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Tentative search for 3 signals of the alpha decays triplet from the ²³⁵U chain: ²²³Ra → ²¹⁹Rn → ²¹⁵Po → ²¹¹Pb

by Silvia (July-August 2024)

The energies and half-life times of the 3 alpha decays are:

In this analysis I consider all the alpha events with ADC > 19000 (to discard the Gadolinium decays). The frequency of the selected events is 0.0314 Hz and the total number is 210152. The average time between two consecutive events is 31.8 s.

Step 1: Search for the signal from the last decay of the chain: ²¹⁵Po → ²¹¹Pb

From the previous ADC calibration for alpha I expect the decay signal around ADC 49000. To identify better the ADC range to consider, I made the following scatter plot, showing the distributions of ADC of two consecutive alpha events with a difference in time dT < 0.1 s. On the y axis, ADC1 indicates the ADC of the first event, on the x axis ADC2 indicates the ADC of the next one. From this plot two spots are evident (plus a fainter spot), indicating that there are two (three?) groups of events connected by a decay with a short life-time.

The next plot clarifies the situation, showing the Log10 of the time difference dT between 2 consecutive events as a function of the ADC of the first event (in the left panel) and of the second event (in the right panel). It is clearly visible a group of events with dT in the range 0.001-0.03 s, with ADC around 43000 for the first event of the pair and ADC around 49000 for the second event. A second group of events with a time difference of order 0.01-1 s probably corresponds to the ²¹⁶Po → ²¹²Pb decay, with half-life of 0.14 s, reported in a previous wiki page.

I select the events with 46500 < ADC <50500, and for each event I plot the time difference dT with the previous alpha event, versus the ADC value of the previous alpha event.

Since the mean life of this decay is much smaller than the mean time dT between two events, I expect no background for this decay. Indeed, in the scatter plot a decay signal (decreasing with dT) is well visible in the range for ADC around 43000 with very few signals outside (excluding a similar but fainter distribution at ADC around 49000). To further reduce the background, I select the events with 41500 < ADC < 45000 interval and then I plot the dT distribution.

I expect an exponential behavior with an almost zero background, and indeed I found a nice exponential, but with a slope corresponding to a half-life of 6.67 +- 0.10 ms, much longer than what expected (1.78 ms).

However the ADC value of the signal is consistent with expectations from the parent ²¹⁹Rn decay, using the calibration curve obtained previously for alpha particles (see the end of this report).

Also the faint distribution around ADC 49000 is probably due to the same decay. Actually, in this decay, a gamma ray with energy 271 KeV is emitted in 11% of cases and with energy 402 keV in 6% of cases. A gamma ray produces a larger signal with respect to an alpha particle of the same energy, and in this case we cannot use the same conversion energy/ADC used for alpha particles.

I have done this simple calculation: I subtract the gamma energy Eg to the Q value: Q' = Q - Eg

I convert Q' into ADC according to the alpha calibration that I have done previously. Then I convert the gamma energy into ADC according to the calibration made by YinJie for beta/gamma particles.

Summing the ADC corresponding to Q' and Eg, I got the ADC values 48256 and 50837 for the energies of gamma rays Eg = 271 and 402, respectively.

In fig.3 there are two signals with ADC consistent with these values, that partly overlap. So it seems that the apparently higher energy signal is only due to the presence of gamma rays.

Moreover, I suppose that the very faint signal at ADC visible around 39000/40000 originates when the gamma ray escapes from the detector without interacting. Subtracting the gamma energy to the Q values, I obtain the ADC values 40810 and 39648, for the two gamma energies, consistent with the observed signal.

All this supports the idea that the signal is really due to the ²¹⁵Po → ²¹¹Pb decay.

To understand why the lifetime is not the expected one, I try to see what happens at longer dT. The next plot, showing dT versus the ADC of the previous event up to dT=50 s, shows that (in addition to the signals with dT of milliseconds, barely visible in this plot) there are many decay signals with dT of order of seconds.

