Half-life measurements in ${}^{164,166}\mathrm{Dy}$ using $\gamma \text{−}\gamma$ fast-timing spectroscopy with the $\nu$-Ball spectrometer

We report on the measurement of lifetimes of excited states in the near-mid-shell nuclei ${}^{164,166}\mathrm{Dy}$ using the gamma-ray coincidence fast-timing method. The nuclei of interest were populated using reactions between an ${}^{18}\mathrm{O}$ beam and a gold-backed isotopically enriched ${}^{164}\mathrm{Dy}$ target of thickness $6.3\mathrm{mg}/{\mathrm{cm}}^2$ at primary beam energies of 71, 76, and 80 MeV from the IPN-Orsay laboratory, France. Excited states were populated in ${}^{164}\mathrm{Dy}$, ${}^{166}\mathrm{Dy}$, and ${}^{178,179}\mathrm{W}$ following Coulomb excitation, inelastic nuclear scattering, two-neutron transfer, and fusion-evaporation reaction channels respectively. Gamma rays from excited states were measured using the $\nu$-Ball high-purity germanium (HPGe)-${\mathrm{LaBr}}_3$ hybrid $\gamma$-ray spectrometer with the excited state lifetimes extracted using the fast-timing coincidence method using HPGe-gated ${\mathrm{LaBr}}_3\text{−}{\mathrm{LaBr}}_3$ triple coincident events. The lifetime of the first $I^{\pi }=2^{+}$ excited state in ${}^{166}\mathrm{Dy}$ was used to determine the transition quadrupole deformation of this neutron-rich nucleus for the first time. The experimental methodology was validated by showing consistency with previously determined excited state lifetimes in ${}^{164}\mathrm{Dy}$. The half-lives of the yrast $2^{+}$ states in ${}^{164}\mathrm{Dy}$ and ${}^{166}\mathrm{Dy}$ were 2.35(6) and 2.3(2) ns, respectively, corresponding to transition quadrupole moment values of $Q_0=7.58\left(9\right)$ and 7.5(4) $e\text{b}$, respectively. The lifetime of the yrast $2^{+}$ state in ${}^{166}\mathrm{Dy}$ is consistent with a quenching of nuclear quadrupole deformation at $\beta \approx 0.35$ as the $N=104$ mid-shell is approached.

Figure 1

Total energy spectrum at beam energies 71, 76, and 80 MeV, in panels (a)–(c), respectively, for events containing at least one $\gamma$ ray detected by a Compton suppressed HPGe detector.

Figure 2

(a) Projection of prompt HPGe-HPGe coincidence matrix. (b) Projection of prompt HPGe-HPGe matrix with $N\ge 4$ and $E>2$ MeV, enhancing fusion evaporation events from ${}^{178}\mathrm{W}$. (c) Projection of prompt HPGe-HPGe matrix with $2\le N\le 3$ and $E<2$ MeV, enhancing events from Coulomb excitation by inelastic excitation of the ${}^{164}\mathrm{Dy}$ target nucleus. These data were taken at a beam energy of 76 MeV.

Figure 3

Projections from a prompt HPGe-HPGe coincidence matrix, with $N\le 4$ for the $2\mu \mathrm{s}$ event, after applying background-subtracted HPGe gates on transitions in ${}^{164}\mathrm{Dy}$ [panel (a)] and ${}^{166}\mathrm{Dy}$ [panels (b)–(d)]. Arrows indicate the energies where gates were set. These data were taken at a beam energy of 76 MeV.

Figure 4

Level scheme of ${}^{166}\mathrm{Dy}$ from the $\gamma$-ray transitions observed in the current work following the ${}^{164}\mathrm{Dy}({}^{18}\mathrm{O},{}^{16}\mathrm{O}){}^{166}\mathrm{Dy}$ reaction. The relative $\gamma$-ray intensities are taken from the 76 MeV beam energy data.

Figure 5

The PRC with reference energy $E_{\mathrm{ref}}=344$ keV. The deviation of the data points from this curve is shown in the inset, and the $3\sigma$ interval of 8 ps is taken as the uncertainty of the PRC.

Figure 6

Gamma-ray coincidence spectra for transitions in ${}^{164}\mathrm{Dy}$. (a)–(c) HPGe-gated, ${\mathrm{LaBr}}_3$ projected $\gamma$-ray spectra to demonstrate the selectivity of the ${\mathrm{LaBr}}_3$ gates used for $\mathrm{\Delta }T(73,169)$. (d)–(f) HPGe-gated, ${\mathrm{LaBr}}_3$ projected $\gamma$-ray spectra used for $\mathrm{\Delta }T(169,259)$. Arrows indicate the energies where gates were set. Note that there are still peaks present at 169 and 73 keV even when this is the gate energy due to Compton coincidences. These plots were produced using combined data from all three beam energies.

Figure 7

Time distribution for the yrast $2^{+}$ state in ${}^{164}\mathrm{Dy}$, obtained using gates on the decay energy $E_d=73$ keV and feeding energy $E_f=169$ keV. The deduced half-life is given in the legend.

Figure 8

(a) 2D projection of the $E\text{−}E\text{−}\mathrm{\Delta }T$ cube showing the coincidence peak at 169-259 keV, and the six background regions used to correct the $\mathrm{\Delta }T$ centroid. (b) Time distribution for $T_{1/2}({}^{164}\mathrm{Dy}$, $4_1^{+})$ with the decay energy $E_d=169$ keV and feeding energy $E_f=259$ keV. (c) 2D projection of the $E\text{−}E\text{−}\mathrm{\Delta }T$ cube showing the coincidence peak at 259-342 keV, and the three background regions used to correct the $\mathrm{\Delta }T$ centroid. (d) Time distribution for $T_{1/2}({}^{164}\mathrm{Dy},6_1^{+})$ with the decay energy $E_d=259$ keV and feeding energy $E_f=342$ keV. These plots were produced using combined data from all three beam energies.

Figure 9

Gamma-ray coincidence spectra for transitions in ${}^{166}\mathrm{Dy}$. (a)–(c) HPGe-gated, ${\mathrm{LaBr}}_3$ projected $\gamma$-ray spectra demonstrating the selectivity of the ${\mathrm{LaBr}}_3$ energy gates used for $\mathrm{\Delta }T(77,177)$. (d)–(f) HPGe-gated, ${\mathrm{LaBr}}_3$ projected $\gamma$-ray spectra used for $\mathrm{\Delta }T(77,273)$. The peak labeled “c” corresponds to a weak contamination from the 237 keV yrast $4^{+}\to 2^{+}$ transition in ${}^{178}\mathrm{W}$, which is the strongest line in the total projection. These plots were produced using combined data from all three beam energies.

Figure 10

Time distribution for the yrast $2^{+}$ state in ${}^{166}\mathrm{Dy}$, obtained using gates on the decay energy $E_d=77$ keV and feeding energy $E_f=177$ keV or $E_f=273$ keV. The deduced half-life from the fit is given in the legend.

Figure 11

Systematics of $B\left(E2\right)\downarrow$ for Gd, Dy, Er, and Yb isotopes with $94\le N\le 104$; data taken from [22, 33, 39, 40, 41, 42, 43, 44, 45, 46]. The $B\left(E2\right)\downarrow$ values for ${}^{164}\mathrm{Dy}$ and ${}^{166}\mathrm{Dy}$ calculated here are added as starred data points. The isotopes are slightly offset at each value of N to allow each data point and error bar to be seen.