Measurement of the ${}^{212}{\mathrm{Po}}$, $^{214}\hbox {{Po}}$ and $^{212}\hbox {{Pb}}$ half-life time with Timepix3

Abstract

The half-life times of the relatively short-lived $\alpha$-decaying isotopes $^{212}\hbox {{Po}}$ and $^{214}\hbox {{Po}}$ were measured with a hybrid pixel detector of Timepix3 technology. Radon daughter products were collected at the backside of a 1 mm thick silicon sensor so that subsequent decays inject the polonium isotopes of interest shallowly into the backside of the sensor. The detector’s high spatial and time resolution allow for particle identification and application of the delayed coincidence technique with low systematic uncertainty even at high rates. We find $t_{1/2}^{^{212}{\hbox {Po}}} = ( 295.02 \pm 0.18{_{\mathrm{stat.}}} \pm 0.17_{\mathrm{syst.}} )\,\hbox {ns}$ and $t_{1/2}^{{}^{214}\mathrm{Po}} = ( 163.64 \pm 0.038{_{\mathrm{stat.}}} \pm 0.093_{\mathrm{syst.}} )\,\upmu \hbox {s}$. Studying the decay of the accumulated radon daughter products after removing the detector from the $^{220}\hbox {{Rn}}$ field, the half-life time of the $\beta$-decay of $^{212}\hbox {{Pb}}$ was measured to be $t_{1/2}^{^{212}{\mathrm{Pb}}} = ( 10.620 \pm 0.011_{\mathrm{stat.}} \pm 0.014_{\mathrm{syst.}} )\,\hbox {h}$. The results are discussed in the context of previous works.

1 Introduction

$^{212}\hbox {{Po}}$ and $^{214}\hbox {{Po}}$ are short-lived unstable isotopes with decay times of few hundreds of ns and about a hundred $\upmu$s. They naturally occur as parts of the uranium and the thoron decay chains, respectively. The half-life times of these polonium isotopes have been determined utilizing the delayed coincidence detection of the subsequent bismuth $\beta$- and the polonium $\alpha$-decay. In early works, proportional counters were the detectors of choice [1], while later on scintillators [2, 3] or semiconductor diodes [4] provided higher precision data. In some of the recent works, the polonium half-life times were found as a by-product of background or contamination studies in detection systems dedicated to searches of dark matter [5] or rare decays [2]. While the $^{214}\hbox {{Po}}$ half-life time is measured with a decent relative uncertainty of 0.03% (i.e. 40 ns) [6, 7], the short decay times of $^{212}\hbox {{Po}}$ are a challenge even for modern detection systems. The quick succession of pulses hereby leads to analog pile-up and the necessity to perform pulse-shape analysis to separate the particle events [2] which comes at the price of a higher systematic uncertainty. Bellini et al. [8] report a relative error of the $^{212}\hbox {{Po}}$ half-life of 0.3% (1 ns) being the measurement with lowest trustworthy error assignment.¹

In the present work, we employ a pixelated semiconductor detector for the measurement of the polonium half-life times. Timepix3 provides a simultaneous measurement of energy and time in each of its pixels. It allows a determination of particle arrival times with nanosecond-scale precision. The energy measurement together with sensor segmentation provide means of assigning traces left in the sensor to different particle species. Requiring a close vicinity of the $\beta$- and $\alpha$-particle, we achieve an excellent signal to background ratio even at high activities. Moreover, redundancy of the time measurement in the set of pixels triggered by individual particle interactions inherently provides means of mitigating or eliminating pile-up and dead-time effects. We present half-life times with very competitive significance for both studied polonium isotopes. Additionally, we determine the half-life time of $^{212}\hbox {{Pb}}$ by measuring the decay curve of nuclei previously “trapped” in the sensor after exposure to $^{220}\hbox {{Rn}}$.

The article is structured as follows. Section 2 describes the detector technology, the experimental setup and the $^{220}$Rn and $^{222}$Rn sources used. In Sect. 3, we demonstrate how the delayed coincidence technique is applied to the continuous data stream provided by Timepix3 and discuss the separation of $\alpha$- and $\beta$-particles. Section 4 presents the data analysis results and the assessment of the systematic uncertainty. We discuss our findings in the context of previous measurements in Sect. 5 and conclude in Sect. 6.

