Lifetimes of the $4_1^{+}$ states of ${}^{206}\mathrm{Po}$ and ${}^{204}\mathrm{Po}$: A study of the transition from noncollective seniority-like mode to collectivity

Low-lying yrast states of ${}^{204}\mathrm{Po}$ and ${}^{206}\mathrm{Po}$ were investigated by the $\gamma –\gamma$ fast timing technique with ${\mathrm{LaBr}}_3$(Ce) detectors. Excited states of these nuclei were populated in the ${}^{197}\mathrm{Au}({}^{11}\mathrm{B},4n){}^{204}\mathrm{Po}$ and the ${}^{198}\mathrm{Pt}({}^{12}\mathrm{C},4n){}^{206}\mathrm{Po}$ fusion-evaporation reactions, respectively. The beams were delivered by the FN-Tandem accelerator at the University of Cologne. The lifetimes of the $4_1^{+}$ states of both nuclei were measured, along with an upper lifetime limit for the $2_1^{+}$ state of ${}^{204}\mathrm{Po}$. A comparison between the derived $B(E2;4_1^{+}\to 2_1^{+})$ values and results from simplified empirical two-state mixing calculations suggests that for the $4_1^{+}$ states of even-even polonium isotopes the transition from single-particle mode at $N=126$ to collective mode, when reducing the number of neutrons, occurs above $N=122$.

Figure 1

The PRD curve of the setup measured with a ${}^{152}\mathrm{Eu}$ source.

Figure 2

Full projections of the HPGe-LaBr-LaBr (blue) and HPGe-LaBr-HPGe (red) coincidence data from the ${}^{198}\mathrm{Pt}({}^{12}\mathrm{C},4n$) reaction at a beam energy of 65 MeV. The inset shows a partial level scheme of ${}^{206}\mathrm{Po}$. The peaks from the transitions used in the analyses are labeled by their energies.

Figure 3

The procedure for extracting the lifetime of the $4_1^{+}$ state in ${}^{206}\mathrm{Po}$. (a) Double-gated spectra from LaBr (blue) detectors and HPGe detectors (red) produced from triple coincidence data by imposing the indicated coincidence conditions (gates). Here the gate on the LaBr detectors is set on the transition feeding the level of interest. The vertical black lines indicate the gate width used to produce the time-difference spectra at the full energy peak (FEP) of the decay transition. The corresponding peak-to-background ratio is 4.38. The vertical green lines indicate the gates used to extract the time response of the background. The panel below presents the fitted time response of the background (dashed green line), together with the PRD curve (magenta line) and the obtained centroid difference (the blue circle). The uncertainties of the latter is within the size of the circle. (b) LaBr delayed and antidelayed time-difference spectra for the 395- and 477-keV feeder-decay combination with additional HPGe gate on the 701-keV transition. (c) Same as (a) but the gate on the LaBr detectors is set on the decay transition. The corresponding peak-to-background ratio is 4.41. All presented spectra are not background subtracted.

Figure 4

Full projections of the HPGe-LaBr-LaBr (blue) and HPGe-LaBr-HPGe (red) coincidence data from the ${}^{197}\mathrm{Au}({}^{11}\mathrm{B},4n$) reaction at a beam energy of 55 MeV. The inset shows a partial level scheme of ${}^{204}\mathrm{Po}$. The peaks from the transitions used in the analyses are labeled by their energies.

Figure 5

The procedure of extracting the lifetime of the $4_1^{+}$ state in ${}^{204}\mathrm{Po}$. The figure is analogous to Fig. 3. The corresponding peak-to-background ratios are 7.06 and 5.34.

Figure 6

The procedure of extracting the lifetime of the $2_1^{+}$ states of ${}^{204}\mathrm{Po}$. The figure is analogous to Fig. 3. The corresponding peak-to-background ratios are 3.9(1) and 3.8(1).

Figure 7

The evolution of the $R_{4/2}$ ratios in even-even polonium (blue circles) and lead (magenta diamonds) isotopes as a function of neutron number. The dashed lines are drawn to guide the eye in order to highlight the peculiar $R_{4/2}$ ratio at $N=124$ (${}^{208}\mathrm{Po}$ and ${}^{206}\mathrm{Pb}$).

Figure 8

The mixing scenario for ${}^{206}\mathrm{Po}$. Panel (a) shows the pure proton (in red) and neutron (in blue) excitations of ${}^{206}\mathrm{Po}$, which are assumed to correspond to the excited states of ${}^{210}\mathrm{Po}$ and ${}^{204}\mathrm{Pb}$, respectively. Panel (b) shows the result from their mixing (in magenta) in comparison with experimental data for ${}^{206}\mathrm{Po}$ in panel (c). The thickness of the arrows are proportional to the $E2$ transition strengths except for the $B(E2;2_1^{+}\to 0_1^{+})$ value of ${}^{206}\mathrm{Po}$ (the rightmost level scheme), where the thickness of the arrow represents the lower limit of transition strength.

Figure 9

The mixing scenario for ${}^{204}\mathrm{Po}$. Panel (a) shows the pure proton (in red) and neutron (in blue) excitations of ${}^{204}\mathrm{Po}$ which are assumed to correspond to the excited states of ${}^{210}\mathrm{Po}$ and ${}^{202}\mathrm{Pb}$, respectively. Panel (b) shows the result from their mixing (in magenta) in comparison with experimental data for ${}^{204}\mathrm{Po}$ in panel (c). The thickness of the arrows are proportional to the $E2$ transition strengths.