X-ray–$\gamma$ fast-timing lifetime measurement of the $6_1^{+}$ state in ${}^{206}\mathrm{Po}$

Low-lying states in ${}^{206}\mathrm{Po}$ were investigated using the fast-timing technique with ${\mathrm{LaBr}}_3\left(\mathrm{Ce}\right)$ and high-purity germanium detectors. The excited states in this nucleus were populated via two consecutive electron capture decays from ${}^{206}\mathrm{Rn}$. The parent isotope was produced in the ${}^{194}\mathrm{Pt}({}^{16}\mathrm{O},4n){}^{206}\mathrm{Rn}$ fusion-evaporation reaction at the FN-Tandem facility at the Institute for Nuclear Physics, University of Cologne. The previously known value for the lifetime of the $4_1^{+}$ state in ${}^{206}\mathrm{Po}$ was confirmed using the generalized centroid difference (GCD) method. The lifetime of the $6_1^{+}$ state was determined from $\beta$ decay in the first application of the GCD method for x-ray–$\gamma$ coincidences. A Monte Carlo based approach was applied to address the indirect population of the $6_1^{+}$ state by the decay of ${}^{206}\mathrm{At}$. The experimental results were examined in the context of the transition of single-particle excitations to collective behavior in the neutron-deficient Po isotopes. The obtained $B(E2;6_1^{+}\to 4_1^{+})$ value suggests that for the $6_1^{+}$ states in even-even Po isotopes the transition from a noncollective regime at $N=126$ to a collective regime occurs at $N\le 120$.

Figure 1

The PRD curve of the setup. The data points have been obtained from ${}^{152}\mathrm{Eu}$ and ${}^{133}\mathrm{Ba}$ calibration sources. The 344 keV transition in ${}^{152}\mathrm{Eu}$ is used as a reference energy [19]. The deviation of each point from the curve is shown in the inset, as well as the $2\sigma$ interval calculated analytically from the covariance matrix of the fit, following the procedure in [20]. The increased uncertainty in the 60–300 keV region stems from the lack of suitable calibration points to determine the exact behavior of the PRD curve.

Figure 2

Full projections obtained from HPGe-LaBr-LaBr (blue) and HPGe-HPGe-LaBr (red) coincidences. Denoted are transitions from the reaction product ${}^{206}\mathrm{Rn}$, the even-even decay products ${}^{206}\mathrm{Po}$ and ${}^{202}\mathrm{Pb}$, and the Coulomb excitation of the target ${}^{194}\mathrm{Pt}$.

Figure 3

Partial level scheme of ${}^{206}\mathrm{Po}$ with the known mean lifetimes of the $4_1^{+}$ and $8_1^{+}$ states, taken from Refs. [13] and [22], respectively. The plot of the $8_1^{+}\to 6_1^{+}$ transition is exaggerated for clarity.

Figure 4

(a) LaBr (blue) and HPGe (red) detector projections, produced after applying double HPGe-LaBr gates on the HPGe-LaBr-LaBr and HPGe-HPGe-LaBr coincidences, respectively. The LaBr gate is set on the decay transition. The HPGe spectrum is scaled by a factor of 0.047. The vertical black lines indicate the LaBr gate width on the feeding transition used to produce the time-difference spectra. The corresponding peak to background ratio for the feeding transition is ${(p/b)}_f=7.0\left(1\right)$. The regions marked in green denote the gates used to extract the centroid difference of the background (see text). (b) The linear fit of the background centroid difference underneath the full-energy peak of the feeding transition (dashed green line), the PRD curve of the setup (violet line), and the experimentally obtained centroid difference (blue point). (c) The delayed (blue) and antidelayed (red) time-difference spectra for the 395–477 keV feeder-decay transitions used for extracting the lifetime of the $4_1^{+}$ state. (d) Analogous to (a) with the LaBr gate set on the feeding transition. The HPGe spectrum is scaled by a factor of 0.055. The corresponding peak to background ratio is ${(p/b)}_d=8.2\left(14\right)$. (e) Analogous to (b).

Figure 5

The figure is analogous to Fig. 4. (a) The LaBr gate on the x-ray region (vertical black lines) is not set on the full width of the x-ray peak in order to increase the peak to background ratio. The three peaks observed in the HPGe spectrum are the ${}^{194}\mathrm{Pt} K_{\alpha }$ and the ${}^{206}\mathrm{Po} K_{\alpha }$ and $K_{\beta }$ x rays. The contribution of the ${}^{194}\mathrm{Pt} K_{\alpha }$ to the time-difference spectra is via random coincidences and is accounted for by the background-correction procedure. The HPGe spectrum is scaled by a factor of 0.5. The corresponding peak to background ratio is ${(p/b)}_f=7.9\left(7\right)$. (b) The linear fit of the background centroid difference (dashed green line), the PRD curve of the setup (violet line), and the experimentally obtained centroid difference (blue point). (c) The delayed (blue) and antidelayed (red) time-difference spectra for the (x-ray) 395 keV feeder-decay transitions used for extracting the lifetime of the $6_1^{+}$ state. (d) The LaBr gate on the decay transition is narrower compared to the LaBr gate used in the extraction of the lifetime of the $4_1^{+}$ state [Fig. 4] in order to increase the peak to background ratio, which is ${(p/b)}_d=2.0\left(5\right)$. The HPGe spectrum is scaled by a factor of 0.02. (e) Analogous to (b).

