Lifetime measurements in ${}^{206}\mathrm{Po}$ with a shell-model interpretation

The lifetimes of the first excited $2^{+}$ and $4^{+}$ states in ${}^{206}\mathrm{Po}$ were measured using the recoil-distance Doppler-shift method. The experimental results were compared to large-scale shell-model calculations that describe the deduced transition probabilities well. Those calculations were extended to the neighboring ${}^{204,208}\mathrm{Po}$ isotopes giving a good overall description of the yrast states. However, the calculations underpredict the energies of the $6_1^{+}$ and $8_1^{+}$ states, which suggests that further improvement of the proton-neutron interaction is required.

Figure 1

(a) $\gamma$-ray spectrum of the backward detector ring taken at the shortest distance of 1 $\mu \mathrm{m}$. (b) Particle-gated single $\gamma$-ray spectrum of the backward detector ring taken at the shortest distance of 1 $\mu \mathrm{m}$. The strongest transitions belonging to ${}^{206}\mathrm{Po}$ are indicated and colored in red. (c) Particle–gated $\gamma$-ray spectrum for all the distances of both detector rings.

Figure 2

[(a),(b),(c)] Fits to spectra of the backward detector ring for different target-to-stopper distances used to obtain the shifted and unshifted components of the $4_1^{+}\to 2_1^{+}$ transition. The dashed black line represents the parametrization of the background used in the fit. The solid black line is the total fit to the spectrum. The red and blue Gaussians correspond to the shifted and the unshifted components, respectively. Panels (d), (e), and (f) are the same as panels (a), (b), and (c) but for the forward detector ring.

Figure 3

(a) The experimentally obtained $R\left(t\right)$ ratios for the $4_1^{+}\to 2_1^{+}$ transition for the backward detector ring together with the Bateman fit to the data points. (b) Same as panel (a) but for the forward detector ring. (c) Probability distributions for the fitted lifetimes obtained using a Monte Carlo procedure, as explained in the text, used to to determined the uncertainty of the measured lifetime. The blue and red distributions are for the forward and backward detector rings, respectively. The violet distribution is the convolution of the two distributions and is used to determine the final uncertainty of the lifetime of the $4_1^{+}$ state.

Figure 4

Same as Fig. 2 but for the $2_1^{+}\to 0_1^{+}$ transition and distances of 1, 20, and 100 $\mu \mathrm{m}$.

Figure 5

Same as Fig. 3 but the analysis was performed for the $2_1^{+}\to 0_1^{+}$ transition and results are for the $2_1^{+}$ state.

Figure 6

Comparison of experimental (left) low-lying yrast states of ${}^{204,206,208}\mathrm{Po}$ with the shell-model calculations SM2 (right). Data are from Tables 2 and 3. The width of the arrows are proportional to the absolute $E2$ transition strengths between the states. The numbers over the arrows are the reduced $E2$ transition probabilities in $e^2$ ${\mathrm{fm}}^4$. The positions of the $8^{+}$ states have been elevated by 100 keV to make the transition strength value to the $6_1^{+}$ state clearly visible.