2 Experimental setup

2.1 Timepix3

Timepix3 [9] is a hybrid pixel detector, developed by the Medipix3 collaboration² hosted at CERN.³ It consists of a readout chip connected to a sensor by means of flip-chip bump bonding. Sensor and ASIC are divided into a square matrix of $256 \times 256$ pixels at a pixel pitch of 55 $\upmu$m covering an area of 1.98 cm$^2$. In each of the 65.536 pixels, energy and time are measured simultaneously in a data-driven readout architecture, providing almost dead-time free measurement up to hit rates of 40 MHits s$^{-2}$ cm$^{-2}$. The per-pixel dead-time amounts to 475 ns. The overall time resolution was found to be below 2 ns [10].

Ionizing radiation interacting in the fully depleted sensor creates free charge carriers which drift toward the corresponding electrodes, inducing a measurable current in the pixels closest to their location. In our case, holes drift towards the pixel site and electrons toward the common backside contact. The induced currents are amplified and converted to a voltage signal with a fixed rise time of $\sim 30$ ns and (energy dependent) time of discharge up to a few $\upmu$s. To provide noise-free operation, the voltage pulse is compared to a globally adjustable threshold level, which was set at 2.7 keV. A continuously running clock of 40 MHz samples the voltage pulse to determine the deposited energy, by its time over threshold (ToT), and the time of arrival (ToA) with respect to the beginning of the measurement. Once the voltage crosses the discriminator threshold level (THL) on its upward slope, ToA is determined and the ToT measurement initiated. The ToT sampling is then stopped once the voltage drops below THL on its downward slope. In order to increase the accuracy of the time measurement a 640 MHz clock from a local ring oscillator measures the time from the actual THL crossing to the next rising edge of the base 40 MHz clock.

An inherent consequence of the fixed rise time in the pulse shaping is the so-called time-walk, which is the dependency of the time measurement on pulse height. A higher energy signal is assigned to earlier timestamps compared to a concurrent low energy signal. In Timepix3, this occurs predominantly at signals with energies below $\sim 10$ keV and can be corrected for as described e.g. in [11].

In the present work, a Timepix3 with a 1 mm thick silicon sensor was used at a reverse bias of 400 V. The Katherine readout [12] was employed for detector control.

2.2 Sources

The Timepix3 detector was exposed to $^{220}\hbox {{Rn}}$ and $^{222}\hbox {{Rn}}$ gas in confined spaces. Their charged daughter products are collected electrostatically at the sensor backside, allowing for recoil injection into the surface layers during the subsequent $\alpha$-particle decays [13, 14]. Figures 1 and 2 show the decay chains of $^{220}\hbox {{Rn}}$ and $^{222}\hbox {{Rn}}$, respectively. Decays occurring after recoil implantation into the sensor are indicated.

$^{220}$Rn decay chain for measurement of $^{212}$Po and $^{212}$Pb decays The experiment with the $^{220}\hbox {{Rn}}$, emanating from a $^{228}\hbox {{Th}}$ source of nominal activity 340.81 kBq, was done in a cardboard box with a volume of 14 l. Due to its short lifetime, the $^{220}\hbox {{Rn}}$ gas flowing into the volume does not have enough time to escape the box. The measurement duration was 7.1 d. After exposure to the source, the detector continued measuring for 10 d to study the decay properties of $^{212}\hbox {{Pb}}$.

Fig. 1

Scheme of the $^{220}$Rn decay chain until stable isotope ${}^{208}{\mathrm{Pb}}$. Bold symbols indicate decays happening after injection to the sensor. Given half-life times and Q-values were taken from [15]

$^{222}$Rn decay chain as a $^{214}$Po source Three flow-through sources of $^{222}\hbox {{Rn}}$ (emanating from $^{226}\hbox {{Rn}}$ sources) were connected in a closed circuit to a sealed metal barrel of volume 150 l. Their nominal activities were 2.068 MBq, 1.915 MBq and 1.723 MBq (as of calibrated on 1 December 2014). The $^{222}\hbox {{Rn}}$ activity in the barrel was around 20 MBq m$^{-3}$. The measurement duration was 9.8 d.

