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Alpha decay triplet from the ²³²Th chain: ²²⁴Ra → ²²⁰Rn → ²¹⁶Po → ²¹²Pb

First energy calibration and contamination evaluation

by Silvia (January 2025)

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

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

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

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

This is the ADC alpha spectrum:

Step 1: Search for the signal from the last decay of the chain: ²¹⁶Po → ²¹²Pb

We know from a previous analysis that the signals from this decay should be in the peak of the ADC spectrum in the interval 40500-46000. I select the events in this interval, and for each event I plot the time difference dT with the previous alpha events, versus the ADC value of the previous alpha events.

In the scatter plot a decay signal (decreasing with dT) is well visible in the range 35500 < ADC < 40500, with very few signals outside. This means that the parent decay must be searched in this ADC interval.

The following figure shows the distribution of the time difference dT between the first selected event and all the events in the range 35500 < ADC < 40500, with -20 < dT < 30 s.

In the region dT > 0 I expect an exponential behavior plus a flat background, but I found that the dT distribution is actually a combination of TWO exponentials. I fit the histogram with a function which for dT>0 is the sum of 2 exponentials with slope p1 and p3 plus a constant value p4, while for negative dT is equal to p4:

F(x) = p0 * exp (-p1*x) + p2 * exp (-p3*x) + p4 (for dT>0)

F(x) = p4 (for dT<0)

The best-fit parameters obtained can be seen in the statistics box of the plot. The slope of the first exponential gives a half-life = 0.141 ± 0.002 s, in agreement with the decay of ²¹⁶Po. Integrating this exponential from zero to infinity I found the number of decays N1=10267 (this value will be used for the contamination evaluation).

The slope of the second exponential (the flatter one) gives a half-life of 4.00 s ± 0.14. The origin of this second component is likely the decay of ²¹⁹Rn → ²¹⁵Po of the ²³⁵U chain, with half-life=3.96 s. Actually the Q value of this decay is 6946 keV, very similar to 6906 keV of the ²¹⁶Po decay, and the Q values of the parent decays are not so different in the two cases, 5979 keV and 6404 keV.

Step 2: Search for the signal from ²²⁴Ra → ²²⁰Rn decay

For each event with dT < 0.63 s (3 times the life time) I search further back, looking for the previous decay, ²²⁴Ra → ²²⁰Rn. The next figure shows the distribution of the time difference dT with the previous alpha events up to dT=1000s, versus the value of the ADC of the previous events.

The distribution is flat in time except in the region around ADC = 33000. I select the alpha events with 31000 < ADC < 35500, and I plot the dT distribution:

An exponential behavior is well visible over a flat background for positive dT. 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 p1 corresponds to a half-life time of 54.9 ± 1.2, which agrees with the expected value of τ = 55.6 s. Integrating this exponential from zero to infinity I found the number of decays N2=9230 (this value will be used for the contamination evaluation).

Step 3: ADC calibration with 4 energy points

To calibrate the ADC in energy, I select the events of the last Figure with dT < 1 τ = 80 s to have a small background.

For each event, I plot the corresponding ADC value, together with the ADC values of the two events that follow in the decay chain.

I fit the 3 curves with 3 Gaussian functions. The results of the fits are shown in the statistics boxes. Using the mean values found, I have 3 points to calibrate the ADC for alpha particles.

Q = 5789 keV — ADC = 33277

Q = 6405 keV — ADC = 38521

Q = 6906 keV — ADC = 42840

Using also the position of the ¹⁵²Gd peak that I fitted before,

Q = 2204 keV — ADC = 9567

I found the curve:

Fitting the points with a second degree polynomial function, I obtain:

E = 436 + 0.195 * A - 1.02 e-6 *A*A

where A is the ADC value.

This curve is practically the same as the one I found in July 2024.

Step 4: Evaluation of the contamination

I integrate the 3 gaussian functions shown in Fig. 6 to evaluate the fraction of signal I lost by using the cuts defined previously and hence the efficiency of the measurements.

Integral of the 1st gaussian (the one on the right) from ADC 40500 to 46000: E1 = 0.979

Integral of the 2nd gaussian (the one in the middle) from ADC 35500 to 40500: E2 = 0.971

Integral of the 3rd gaussian (the one on the left) from ADC 31000 to 35500: E3 = 0.976

The total efficiency to detect the first decay (216Po → 212Pb) is E1*E2

So the contamination of this decay is: C1 = N1 / E1 / E2 / time / mass = 2.48 ± 0.02 mBq/kg

where N1 = 10267, time = 77.5 days and mass = 0.6509 kg.

The total efficiency to detect the second decay (220Rn → 216Po) is E1*E2*E3*Fd

where Fd = 0.954 is the fraction of selected events of 216Po decay with dT < 0.63 s

So the contamination of this decay is: C2 = N2 / E1 / E2 / E3 / Fd / time / mass = 2.39 ± 0.02 mBq/kg .

This value is lower than the previous one because in the calculations of E3, the unknown fraction of decays with energy 5448 keV (branching ratio 4.9%) that falls outside the ADC interval 31000-35500 is not considered.