Lifetimes and structures of low-lying negative-parity states of ${}^{209}\mathrm{Po}$

The $5/2_1^{-}$, $9/2_1^{-}$, and $11/2_1^{-}$ states in ${}^{209}\mathrm{Po}$ were populated in the $\beta$ decay of ${}^{209}\mathrm{At}$ and their lifetimes measured using the electronic $\gamma \text{−}\gamma$ fast timing technique. The lifetime of the $9/2_1^{-}$ state is measured for first time. The lifetime of the $5/2_1^{-}$ is measured to be shorter than the value adopted in the literature while the lifetime of the $11/2_1^{-}$ state agrees well with the previous measurement. In order to get deeper insight into the structure of the states, a shell-model calculation was carried out adopting a microscopic effective interaction derived from the realistic CD-Bonn potential. The comparison between theoretical and experimental data for the low-lying negative-parity states of ${}^{209}\mathrm{Po}$ supports the reliability of the predicted wave functions, which are found to be dominated by the coupling of a neutron hole to the yrast states of ${}^{210}\mathrm{Po}$. However, it also points to the important role played by minor wave-function components in describing the reduced electromagnetic strengths, suggesting the need of additional configuration mixing for achieving a better quantitative agreement.

Figure 1

(a) The full projections of off-beam HPGe-HPGe coincidence data. (b) $\gamma$ spectrum in coincidence with the $5/2_1^{-}\to 1/2_1^{-}$ transition in ${}^{209}\mathrm{Po}$, together with a level scheme of ${}^{209}\mathrm{Po}$ populated in the e.c. decay of ${}^{209}\mathrm{At}$. Transitions belonging to the ${}^{209}\mathrm{Po}$ are indicated and colored in red. Transitions belonging to ${}^{210}\mathrm{Po}$ are indicated with an asterisk and colored in blue.

Figure 2

The fitted PRD of the setup (solid line), together with the data points used to fit the curve. The dashed lines represent the confidence interval corresponding to $1\sigma$ standard deviation. The calibration was performed with a ${}^{152}\mathrm{Eu}$ source.

Figure 3

(a) LaBr (blue) and HPGe (red) detector projections in HPGe-LaBr gates, where the gate in the LaBr spectrum is set on the decay transition. The vertical dashed lines indicate the gates used to produce the time difference spectra displayed in (c). (b) same as (a) but the LaBr gate is set on the feeding transition. (c) Time-difference spectra for the 782-545 keV used to extract the lifetime of the $5/2_1^{-}$ state. (d), (e), (f) and (g), (h), (i) represent data taken as in (a), (b), (c) but used to extract the lifetimes of the $9/2_1^{-}$ and the $11/2_1^{-}$ states, respectively.

Figure 4

Comparison of experimental low-lying negative-parity excited states of ${}^{209}\mathrm{Po}$ (a) with the calculated ones (b) (for details see the text). The experimental data are taken from Ref. [31]. The energies of the levels are given in keV. The arrows represent some of the transitions discussed the text. The widths of the arrows are proportional to the absolute $E2$ transition strengths.

Figure 5

Composition of selected states in ${}^{209}\mathrm{Po}$. See text for details.

Figure 6

Calculated and experimental $|\langle J_f|\left|E2\right||J_i\rangle |$ matrix elements. For each $E2$ transition, the blue bar represents the contribution from the dominant component of the initial and final wave function, while the green bar the remaining one. The percentages refer to experimental data.