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Preliminary activity measurement fot the GAGG

by LorenzoA (September 2024)

0) Analysis method used for the measurement of the activity

We have investigated in previous notes the alpha triplets ²²⁴Ra → ²²⁰Rn → ²¹⁶Po → ²¹²Pb and ²²³Ra → ²¹⁹Rn → ²¹⁵Po → ²¹¹Pb, respectively from the decay chain of ²³²Th and ²³⁵U. Now I want to investigate their activity. I briefly explain the method used to do this: I select the alpha from the last decay of the chain, and I search for a coincidence with the father but I don't search in a time window that satisfies the condition 0< diff < 10*t_half, instead I search in a window where -10*t_half< diff < 10*t_half. In this way when I plot the histogram of the time difference I have a constant background from -10*t_half up to 0, and then from 0 up to 10*t_half I have the exponential decay plus the same constant background that is present when t<0. The function used to fit this histogram is:

f(t; A, t_half, B) = ( A / 2 )·( 1 + Erf(t) )·exp( - ln(2)·t / t_half) + B

In this way we can estimate with more precision the background, and this is fundamental for the activity. All the informations regarding the number of events that do the select decay are given by the function ( A / 2 )·( 1 + Erf(t) )·exp( - ln(2)·t / t_half), and so using the same binning of the histogram we can calculte the number of events with this function. In particular we have N = ∑ f( t_i ), and so the activity is given by:

Activity = N / ( Time_measure · mass · efficiency )

where Time_measure is 77.5 days, mass = 0.6509 Kg and the efficiency is given by the selection of the interval of the alpha particles. In particular both the alpha particles are selected in a certain ADC range, which I will call ADC_lw, ADC_up where lw stands for lower and up for upper. From the previous analysis we know the mean and sigma of the gaussian distribution of the selected alpha particle, and so the efficiency is given by the integral of the normal distribution from the value ( ADC_lw - mean ) / ( sigma ) up to ( ADC_up - mean ) / ( sigma ). This is done for both the alpha particle that are selected, in this way giving efficiency1 (first alpha) and efficiency2 (second alpha), and so the total efficiency = efficiency1 · efficiency2. The error of the activity can be estimated in the following way:

Error_activity = sigma_N / ( Time_measure · mass · efficiency ) where sigma_N ≈ N · ( sigma_A / A )

1) Results for the alpha triplet ²²⁴Ra → ²²⁰Rn → ²¹⁶Po → ²¹²Pb from ²³²Th decay chain

At first I consider the alpha from ²¹⁶Po, selecting ADC range [41000, 45000], and I search the alpha from ²²⁰Rn in the range [36000, 41000] and in the time window [-40*t_half, 40*t_half] where t_half = 0.145 s is the half life of ²¹⁶Po. In this case I select such a large time window because there are some events from ²¹⁹Rn (t_half = 3.96 s), and so to describe this I use an additional exponential given by ( C / 2 )·( 1 + Erf(t) )·exp( - ln(2)·t / t_half). In the figure below is plotted the histogram of the delta_t distribution, where the yellow function is the one given by ²¹⁶Po, the green one is given by ²¹⁹Rn, in magenta is represented the constant background and the red function is the sum of all the signal.

We can see from the statistic box that both the half lifes are consistent with the expected values. Counting the events given by the yellow function I got 9869, and so I estimated an activity of 2.499 ± 0.056 mBq/Kg.

I select now the alpha events from ²²⁰Rn for which I found a coincidence with ²¹⁶Po, and I search back in time for ²²⁴Ra in ADC [31000, 35500] in a time window of [-20*t_half, 20*t_half], where this time t_half = 55.6 s. In the figure below is plotted the histogram of the delta_t distribution, where the yellow function is the one given by ²²⁰Rn, in magenta is represented the constant background and the red function is the sum of the two.

