Fast-timing lifetime measurement of ${}^{152}\mathrm{Gd}$

The lifetime $\tau \left(0_2^{+}\right)$ of ${}^{152}\mathrm{Gd}$ has been measured using fast electronic scintillation timing (FEST) with an array of high-purity germanium (HPGe) and cerium-doped lanthanum bromide (${\mathrm{LaBr}}_3$) detectors. ${}^{152}\mathrm{Gd}$ was produced via an $(\alpha ,n)$ reaction on a gold backed ${}^{149}\mathrm{Sm}$ target. The measured lifetime of $\tau \left(0_2^{+}\right)=96\left(6\right)\mathrm{ps}$ corresponds to a reduced transition strength of $B(E2;0_2^{+}\to 2_1^{+})=111\left(7\right)$ W.u. and an $E0$ transition strength of ${\rho }^2\left(E0\right)=39\left(3\right)\times {10}^{-3}$ to the ground state. This result provides experimental support for the validity of a correlation that would be a novel indicator for a quantum phase transition (QPT).

Figure 1

(a) The $R_{4/2}$ ratio for the Gd and Sm isotopes around $N=90$. A sudden rise in the ratio is visible between $N=88$ and $N=90$. (b) $R_{4/2}$ vs proton number for $N=84$ to $N=94$. The gap between $N=88$ and $N=90$ increases up to $Z=64$ [13]. (c) Two-neutron separation energy $S_{2n}$ vs neutron number $N$ for Sm and Gd isotopes. (d) $B(E2;2_1^{+}\to 0_{gs}^{+})$ vs neutron number. Data were taken from the Nuclear Data Sheets [14, 15, 16, 17, 18, 19, 20, 21, 22, 23].

Figure 2

(a) The $E0$ transition rate ${\rho }^2\left(E0\right)$ for the Gd and Sm isotopes around $N=90$. For ${}^{158}\mathrm{Gd}$ also the ${\rho }^2(E0;0_3^{+}\to 0_{gs}^{+})$ transition strength is given. See text. (b) Product $B{\left(E2\right)}_1\times B{\left(E2\right)}_2$ over neutron number for the Gd and Sm isotopes. Data were taken from the Nuclear Data Sheets [14, 15, 16, 17, 18, 19, 20, 21, 22, 23] and [31, 38].

Figure 3

(a) Energy projection of a $E_{{\text{LaBr}}_3}-E_{{\text{LaBr}}_3}-\mathrm{\Delta }t$ cube in the energy range from 200 to 600 keV. An additional gate was set in the HPGe detectors on the $4_2^{+}\to 2_2^{+}$ transition at 351 keV. Marked red are the important transitions to determine $\tau \left(0_2^{+}\right)$. (b) Coincidence spectrum gated on the 271 keV $0_2^{+}\to 2_1^{+}$ transition in spectrum (a). (c) Total projection of the $E_{\text{HPGe}}-{\mathrm{E}}_{\text{HPGe}}$ matrix. (d) Zoom-in on the region of interest between 225 and 325 keV.

Figure 4

(a) Partial level scheme of ${}^{152}\mathrm{Gd}$ after ${\beta }^{-}$ decay of ${}^{152}\mathrm{Eu}$. (b) Coincidence $\gamma$-ray spectrum for the ${\mathrm{LaBr}}_3$ detectors obtained by gating on the $2_1^{+}\to 0_{gs}^{+}$ transition at 344 keV of ${}^{152}\mathrm{Gd}$ after ${\beta }^{-}$ decay of ${}^{152}\mathrm{Eu}$.

Figure 5

Top: Time-difference spectra for the combination of start gate on 315 keV ($2_2^{+}\to 0_2^{+}$) and stop gate on 271 keV ($0_2^{+}\to 2_1^{+}$) in green (dashed line) and vice versa in red with an additional gate on 344 keV ($2_1^{+}\to 0_{gs}^{+}$) in the HPGe detectors. Bottom: The same with a different gate for the HPGe detectors ($4_2^{+}\to 2_2^{+}$ at 351 keV). The right top corner shows a partial level scheme of ${}^{152}\mathrm{Gd}$. Marked in orange is the HPGe gate.

Figure 6

(a) Experimental values of ${\rho }^2\left(E0\right)$ values for the $0_2^{+}\to 0_1^{+}$ transition for Gd and Sm isotopes. Blue (filled diamond) value from this work. For ${}^{158}\mathrm{Gd}$ the ${\rho }^2(E0;0_3^{+}\to 0_1^{+})$ value is shown, too. See text. (b) Product $B{\left(E2\right)}_{1}B{\left(E2\right)}_2$ of Gd and Sm isotopes. Blue (filled diamond) value from this work. For $N=86$ isotopes, there is no lifetime data of the $0_2^{+}$ state. Product $B{\left(E2\right)}_{1}B{\left(E2\right)}_2$ was approximated; see text. Data taken from Table 2.