Fig. 2

Scheme of the $^{222}$Rn decay chain until the metastable isotope ${}^{210}{\mathrm{Pb}}$ ($t_{1/2}=22$ a). Bold symbols indicate decays happening after injection to the sensor. Given half-life times and Q-values were taken from [15]

3 Data analysis

3.1 Methodology

$^{220}\hbox {{Rn}}$ and $^{222}\hbox {{Rn}}$ decaying in air create the charge daughter nuclei $^{216}{{\hbox {Po}}}$ and $^{218}{{\hbox {Po}}}$, which are collected at backside of the Timepix3 sensor. In the following decay, either the $\alpha$-particle or the recoil nucleus is injected into the sensor [13]. In the desirable latter case, all subsequent decays until $^{208}$Pb (stable) and $^{210}$Pb ($t_{1/2}=22$ a) happen within the sensor and are recorded. For the measurement of the polonium half-life times, we search for the characteristic signature of a $\beta$- shortly followed by an $\alpha$-decay (further referred to as “Bi$\rightarrow$Po”). Therefore, for each detected $\alpha$-particle (see Sect. 3.2) we search for preceding $\beta$ signatures within fixed time windows of 10 $\upmu$s and 12 ms (for $^{212}\hbox {{Po}}$ and $^{214}\hbox {{Po}}$, respectively). Moreover, we require that the electron has at least one pixel closer to the center of the $\alpha$-particle cluster than $r_{\mathrm{search}} = 5$ pixels (see Sect. 3.4).

The half-life times of $^{212}\hbox {{Po}}$ and $^{214}\hbox {{Po}}$ are then extracted from the time difference spectra of the particles in the Bi$\rightarrow$Po events. The half-life of $^{212}\hbox {{Pb}}$ was determined by recording the number of $^{212}\hbox {{Po}}$ decays as a function of time after removing the detector from the container filled with $^{220}\hbox {{Rn}}$ gas (Sect. 4).

3.2 Selection of $\alpha$ and $\beta$ events

Timepix3 data are sent off the chip in a stream of pixel hits, which is partially unsorted in time. Energy calibration and time-walk correction are applied and pixels are sorted into clusters using temporal coincidence and spatial neighborhood. After sorting chronologically, groups of concurrent pixels are defined using a floating time window of 17 ns (i.e. the maximal time between two consecutive pixels in a cluster is less than 17 ns). Within this set of coincident pixels, spatial neighborhood is required in order assign them to the same cluster. Each cluster is then characterized by a set of features indicating particle type and energy deposition, while clusters with contact to either of the edges of the pixel matrix were excluded from further analysis.

Fig. 3

Scatter plot of the maximal energy in a single pixel versus the number of pixels in a cluster: a for the measurement in the $^{222}$Rn environment; b for the measurement in the $^{220}\hbox {{Rn}}$ environment. Solid black lines define two regions splitting the data set into $\alpha$- and $\beta$-particle signatures. Dashed black lines indicate selection cut variations used for the systematic error assessment

Figure 3a, b show the scatter plot of the maximum energy measured in a single pixel $E_{\mathrm{max}}$ versus the number of pixels $N_{\mathrm{pixels}}$ of a cluster for the measurement in the $^{222}\hbox {{Rn}}$ and $^{220}\hbox {{Rn}}$ environment, respectively. While the selection cut $E_{\mathrm{max}} > 200\,$keV is sufficient to select $\alpha$-particles in the $^{222}\hbox {{Rn}}$ measurement, due to the short succession of the $\alpha$-particle and electron in the $^{220}\hbox {{Rn}}$ chain, analog pile-up can cause distortion of energy measurements in some pixels of the electron track, resulting in unphysically high $E_{\mathrm{max}}$ values. Thus, the $\alpha$-particle selection criteria were modified to $E_{\mathrm{max}} > 200\,$keV and $N_{\mathrm{pixels}} > 100$ in this case. In order to assess possible systematic effects arising from the particle selection, we will later perform the analysis with the different selection cuts (dashed lines in Fig. 3).

Example $\alpha$ and $\beta$ clusters, selected according to the defined criteria, are depicted in Fig. 4a, b, respectively. $\alpha$-particle events are seen as large round clusters with a collar of low energy pixels, which is characteristic for highly ionizing particles [16]. Both, the area of the initial charge cloud [17] and the area of the collar depend on deposited energy. The different $\alpha$-particle cluster sizes in Fig. 4a are thus due to the detection of $\alpha$-particles from different isotopes as well as $\alpha$-particles emitted in decays happening at some distance to the sensor.

Fig. 4

a Set of 50 $\alpha$-particle clusters; b set of 500 $\beta$ clusters. The left event displays show the deposited energy (in keV), right displays the relative time (in ns) within these clusters

3.3 Cluster timestamp assignment

The short range of $\alpha$-particles leads to a highly localized charge carrier creation at the backside contact, so that drift time differences can be neglected. The time structures of $\alpha$-particle clusters, shown in Fig. 4a on the right, purely reflect the temporal responses of the amplifier circuits. We define the timestamp of the $\alpha$-particle as the time of the pixel with the highest energy measurement $t_{\alpha } = t_{i}$ with $E_{i} = E_{\mathrm{max}}$.

