements and shape coexistence in ${}^{97}\mathrm{Sr}$

Delayed $\gamma$ rays from neutron-rich $A=97$ fission fragments were measured using the Lohengrin spectrometer at the high-flux reactor of the Institut Laue-Langevin in Grenoble. Several lifetimes of excited states in ${}^{97}\mathrm{Sr}$ were measured using the fast-timing technique. The nucleus ${}^{97}\mathrm{Sr}$ exhibits shape coexistence and is located exactly at the border of the spherical ($N\le 58$) and deformed ($N\ge 60$) ground-state deformation. It is of particular interest to study the shape-coexisting structures at the spherical-deformed border ($N=59$). The determined lifetimes within this work are compared to an interacting boson-fermion model calculation that is based on the microscopic energy density functional to provide a better understanding of the spherical-deformed border in strontium isotopes.

Figure 1

The calibrated time-walk (TW) curve relative to the energy $E=344$ keV. The standard deviation is calculated and the $2\sigma$ interval is chosen to be the error of the TW curve with 3 ps.

Figure 2

Upper panel: The level scheme of ${}^{97}\mathrm{Sr}$ below the isomeric ${(9/2)}^{+}$ state at 830.8 keV. Within the brackets the relative intensities of the transitions are given. The scheme only contains transitions observed in this work. In a similar experiment a ${(3/2,5/2)}^{+}\to 7/2^{+}$ (214.4 keV) transition has been observed [31] which is included in the calculation for the transition probabilities. Lower panel: Mass $A=97$ gated coincidence spectra using the ionization chamber of the Lohengrin setup. The important lines of ${}^{97}\mathrm{Sr}$ and the contaminates are indicated.

Figure 3

(a) The 308.3-keV transition after applying a 3-$\mu \mathrm{s}$ gate on $A=97$ on the ionization chamber and a LaBr gate on the ${(3/2,5/2)}^{+}\to 3/2^{+}$ (355.4 keV) transition. (b) The 355.4- and the 522.5-keV transition after applying a 3-$\mu \mathrm{s}$ gate on $A=97$ on the ionization chamber and a LaBr gate on the $9/2^{+}\to {(3/2,5/2)}^{+}$ (308.3 keV) transition. (c) The interpolated background time response with the reference energy of 355.4 keV for the feeding transition of the ${(3/2,5/2)}^{+}$ state. (d) The interpolated background time response with the reference energy of 308.3 keV for the decaying transition of the ${(3/2,5/2)}^{+}$ state. (e) The resulting time distribution for the ${(3/2,5/2)}^{+}$ state at 522.5 keV. (f) and (g) The 141.0 (167.1)-keV transition after applying an ionization chamber gate in $A=97$ and a LaBr gate in the $3/2^{+}\to 1/2^{+}$ ($7/2^{+}\to 3/2^{+}$) transition with an energy of 167.1 (141.0) keV. (h) The resulting time distribution for the $3/2^{+}$ state at 167.1 keV, where three different methods were used to determine the lifetime.

Figure 4

The experimental (left) and theoretical (right) states with their spins and energies for ${}^{97}\mathrm{Sr}$ up to 2.5 MeV. The experimental energies and spins are taken from Refs. [14, 49, 50, 51].