Lifetime measurements of excited states in ${}^{162}\mathrm{W}$ and ${}^{164}\mathrm{W}$ and the evolution of collectivity in rare-earth nuclei

Lifetimes of the first excited $2^{+}$ states in the extremely neutron-deficient ${}^{162}\mathrm{W}$ and ${}^{164}\mathrm{W}$ nuclei have been measured using the recoil distance Doppler shift technique. Experimental $B\left(E2\right)$ data for the isotopic chains of hafnium, tungsten, and osmium, from the midshell region near the $\beta$-stability line towards the $N=82$ closed shell and the most neutron-deficient nuclides, are compared with predictions of nuclear deformations and ${2_1}^{+}\to {0_{\mathrm{g}.\mathrm{s}.}}^{+}$ reduced transition strengths from different classes of state-of-the-art theoretical model calculations. The results reveal striking differences and deficiencies in the predictive power of current nuclear structure models.

Figure 1

(a) $\alpha$-tagged background-subtracted spectra used for the lifetime determination in ${}^{162}\mathrm{W}$ for three different target-to-degrader distances. (b) Normalized intensity as a function of target-to-degrader distance of $\gamma$ rays from the ${2_1}^{+}\to {0_{gs}}^{+}$ transition in ${}^{162}\mathrm{W}$ emitted before (red symbols) and after (blue symbols) the degrader foil. Inset: lifetime of the $2^{+}$ state evaluated for three target-to-degrader distances in the region-of-sensitivity along with the weighted mean of 27 ps (solid blue line) and its uncertainty $\pm 11$ ps (dashed black lines).

Figure 2

Top: Evolution of ${2_1}^{+}$ energies for W isotopes as a function of neutron number, $N$. Experimental data are compared with the HFBD1S calculations with beyond-mean-field (BMF) corrections from Ref. [43] and phenomenological CSM calculations from Ref. [42]. Bottom: Reduced transition probabilities (in W.u.) for W isotopes (bottom). The experimental $B\left(E2\right)$ values for ${}^{162}\mathrm{W}$ and ${}^{164}\mathrm{W}$ have been measured in the present work, ${}^{166}\mathrm{W}$ has been taken from Ref. [45] and the rest of the data comes from Ref. [5] and references therein. The results of different theoretical model calculations (see text for details) are shown as symbols connected by dashed lines. $B\left(E2\right)$ values obtained using the Raman-Grodzins empirical formula (Raman) [2] are also shown for comparison.

Figure 3

Same as Fig. 2 (bottom) for the Hf and Os isotopic chains for neutron numbers from $N=88$ to $N=104$. The experimental $B\left(E2\right)$ values for the Hf isotopes have been taken from Ref. [5] and references therein while the data for ${}^{168}\mathrm{Os}$, ${}^{172}\mathrm{Os}$, ${}^{174}\mathrm{Os}$, ${}^{176}\mathrm{Os}$, and ${}^{178,180}\mathrm{Os}$ come from Refs. [46, 47, 48, 49, 50], respectively.