The time structure of electrons (Fig. 4b-left) resembles the drift times of charge carriers created along the electron trajectories and indicates the interaction depth. Greater timestamps correspond to pixels closer to the backside of the sensor [11]. We use the pixel with the largest timestamp as the reference time $t_{\beta } = \max \{E_{i}\}, \ E_{i} > 10\,{\mathrm{keV}},$ where $i \in \{0\ldots N_{\mathrm{pixels}}\}$. $N_{\mathrm{pixels}}$ denotes the number of pixels in the track. Only pixels with energies above 10 keV are considered.

3.4 Coincidence event selection

Bi$\rightarrow$Po events are selected using concurrency and spatial vicinity. Each $\alpha$-particle opens a window of $t_{^{212}\hbox {{Po}}} = 10\,\upmu$s and $t_{^{214}\hbox {{Po}}} = 12\,$ms backwards in time. Only $\beta$-particle tracks with at least one pixel closer to the $\alpha$-particle center than $r_{\mathrm{search}} = 5$ pixels are considered. 30 representative Bi$\rightarrow$Po events are depicted in Fig. 5. The colors assigned to the pixels indicate the time differences between the $\alpha$ and $\beta$-clusters $dt = t_{\beta } - t_{\alpha }$. It is clearly seen that $\alpha$-particle clusters cover a significantly larger area than the electron tracks, so that even if an electron track “steals” pixels from the $\alpha$-particle cluster due to analog pile-up or dead-time, there is still a good amount of pixels available for the timestamp assignment of the $\alpha$-particle.

The energy deposition spectra of $\alpha$- and $\beta$-particles of the Bi$\rightarrow$Po events found in the data sets are depicted in Fig. 6. To reduce pile-up in the electron spectrum, only $^{212}$Bi$\rightarrow$ $^{212}$Po events with $dt > 1\,\upmu$s were used. The $\beta$-spectra show the expected behavior with endpoints at the Q-values of the decays, i.e. $Q_{^{214}Bi} = 3.270$ MeV and $Q_{^{212}{{\hbox {Bi}}}}=2.252$ MeV. The $^{214}\hbox {{Po}}$ $\alpha$-particle peak in Fig. 6a is seen at the expected $E_{\alpha }=7.833$ MeV [15] while the bump at $\sim 6.1$ MeV indicates random coincidences with $\alpha$-particles from the decay of the $^{218}{{\hbox {Po}}}$ collected at the sensor surface. The tails towards lower energies in the spectrum can be explained by random coincidences with Rn and Po decaying before reaching the backside electrode thus losing a part of their energy in air. The $\alpha$-particle peak in the energy deposition spectrum of $^{212}\hbox {{Po}}$ in Fig. 6b shows a peak at $E_{\alpha } = 8.785$ MeV [15]. Since a much shorter coincidence window was used there is less contribution from random coincidences.

Fig. 5

Visualization of 30 $^{214}\hbox {{Bi}}\rightarrow ^{214}$Po events after coincidence matching. $\beta$-particle pixels’ timestamps are set to 1. The color of the $\alpha$-particle pixels gives the time difference dt between birth and decay of the $^{214}\mathrm{Po}$ nucleus. The decay events are additionally labeled with dt

Fig. 6

Energy spectra of the $\alpha$ and $\beta$ particles measured in coincidence. a for $^{214}\hbox {{Bi}}$ $\rightarrow$ $^{214}\hbox {{Po}}$; b for $^{212}{{\hbox {Bi}}}\rightarrow ^{212}\!\!\!\hbox {{Po}}$, only events with $dt > 1\,\upmu$s were used to reduce the impact of pile-up. The inset shows the $\beta$ spectrum with a logarithmic y-axis

4 Results

The time difference spectra are shown in Fig. 7a, b for $^{214}$Bi$\rightarrow ^{214}$Po and $^{212}$Bi$\rightarrow ^{212}$Po, respectively. Fitting the delayed coincidence spectra with

$$\begin{aligned} f(t) = A \times \exp \left( - \frac{\ln (2)}{t_{1/2}} t\right) + B, \end{aligned}$$

(1)

we determine the half-life times $t_{1/2}$. Other fit parameters are A, which is the isotope activity at $t=0$, and a constant B, describing the background signal from random coincidences.

