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Alpha decays triplet from the ²³⁵U chain: ²²³Ra → ²¹⁹Rn → ²¹⁵Po → ²¹¹Pb

Final alpha energy calibration and contamination evaluation

by Silvia (January 2025)

Updated analysis with the new event reconstruction (v3) and the corrected event time.

In this analysis all alpha events (selected with the cut disp=chi2amp/integral < 53) with ADC > 19000 (to discard the Gadolinium decays) are considered.

The run time is 77.5 days, the frequency of the selected events is 0.0307 Hz and the total number of events is 205829. The average time between two consecutive events is 32.6 s.

The alpha ADC alpha spectrum if given in Fig.1.

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

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 < 0.01 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 a spot is evident (plus some fainter spots), indicating the events connected by a decay with a short life-time.

I select the events with 46000 < ADC <54000, and for each event I plot the time difference dT with the previous alpha events, versus the ADC value of the previous alpha events.

Since the mean life time of this decay is much smaller than the mean time dT between two consecutive events, I expect no background. Indeed, in the scatter plot a decay signal (decreasing with dT) is well visible around ADC 43000 with few signals outside. I assume that these events correspond to the most probable decay (branching ratio 79%, energy 6819 keV). The events corresponding to the decays with lower brabching ratios and energies, are probably the faint spot on the left of the mail signal. The spot on the right will be discussed later.

I select the events with 40500 < ADC < 46000 and then I plot the dT distribution.

I found an exponential with almost zero background (however with a very small group of events with small negative dT, whose origin I do not understand). The fit of the histogram with dT>0 gives a half-life of 1.734 +- 0.025 ms, consistent with expectations. So the problem found in July (half-life of about 6.7 ms) is now solved, using the correct times of events. Integrating the exponential function from zero to infinity, I got the number of decays N1 = 5245.

It has to be noted that also the faint distribution in Fig.3 around ADC 49000/50000 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.

Mayby the very faint signal at ADC visible around 38000/40000 could also originate 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.

If I consider all additional events likely related to the same decay (selecting 38000 < ADC < 54000), the fit of the dT distribution gives a half-life of 1.760 +- 0.023 ms, and integrating the exponential function I found a number of decays N1=6392 (this value will be used for the evaluation of the contamination).

Step 2: Search for the parent signal from ²¹⁹Rn → ²¹⁵Po

I select the events of Fig.4 with 0 < dT < 0.02 s and I search backwards, looking for a possible previous decay.

The next figure shows the distribution of the time difference dT with the previous alpha events up to dT=50 s, versus the value of the ADC of the previous events.

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 35500 < ADC < 40500, where the signal is stronger, and I plot the dT distribution:

I fit the histogram with a function which for dT>0 is the sum of an exponential with slope p1 plus a constant value p2, while for negative dT is equal to p2:

F(x) = p0 * exp (-p1*x) + p2 (for dT>0)

F(x) = p2 (for dT<0)

The found slope gives a half-life time of 3.83 +- 0.08 s, consistent with the ²¹⁹Rn decay. Integrating the exponential from zero to infinity, I obtain the number of decays N2 = 3901.

If I consider all events with ADC 31000-44000 and the parent events with ADC 38000-54000, I got a half-life of 3.93 +- 0.07 s, and integrating the exponential I obtain a numer of decays N2=6251 (this value will be used in the contamination evaluation).

Step 3: Calibration with 6 energy points

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 = 37622

Q = 6946 keV — ADC = 43177

Q = 7526 keV — ADC = 48427

Adding the 3 new points to the 4 points of the calibration found in the triple decay of the 232Th chain, 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 that 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.5.

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.5.

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) = 480 + 0.189 * A - 9.0e-7 * A*A

where A is the ADC value.

This expression is practically the same that I found in July.

Step 4: Evaluation of the contamination

To evaluate the efficiency of the measurement of the first decay (215Po → 211Pb), I integrate the first gaussian shown in Fig. 7 (the one on the right) to evaluate the fraction of signal I lost by using the ADC cuts defined previously, and I obtain E1 = 0.974.

For the other decays I used a wide ADC intervals in order to consider all the different energy emissions (alphas and gammas), so I assume: E2 = 1 and E3 = 1.

The contamination of 215Po → 211Pb decay is: C1 = N1 / E1 /E2 /time / mass = 1.51 ± 0.02 mBq/kg ,

where N1 = 6392.

The contamination of 219Rn 215Po decay is: C2 = N2 / E1 / E2 / E3 / Fd / time / mass = 1.47 ± 0.02 mBq/kg ,

where N2 = 6251 and Fd = 1.00 is the fraction of selected events of 215Po decay with dT < 0.02 s