Figure 6

Schematic representation of the contributions to the experimentally determined lifetime of the $6_1^{+}$ state. The EC of ${}^{206}\mathrm{At}$ populates the $6_1^{+}$ either directly or through one or more intermediate excited states in ${}^{206}\mathrm{Po}$ (denoted as an ellipse) characterized with an effective lifetime ${\tau }_{\mathrm{side}}$. Note that the contribution from the long mean lifetime of the $8_1^{+}$ state [335(6) ns] is absorbed in ${\tau }_{\mathrm{side}}$ but is highly suppressed due to the applied 2 ns TAC coincidence window (see text).

Figure 7

The doubly gated HPGe projection from triple HPGe-HPGe-HPGe coincidences with the gates set on the $2_1^{+}\to 0_{\mathrm{GS}}^{+}$ (701 keV) and $6_1^{+}\to 4_1^{+}$ (395 keV) transitions. The histogram is presented with 2 keV per bin and the bins in the spectrum above 500 keV are scaled by a factor of 4 for better visibility. Denoted are the known transitions directly populating the $6_1^{+}$ state (star); transitions known from the level scheme of ${}^{206}\mathrm{Po}$ (filled circle); transitions known to be from ${}^{206}\mathrm{Po}$ that are not placed on the level scheme (empty circle); and newly observed transitions (diamonds) that are assumed to be from ${}^{206}\mathrm{Po}$ due to the double HPGe coincidence conditions imposed. Note that there are two known transitions with an energy close to 806 keV in the level scheme of ${}^{206}\mathrm{Po}$ (805.9 keV ${11}_2^{-}\to 9_1^{-}$ and 806.6 keV ${13}_1^{-}\to {11}_1^{-}$). The observed line at 806.5 keV is therefore considered a new transition as both the current experimental data and Ref. [26] show that the ${11}_2^{-}$ and ${13}_1^{-}$ states are not populated in the EC of ${}^{206}\mathrm{At}$, which has a ground-state spin 5.

Figure 8

Cumulative distribution of counts outside the $\left|\mathrm{\Delta }T\right|=2$ ns coincidence window for the delayed (D, blue) and antidelayed (AD, red) spectra, constructed starting from the corresponding partitioning points $T_p^{\text{D},\text{AD}}=\pm 2$ ns. Positive ($\mathrm{\Delta }T>2\mathrm{ns}$) and negative ($\mathrm{\Delta }T<-2\mathrm{ns}$) time differences are denoted by $+$ and $-$, respectively. The ${\text{D}}^{+}$ and ${\mathrm{AD}}^{-}$ distributions (solid lines) contain FEP and background counts, while the ${\mathrm{AD}}^{+}$ and ${\text{D}}^{-}$ distributions (dashed lines) contain only the respective background counts. The differences ${\text{D}}^{+}-{\text{AD}}^{+}$ and ${\text{AD}}^{-}-{\text{D}}^{-}$ provide a measure of the pure FEP counts in the delayed and antidelayed distributions outside the $\left|\mathrm{\Delta }T\right|=2$ ns coincidence window, respectively. At integration windows above 10 ns these differences become nearly constant, which indicates that all FEP counts have been accounted for. The average of these two differences, taken at the 20 ns integration window, determines a statistically significant excess of 20(9) FEP counts. Note that the divergence between the ${\mathrm{D}}^{+}$ and ${\mathrm{AD}}^{-}$ and the respective ${\mathrm{AD}}^{+}$ and ${\mathrm{D}}^{-}$ beyond 8 ns can be interpreted as a change in the underlying distribution of random background coincidences.

Figure 9

The averaged value of the Monte Carlo target function [Eq. (8)] for the pairs of $B\left(E2\right)$ values around the identified minimum. The points for which the value of $C_{\alpha }$ differs from ${\tau }_{\exp }=313\left(23\right)$ ps are omitted. The lower limit for $\tau \left(6_1^{+}\right)$ is taken from the point with the highest $B(E2,6_1^{+}\to 4_1^{+})$ within the region of the minimum, constrained by the uncertainty in ${\tau }_{\exp }$. At higher $B(E2,J^{\pi }\to 6_1^{+})$ values the resulting band asymptotically approaches the $B(E2,6_1^{+}\to 4_1^{+})$ values that correspond to ${\tau }_{\exp }$.

Figure 10

(a) The evolution of the excitation energy of the yrast states in even-even Po isotopes as a function of the neutron number. (b) The evolution of the $R_{J/2}$ ratios for the $4_1^{+},6_1^{+}$, and $8_1^{+}$ states in even-even Po isotopes as a function of the neutron number.

Figure 11

Experimental $B\left(E2\right)$ values for even-even Po isotopes with $N\le 126$. The uncertainty for the $B(E2;2_1^{+}\to 0_{\mathrm{GS}}^{+})$ at $N=122$ is partly omitted to highlight the low-$B\left(E2\right)$ region where the systematics of the $6_1^{+}$ state can be observed. The $B(E2;6_1^{+}\to 4_1^{+})$ values have the same behavior as the $B(E2;8_1^{+}\to 6_1^{+})$ values. Both differ significantly from the behavior of the $B(E2;4_1^{+}\to 2_1^{+})$ values for which collectivity is already present at $N=122$ [13]. The value for the $6_1^{+}\to 4_1^{+}$ transition in ${}^{206}\mathrm{Po}$ ($N=122$) is from the current paper. The value for the $4_1^{+}\to 2_1^{+}$ transition in ${}^{206}\mathrm{Po}$ ($N=122$) is the weighted average between the result from the current paper and that from Ref. [13], while the value for the $4_1^{+}\to 2_1^{+}$ and $2_1^{+}\to 0_{\mathrm{GS}}^{+}$ transitions in ${}^{208}\mathrm{Po}$ ($N=124$) are taken from Ref. [33].