Lifetime measurements probing collectivity in the ground-state band of ${}^{32}\mathrm{Mg}$

The signatures of inversion between normal and intruder configurations of particle-hole excitations across the $N=20$ shell gap in the neutron-rich isotope ${}^{32}\mathrm{Mg}$ have long been of keen interest. Electromagnetic transition rates in the ground-state band are key quantities that provide insights into collective properties associated with the contributions of the 2p2h and 4p4h intruder configurations. The combination of TRIPLEX, GRETINA, and the S800 spectrograph enables model-independent lifetime measurements to determine electromagnetic transition rates in rare isotopes. The reduced $E2$ transition rates in ${}^{32}\mathrm{Mg}$ between the $2_1^{+}$ and $0_1^{+}$ states and between the $4_1^{+}$ and $2_1^{+}$ states have been measured, the latter representing the first experimental $B\left(E2\right)$ value for this transition. The $B\left(E2\right)$ strengths indicate large collectivity and strong contributions from the 2p2h and 4p4h intruder configurations that may change with spin in the ground-state band of ${}^{32}\mathrm{Mg}$.

Figure 1

The experimental setup in this work. GRETINA modules of high-purity Ge detectors surround the foils positioned by the TRIPLEX device. The target (T), first degrader (D1), and second degrader (D2) foils are shown (the size and separation of the foils are not to scale). The ${}^{34}\mathrm{Si}$ secondary beam reacts on the foils and the ${}^{32}\mathrm{Mg}$ reaction product leaves the target chamber and proceeds to the S800 spectrograph where it is identified.

Figure 2

A $\gamma$-ray spectrum observed in coincidence with ${}^{32}\mathrm{Mg}$ reaction products with only the target foil T installed. The data are shown with black dots and error bars. The exponential background is shown with a solid gray line. The results of a geant4 simulation in addition to the background is shown with a solid red line that closely matches the data points.

Figure 3

A partial level scheme of ${}^{32}\mathrm{Mg}$ showing the states and transitions observed in this work. The width of each arrow is proportional to the intensity of the transition.

Figure 4

A Doppler-shift-corrected $\gamma$-ray spectrum observed in coincidence with ${}^{32}\mathrm{Mg}$ reaction products with all three foils installed with large separation in the TRIPLEX device. The 885-keV peak appears with two components corresponding to reactions on the target (T) and first degrader (D1) foils at a separation of 25 mm. The data (black dots and error bars) are fit with a simulation (solid red line). $\gamma$ rays emitted at an angle $\theta <{70}^{\circ }$ were considered. The contribution of neutron-induced background is scaled by $\times 5$ and is shown with a dashed gray line. The simulation that best fits the data assumes $r\left(2_1^{+}\right)=2.8$, meaning there are 2.8 reactions on the target for every 1 reaction on the first degrader.

Figure 5

A Doppler-shift corrected $\gamma$-ray spectrum observed in coincidence with ${}^{32}\mathrm{Mg}$ reaction products with all three foils installed with large separation in the TRIPLEX device. The 1437-keV peak appears with two components corresponding to reactions on the target (T) and first degrader (D1) foils at a separation of 25 mm. The data (black dots and error bars) are fit with a simulation (red line). $\gamma$ rays emitted at an angle $\theta <{70}^{\circ }$ were considered. The simulation that best fits the data assumes $r\left(4_1^{+}\right)=0.9$, meaning there are 0.9 reactions on the target for every 1 reaction on the first degrader.

Figure 6

Doppler-shift corrected $\gamma$-ray spectra observed in coincidence with ${}^{32}\mathrm{Mg}$ reaction products showing the 885-keV peak from the four settings used to measure lifetimes. The target and first degrader foils were touching for all four settings, while the first and second degrader foils had a separation of 0.5, 0.7, 1.0, and 2.0 mm. $\gamma$ rays emitted at an angle $\theta <{50}^{\circ }$ were considered. The two peak components correspond to decays after the first degrader (D1) and second degrader (D2) foils, respectively. The data are shown with black dots and error bars, while a simulation result assuming a lifetime of $\tau \left(2_1^{+}\right)=19$ ps is shown with a solid red line.