Clearly we expect the same activity that I got before, counting the events given by the yellow fucntion we get 9828, and so an activity of 2.329 ± 0.078 mBq/Kg which is quite close.

2) Results for the alpha triplet ²²³Ra → ²¹⁹Rn → ²¹⁵Po → ²¹¹Pb from ²³⁵U decay chain I select the alpha from ²¹⁵Po in the ADC range [46500, 50500], and I search the alpha from ²¹⁹Rn in the range [41500, 45000] and in the time window [-20*t_half, 20*t_half] where t_half = 1.78 ms is the half life of ²¹⁵Po.

Here we have always the same problem that the half life estimated from the fit is not compatible with the one expected from the decay. In this case we also have almost zero background but ,because the function does not describe so well the distribution, using the method described above I get 3174 events, which leads to an activity of 0.903 ± 0.025 mBq/Kg. Anyway because the half life is not consistent I would take this result with a grain of salt.

I select now the events from ²¹⁹Rn for which I found a coincidence with ²¹⁵Po, and I search back in time for ²²³Ra in ADC [36000, 39000] in a time window of [-20*t_half, 20*t_half], where this time t_half = 3.96 s. In the figure below is plotted the histogram of the delta_t distribution, where the yellow function is the one given by ²²⁰Rn, in magenta is represented the constant background and the red function is the sum of the two.

Using the method described above I get 2481 events, and so an activity of 0.768 ± 0.034 mBq/Kg which is similar to the one from ²¹⁵Po.

Summary table of the activity measurement

3) Preliminary study of the activity of ²³²Th, ²³⁸U and ²³⁴U (from ²³⁸U decay chain)

We have not yet analyzed the first 2 peaks (excluding Gd) that are present in the alpha spectrum, this because they are at lower energy and their half life is long, making the delayed coincidences analysis impossible. What we can do is try to fit this 2 peaks. The first step in doing this is to convert the ADC in energy using the alpha calibration curve, then we also need the energy resolution, because the idea is to fit this 2 peaks with different gaussians with fixed mean (energy) and sigma, each energy corresponding to a different Q-value and so each gaussian represents a different alpha. Here I report the energy resolution curve for the alpha used in this analysis:

The function used to describe the energy resolution is √( A*A + B*B/E ), where A and B are the two parameters and E is the energy.

Because the two alpha peaks are observed at around 4200 keV and 4850 keV the possible alpha candidate used in the fit are:

The fit was performed using four gaussians and a constant background, because the mean and sigma of each gaussian is fixed the parameters are 5 ( four amplitude, one for each gaussian and a constant bkg). To account for a possible miscalibration another free parameter is added, and is multiplied at the mean of every gaussian. The result of the fit is illustrated in the figure below:

The parameter used to account for the miscalibration converges to 0.995961 (0.4 %). The χ2/NDF of the fit is 1930/994=1.94. We can see that the amplitude of the gaussian from ²³⁰Th converges to zero, meaning that it's possible that this alpha is not present. What we can see from the fit is that almost for certain there is a presence of ²³⁸U and ²³⁴U, and so the GAGG is contaminated with the upper part of the ²³⁸U decay chain, while the lower part is not present.

Clearly these are preliminary results because as we can see the fit is not so good, and there is also the problem that from the fit it appears that there is more contamination coming from the α of ²³⁴U in respect to the one from ²³⁸U, which is clearly impossible because ²³⁴U is a product coming from the ²³⁸U decay chain. Another result is that for sure we find the alpha from ²³²Th, compatible with the fact that we also find the alpha triplet ²²⁴Ra → ²²⁰Rn → ²¹⁶Po → ²¹²Pb. Instead, regarding the ²³⁵U decay chain, I don't find the alpha from ²³⁵U which has a Q value of 4678 keV. This means that the alpha triplet ²²³Ra → ²¹⁹Rn → ²¹⁵Po → ²¹¹Pb of this decay chain is coming from a contamination of ²²⁷Ac.