Fig. 7

Decay curves of a $^{214}\hbox {{Po}}$ and b $^{212}\hbox {{Po}}$. An exponential fit with constant background was used to determine the half-lifes (upper plots). Deviation of data from fit expressed in units of the statistical error $\sigma$

The decay curve of $^{212}\hbox {{Pb}}$ is shown together with the exponential fit in Fig. 8.

Fig. 8

Same as Fig. 7, but for $^{212}$Pb

Systematic error assignment We consider systematic errors from the detector’s time measurement $\delta _{\mathrm{hardware}}$ and the data analysis methodology $\delta _{\mathrm{analysis}}$.

$\delta _{\mathrm{hardware}}$ was assessed by measuring the deviation of the Timepix3 time measurement from the 1 PPS (pulse-per-second) of the GPS signal over a period of 6 days. We find $\frac{f_{\mathrm{Timepix3}}-f_{\mathrm{PPS}}}{f_{\mathrm{PPS}}} = 4.32 \times 10^{-5}$ or $f_{\mathrm{Timepix3}} = 39.996$ MHz. The deviation from the nominal 40 MHz was accounted for by multiplying the found half-life times with $C = 1.0000432$. Fluctuations around this value define the uncertainty $\delta _{\mathrm{hardware}} = \delta C \le 10^{-7}$ and are negligible.

$\delta _{\mathrm{analyis}}$ constitutes inaccuracies from the described particle identification $\delta _{\mathrm{pid}}$, coincidence matching methodology $\delta _{\mathrm{search}}$ and the fitting routine $\delta _{\mathrm{fit}}$. $\delta _{\mathrm{pid}}$ was determined by performing the analysis at different $\alpha$-particle selection cuts, while $r_{\mathrm{search}}$ was kept at 5 pixels. Analogously, $\delta _{\mathrm{search}}$ was found by variation of the search radii $r_{\mathrm{search}} \in \{3, 5, 10\}\,\hbox {pixels}$ (while default cut values were used).

We then fit Eq. 1 to each of the 5 resulting time spectra. By using different bin widths and lower bounds of the fit range, we obtain sets of tuples $(t_{1/2}, \Delta )$, where $\Delta$ stands for the fit error. For each set, we calculate the weighted average half-life times and standard deviations according to

$$\begin{aligned} \langle t_{1/2} \rangle _{j} = \left( \frac{\sum _{i} t_{1/2,i}/\Delta _{i}^2}{\sum _{i} 1/\Delta _{i}^2} \right) _{j} \,\mathrm{and} \end{aligned}$$

(2)

$$\begin{aligned} \sigma _{j} = \frac{1}{\sqrt{N}}\sqrt{(t_{1/2,i}-\langle t_{1/2} \rangle _{j})^2}. \end{aligned}$$

(3)

j indexes the sets at varying analysis parameters and i the results at different fit settings within set j. We define:

• $\delta _{\mathrm{pid}}$ is the standard deviation calculated from the subset with differing particle selection cuts $j \in \{ \hbox {cut}1,\,\hbox {cut}2,\,\hbox {cut}3\}$;

• $\delta _{\mathrm{search}}$ is the standard deviation calculated from the subsets at different search radii $j \in r_{\mathrm{search}} = \{3,5,10\}$;

• $\delta _{\mathrm{fit}}$ is the average of $\left( \sigma _{\mathrm{fit}} \right) _{j}$ for $j \in \{0,\ldots , 5\}$.

$\delta _{\mathrm{syst}}$ is calculated by adding the individual contributions in quadrature. Table 1 summarizes the values determined.

Measured half-life values The half-life times were obtained by calculating the weighted mean (Eq. 2) for all $n = j \times i$ tuples to be:

$$\begin{aligned}&t_{1/2}^{ {}^{212}\mathrm{Po} } = ( 295.02 \pm 0.18_{\mathrm{stat.}} \pm 0.17_{\mathrm{syst.}} )\,{\mathrm{ns}}, \end{aligned}$$

(4)

$$\begin{aligned}&t_{1/2}^{^{214}{\mathrm{Po}}} = ( 163.64 \pm 0.038_{\mathrm{stat.}} \pm 0.093_{\mathrm{syst.}} )\,\upmu {\mathrm{s}} \end{aligned}$$

(5)

and

$$\begin{aligned} t_{1/2}^{{}^{212} \mathrm Pb} = ( 10.620 \pm 0.011_{\mathrm{stat.}} \pm 0.014_{\mathrm{syst.}} )\,{\mathrm{h}}. \end{aligned}$$