Figure 7

The results for the $2_1^{+}$ lifetime for each of the 0.5-, 0.7-, 1.0-, and 2.0-mm settings independently. The weighted average of the four settings is shown as a solid red line at $\tau \left(2_1^{+}\right)=18.9$ ps. $1\sigma$ error bars are shown for the statistical uncertainty of each independent setting (black dots and error bars) and the final weighted average (dashed black horizontal lines).

Figure 8

A Doppler-shift corrected $\gamma$-ray spectrum showing the 1437-keV peak from the decay of the $4_1^{+}$ state of ${}^{32}\mathrm{Mg}$. The spectrum is the sum of all runs where the target and first degrader foils were touching, regardless of the separation between the first and second degrader foils. $\gamma$ rays emitted at an angle $\theta <{70}^{\circ }$ were considered. The data are shown with black dots and error bars, while the closest simulation result with a lifetime of $\tau \left(4_1^{+}\right)=0.9$ ps is shown with a solid red line. For comparison, a simulation with a lifetime of 0.3 ps is shown with a dotted blue line and a simulation with a lifetime of 1.5 ps is shown with a dashed green line.

Figure 9

A Doppler-shift-corrected $\gamma$-ray spectrum in coincidence with ${}^{30}\mathrm{Mg}$ reaction products in the three-foil, large separation setting. The data are shown with black dots and error bars. The geant4 simulation result is shown with a solid red line, and the exponential background is shown with a solid gray line. No gate was placed on the $\gamma$-ray emission angle $\theta$. Two peaks are seen corresponding to the decays of the $2_1^{+}$ and $4_1^{+}$ states. Both peaks have only one component corresponding to reactions on the target foil.

Figure 10

A Doppler-shift corrected $\gamma$-ray spectrum in coincidence with ${}^{30}\mathrm{Mg}$ reaction products in the three-foil settings with zero separation between the T and D1 foils. $\gamma$ rays emitted at an angle $\theta <{50}^{\circ }$ were considered. The peak at 1483 keV corresponds to the decay of the $2_1^{+}$ state. The data (black dots with error bars) is matched well with the simulation results that assume a lifetime of 2.3 ps (solid red line). For comparison the simulation results are shown for a lifetime of 1.5 ps (dotted blue line) and 3.1 ps (dashed green line).

Figure 11

The $B(E2;2_1^{+}\to 0_1^{+}$) value in ${}^{32}\mathrm{Mg}$ reported in experiments over the past few decades. The present recoil-distance method result is shown with a red square. The Coulomb-excitation measurements from Refs. [6, 8, 9, 11] are shown with open circles. The open triangles are the results from Refs. [7, 10]. The upward-pointing triangles reflect the $B\left(E2\right)$ values without feeding corrections while the corresponding downward-pointing triangles take into account feeding corrections. The saltire symbol ($\times$) represents the fast-timing measurement of Ref. [12].

Figure 12

The $B(E2;2_1^{+}\to 0_1^{+})$ values in the Mg isotopic chain from ${}^{28}\mathrm{Mg}$ to ${}^{40}\mathrm{Mg}$. The present ${}^{32}\mathrm{Mg}$ result is shown with a filled black circle. The experimental values from other results are shown with black saltires $(\times )$ and are from Refs. [36, 37, 38, 39]. Theoretical calculations are also shown for the SDPF-M [18] (red line and open diamonds), SDPF-U-MIX [16] (blue line and open inverted triangles), AMPGCM [19, 20] (purple line and open circles), EKK [22] (emerald green line and open squares), USDA [40] (brown line and open triangles), and CHFB $+$ LQRPA calculations [21] (sage green line and open stars).