Low collectivity of the $2_1^{+}$ state of ${}^{212}\mathrm{Po}$

The lifetime of the $2_1^{+}$ state of ${}^{212}\mathrm{Po}$ was measured in the ${}^{208}\mathrm{Pb}$(${}^{12}\mathrm{C},{}^8\mathrm{Be}$)${}^{212}\mathrm{Po}$ transfer reaction by $\gamma$-ray spectroscopy employing the recoil distance Doppler shift (RDDS) method. The derived absolute $B\left(E2\right)$ value of 2.6(3) W.u. indicates a low collectivity and contradicts previous claims of $\alpha$-cluster components in the structure of the $2_1^{+}$ state. It is demonstrated that a consistent description of the properties of the $2_1^{+}-4_1^{+}-6_1^{+}-8_1^{+}$ sequence in ${}^{212}\mathrm{Po}$ cannot be achieved in the framework of a single-$j$ shell-model calculation, either. This puzzle is traced to the properties of the seniority-2 configurations in ${}^{210}\mathrm{Pb}$ and ${}^{210}\mathrm{Po}$.

Figure 1

(a) The projection of the particle-$\gamma$ matrix obtained at plunger distance ($D$ = 43 $\mu \mathrm{m}$) by coincident detection of charged particles in the solar-cell array and a $\gamma$ ray at a polar angle ${\mathrm{\Theta }}_{\gamma }={142}^{\circ }$. The marked ranges represent parts of the particle spectrum found to be in coincidence with the $\gamma$ rays from the indicated nuclei. (b) The $\gamma$-ray spectrum in coincidence with the group of particles indicated as “${}^{212}\mathrm{Po}$ and ${}^{200}\mathrm{Tl}$” in (a).

Figure 2

Unshifted and shifted components of the 727-keV ($2_1^{+}\to 0_1^{+}$) transition observed at backward angles (a) and at forward angles (b) for three different target-to-stopper distances: 25 $\mu \mathrm{m}$, 43 $\mu \mathrm{m}$, 100 $\mu \mathrm{m}$. The dot-dashed lines (blue) represent the positions of the Doppler-shifted peak; the dashed lines (red) represent the unshifted peak positions. At the upper corners are shown the peaks of the 405-keV ($4_1^{+}\to 2_1^{+}$) transition at the same detector angle and distance as those for the $2_1^{+}\to 0_1^{+}$ transition.

Figure 3

Partial level scheme of ${}^{212}\mathrm{Po}$ showing the excited states which feed the first excited $2^{+}$ state directly. The thicknesses of the arrows are proportional to the observed $\gamma$ -ray intensities.

Figure 4

The lifetime of the first excited $2^{+}$ state of ${}^{212}\mathrm{Po}$ determined at forward (a) and backward angles (b). The middle panels show the shifted intensities at different distances. Continuous curves are fitted through the points to calculate the derivative. In the bottom panels, curves that represent the product between the time derivatives of the shifted intensities and the lifetime of the level are compared with the experimental unshifted intensities. Out of this comparison, the lifetimes corresponding to each distance in the region of sensitivity are extracted, as seen in the upper panel. The horizontal lines represent the weighted mean values.

Figure 5

The $B(E2;2_1^{+}\to 0_1^{+})$ values in Weisskopf units in nuclei having two valence protons and two valence neutrons. The data for ${}^{212}\mathrm{Po}$ is from the present work. The other data is taken from [34]. The dashed line is drawn to guide the eye.

Figure 6

A graphical representation of the results from Table 1 for the single-$j$ shell-model calculations (SM1-$gh$ and SM2-$gh$) for the low-lying states in ${}^{212}\mathrm{Po}$ in comparison with experimental data (Expt). The thickness of the arrows is proportional to the $B(E2;2_1^{+}\to 0_1^{+})$ values in ${\mathrm{e}}^2{\mathrm{fm}}^4$. The latter are also presented by the numbers next to the arrows.

Figure 7

A graphical representation of the results from Tables 2 and 3 for realistic shell-model calculations (SM) for the low-lying states in ${}^{210}\mathrm{Pb}$ and ${}^{210}\mathrm{Po}$ in comparison with experimental data (Expt). The thickness of the arrows is proportional to the $B(E2;2_1^{+}\to 0_1^{+})$ values in ${\mathrm{e}}^2{\mathrm{fm}}^4$. The latter are also presented by the numbers next to the arrows.