Half-life of the yrast $2^{+}$ state in ${}^{188}$W: Evolution of deformation and collectivity in neutron-rich tungsten isotopes

The half-life of the yrast $I^{\pi }=2^{+}$ state in the neutron-rich nucleus ${}^{188}$W has been measured using fast-timing techniques with the HPGe and LaBr${}_3$:Ce array at the National Institute of Physics and Nuclear Engineering, Bucharest. The resulting value of $t_{1/2}=0.87\left(12\right)$ ns is equivalent to a reduced transition probability of $B(E2;2_1^{+}\to 0_1^{+})=85\left(12\right)$ W.u. for this transition. The $B(E2;2_1^{+}\to 0_1^{+})$ is compared to neighboring tungsten isotopes and nuclei in the Hf, Os, and Pt isotopic chains. Woods-Saxon potential energy surface (PES) calculations have been performed for nuclei in the tungsten isotopic chain and predict prolate deformed minima with rapidly increasing $\gamma$ softness for ${}^{184–192}$W and an oblate minimum for ${}^{194}$W.

Figure 1

HPGe $\gamma$ ray spectrum in coincidence with the 143-keV transition detected in the HPGe detectors. Peaks belonging to ${}^{188}$W [12] are labeled by their energies in keV. The inset shows a partial level scheme for ${}^{188}$W relevant to this work, adapted from Ref. [12].

Figure 2

LaBr${}_3$:Ce $\gamma$-ray spectra in coincidence with the (a) 296-keV, (b) 432-keV, and (c) 485-keV transitions detected in the HPGe detectors. Peaks belonging to ${}^{188}$W [12] are labeled by their energies in keV. The regions inside the dashed lines were used as “start” gates for the time difference spectra. Note that areas of strong contamination, such as the peak at $\sim$350 keV in (b) were rejected from these gates (see text for details).

Figure 3

Time spectrum for the decay of the yrast 2${}^{+}$ state in ${}^{188}$W measured from the time difference between the 143-keV transition and all observed feeding transitions (see text for details). The solid line represents a fit to the data giving a half-life of $t_{1/2}=0.87\left(12\right)$ ns. The dashed and dotted lines represent 1$\sigma$ and 3$\sigma$ deviations in the half-life, respectively.

Figure 4

Experimental values of (a) $E\left(4_1^{+}\right)/E\left(2_1^{+}\right)$ and (b) $B(E2;2_1^{+}\to 0_1^{+})$ in even-$A$ tungsten isotopes. The data are taken from the Nuclear Data Sheets [14, 16, 19, 20, 21, 22, 23] except the $B(E2;2_1^{+}\to 0_1^{+})$ for ${}^{178}$W [24]. The $B(E2;2_1^{+}\to 0_1^{+})$ for ${}^{188}$W is from this work.

Figure 5

Experimental values of (a) $E\left(2_2^{+}\right)/E\left(2_1^{+}\right)$ and (b) $E\left(0_2^{+}\right)/E\left(2_1^{+}\right)$ in even-$A$ tungsten isotopes. The data are taken from the Nuclear Data Sheets [14, 16, 19, 20, 21, 22, 23] except the $E\left(2_2^{+}\right)$ in ${}^{190}$W, which is taken from Ref. [9]. The 886-keV level in ${}^{188}$W is assumed to be the $0_2^{+}$.

Figure 6

Experimental (a) $E\left(4_1^{+}\right)/E\left(2_1^{+}\right)$ and (b) $B(E2;2_1^{+}\to 0_1^{+})$ values in even-$A$ Hf, W, Os, and Pt isotopes. Data points are taken from Nuclear Data Sheets [14, 16, 19, 20, 21, 22, 23, 25, 26, 27, 28, 29, 30] except the $B(E2;2_1^{+}\to 0_1^{+})$ for ${}^{174}$Hf, ${}^{176}$W [31], and ${}^{178}$W [24]. The $B(E2;2_1^{+}\to 0_1^{+})$ for ${}^{188}$W is from the current work.

Figure 7

Potential energy surface calculations for the ground-state configurations of even-$A$ tungsten isotopes. The white dots indicate the minima of the surfaces and the contours are separated by 400 keV.