I select the events with 41500 < ADC < 45000 (the same of the the millisecond signal) and then I plot the dT distribution up to 100 s.

I fit the histogram from 1 to 20 s (to exclude the ms signals) with an exponential function and I found a slope corresponding to a half-life of 3.85 s. This value is consistent with the 219Rn decay (half-life 3.98 s), that in principle should precede the 215Po decay. So, it seems that in some case the the second signal of the 3 decays chain is lost. In any case this component is too low to affect the slope of the 6.67 ms decay signal, that I don't know how to explain.

I extend the search of the previous event to other ADC intervals. Selecting the events with 36000 < ADC < 39000, where in Fig.5 the decay signal is maximum, I got the following dT distribution:

Fitting the histogram with an exponential for dT < 20 s, I obtain a half-life of 3.4 +- 0.07 s. Also in this case the value is similar to the half-life of 219Rn decay.

Step 2: Search for a possible parent alpha decay of the signal with half-life 6.67 ms

I select the events of Fig.4 with dT < 50 s and I search backwards, looking for a possible previous decay.

The next figure shows the distribution of the time difference dT with all the previous alpha events up to dT=50 s, versus the value of the ADC of the previous events. In this case, I don’t consider only the previous event, because I don’t know the half-life time of the possible parent.

The distribution shows an excess over the flat background for small dT in the region 31000 < ADC< 44000, with a complex structure that seems to be a superposition of different decays. I select the alpha events in the band 36000 < ADC < 39000, where the signal is stronger, and I plot the dT distribution:

I fit the histogram with a function that is the sum of an exponential with slope p1 plus a constant value p2:

F(x) = exp (p0+p1x) + p2

The best-fit parameters found are displayed in the statistics box.

The slope gives a half-life time of 3.82 +- 0.10 s, consistent with the ²¹⁹Rn decay.

I try to select the events in the band 39500 < ADC < 41500, where there seems to be a fainter group of events, and I find a time distribution similar to the previous one, but with less statistics. The fit gives an exponential with a slope consistent with the previous one.

Step 3: Calibration update

Assuming that the signal with half-life 6.7 ms is the 215Po decay (with some problem…), I plot the ADC distribution of the 3 consecutive decay signals:

Fitting the histograms with 3 gauss functions, I obtain the mean value of each “peak” and then I associate these values to the corresponding Q values.

Q = 5979 keV — ADC = 37604

Q = 6946 keV — ADC = 43175

Q = 7526 keV — ADC = 48438

Adding the 3 new points to the 4 points of the calibration shown in the previous wiki page, and fitting all the 7 points with a second order polynomial function, I obtain the following curve (the new points are the red ones):

Two new points are in line with the old ones, while the point at 5979 keV (corresponding to the ²²³Ra decay) is not in the expected position.

The origin of this problem is easily found. Actually in most ²²³Ra decays several gamma rays of different energies are emitted, making impossible to associate an alpha energy to an ADC value. These additional gamma rays produce an ADC signal larger than what expected by the alpha particle alone, producing the observed shift of the point towards higher ADC values.

More precisely, in 51.2% of decays the daughter nucleus is found in an excited state of energy 158.6 keV above the ground state. This is the most probable state. This excitation energy is emitted via gamma rays or electron excitation.

With the same method described above for the 219Rn decay, I subtract this “gamma” energy to the Q value and I convert the energy into ADC for the alpha and the gamma components separately. I obtain ADC = 37852, consistent with the position of the maximum signal in Fig.8.

The second most probable state (25.0%) has an excited energy of 269.5 keV. A similar calculation gives an ADC = 40153, consistent with the position of a second strong signal in Fig.8.

Since in this decay it is difficult to find an alpha particle alone, I discard the point under discussion and make a new calibration curve using the remaining two new points plus the old four ones:

According to the best fit values, the formula to convert ADC into alpha energy is:

E (keV) = 483 + 0.189 * A - 8.98e-7 * A*A

where A is the ADC value.