(6)

Table 1 Overview of systematic errors for the half-life measurements

5 Discussion

Tables 2, 3 and  4 present our results in the context of previously measured half-life times for $^{212}\hbox {{Po}}$, $^{214}\hbox {{Po}}$ and $^{212}\hbox {{Pb}}$, respectively. For better comparison, systematic and statistical uncertainties were added in quadrature. The deviations of the half-life time found in the present and other works $\Delta = t_{1/2,i} - t_{1/2,{\mathrm{this \, work}}}$ are given in units of the combined uncertainty $\sigma = \sqrt{\Delta _{i}^2+\Delta _{{\mathrm{this\, work}}}^2}$.

Table 2 Half-life times of $^{212}\hbox {{Po}}$ from literature. Only values with competitive uncertainties are listed. The deviation of previous measurements from the value of the present work are given in units of the combined uncertainty

Table 3 Half-life times of $^{214}\hbox {{Po}}$ from literature. Only values with uncertainties less than 1 $\upmu$s are listed. The deviation of previous measurements from the value of the present work are given in units of the combined uncertainty

Table 4 Half-life times of $^{212}\hbox {{Pb}}$ found in literature. Only values with uncertainties less than 0.1 h are listed. The deviation of previous measurements from the value of the present work are given in units of the combined uncertainty

Our results of the $^{212}\hbox {{Po}}$ half-life are consistent on a 1 $\sigma$-level with the measurements [5, 8] used for calculation of the reference value in the 2020 version of the Nuclear Data Sheets [18]. We hereby increase the significance by a factor of 3.3–4 compared with the individual results and by a factor of 2.7 compared with the combined value [18].

A recent proceedings paper by Alexeyev et al. [20] presents a half-life time value with a precision which is 3 times better, but also deviating significantly (3.5 $\sigma$) from our result. However, their (systematic) error assessment – if done at all – is based on a different methodology than the one used in this and previous works [5, 8]. While the standard deviations of the half-life values from fits at different lower bounds are usually included in the systematic error, Alexeyev et al. neglect this contribution even though stating that “by changing the time delays the half-life value varies within 0.07%” [21]. We assess their “minimal systematic uncertainty” by calculating the standard deviation of the values given in Fig. 3 of [21] to be $\delta _{\mathrm{fit}}^{{\mathrm{Alexeyev}},^{212}\hbox {{Po}}} = 0.1$ ns. The question whether other systematic uncertainties were properly accounted for remains.

The Nuclear Data Sheets, released in 2021 [19] use the $^{214}\hbox {{Po}}$ half-life values obtained by Alexeyev et al. in [6] and [7] for evaluation of the reference value. A later work of these authors [20] presents the $^{214}\hbox {{Po}}$ half-life with currently highest precision. It is a factor of 3.3 better than ours. Again, their systematic error assessment seems incomplete. We use the standard deviation of the half-life values given in Fig. 5 of [6] to determine their minimal systematic error to be $\delta _{\mathrm{fit}}^{{\mathrm{Alexeyev}}, ^{214}\hbox {{Po}}} = 0.48\,\upmu$s. This uncertainty should probably be added to all of their results: [3, 6, 7, 20]. The questions whether other systematic effects are properly taken into account remains.

Only few works dedicated to the measurement of the $^{212}\hbox {{Pb}}$ half-life were found in literature. Their results are listed in Table 4. We find an agreement within 1 $\sigma$ with all previous measurements.

6 Conclusion

The half-life times of the unstable isotopes $^{212}\hbox {{Po}}$, $^{214}\hbox {{Po}}$ and $^{212}\hbox {{Pb}}$ were measured with competitive accuracy with hybrid pixel detectors. Overall, a good agreement with previous measurements was found. The continuous data acquisition and a simultaneous measurement of the energy and time in each of the pixels provided means of achieving a high signal to noise ratio even at high event rates while particle separation was achieved by track categorization and ion spectroscopy.

While the recoil injection used in the present work comes with a low yield, undefined interaction depth and is basically restricted to the radon decay chains, exposing the sensor to radioactive ion beams would allow to study decay chains of more or less exotic nuclei. Hereby, particle identification together with the precise time measurement provides means of measuring decay times of the intermediate states, the energies of emitted particles and might allow a precise determination of branching ratios. The feasibility of such a measurement was demonstrated with the predecessor of the Timepix3 detector in [26].