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Study of the ²¹²Bi (35.94 %)→ ²⁰⁸Tl → ²⁰⁸Pb decay in the 3-5 MeV gamma region

by LorenzoA (September 2024)

The energy and the half-life times of the two decays are:

For the ²⁰⁸Tl → ²⁰⁸Pb decay we have always a γ at 2615 keV, then we have a continuum from 3 MeV up to 5 MeV. This continuum is the only background present in the β/γ band above 3 MeV and the objective of this note is to see if we can eliminate this background by searching for the coincidence of the alpha decay. This background subtraction is important because if possible we could search for neutrons in the 3-10 MeV region instead of the 5-10 MeV range.

Using the calibration curve for alphas obtained by Silvia I converted the Q value of the ²¹²Bi decay in ADC:

Q=6207 keV → ADC = 36680

In this energy range the most disturbing decays are given by ²²⁴Ra (²³²Th decay chain) and ²²³Ra (²³⁵U decay chain), which have respectively a Q value of 5789 keV , 5979 keV and half-life times of 3.6 and 11.4 days. So in theory these background should be negligible, and they both should be at lower ADC values than the ²¹²Bi alpha. Instead we know from Silvia's note that the alpha from ²²³Ra is shifted at higher ADC values, in particular:

²²⁴Ra Q=5789 keV → ADC=33310

²²³Ra Q=5979 keV → ADC=37600

So in reality the signal of ²¹²Bi is found right in the middle of these two alphas, particularly close to the one from ²²³Ra. This is a problem because when selecting the alpha signal of ²¹²Bi to found the coincidences with the ²⁰⁸Tl gammas in 3-5 MeV region I would get a lot of “contamination” coming from these two alphas.

To solve this problem I redid the delayed coincidence analysis for the two alpha triplet ²²⁴Ra → ²²⁰Rn → ²¹⁶Po → ²¹²Pb and ²²³Ra → ²¹⁹Rn → ²¹⁵Po → ²¹¹Pb, and deleted the alphas of ²²⁴Ra, ²²³Ra for which I had found a coincidence with ²²⁰Rn, ²¹⁹Rn in a time window of 10 half life. By following this procedure I was able to lower the background given by the alphas of ²²⁴Ra, ²²³Ra when selecting the events of ²¹²Bi.

So I selected the gamma events in the 3-5 MeV region, and got 1400 events in 77.5 days of data. This corresponds to roughly 18 events per day. or in other words an event every 80 minutes. Having selected this events I opened a time window of 20 half life, searching for coincidences with the alpha of ²¹²Bi. The plot below shows the time difference of two coincident events against the ADC of the alpha.

To further reduce the background I only select the events in the range of ADC [35400,38600] (8663 events, roughly 112 events per day), and then I plot the histogram of the time difference of two coincident events up to 20 half life:

The value p1 reported in the statistic box is the half life in seconds, which is close to the expected value that is t_1/2 =183 s.

Now that we have found the coincidences beetween the gammas of ²⁰⁸Tl and the alphas of ²¹²Bi they can be subtracted from the gamma spectrum. To do this I selected the coincidences in a time window of 5 half life, because using a higher value would introduce too much dead time. For reference in the figure below I report the case with a time window of 5 half life (left) and 10 half life (right).

It can be see that if the time window is set to 5t_1/2 we can reduce the gamma events significantly above 4 MeV, having in this way only 7 events in 77.5 days of data in the 4-5 MeV region. Clearly if we use 10t_1/2 we are able to cut almost all events above 3.2 MeV.

All of this seems promising, but one has also to check if this background subtraction with coincidences affects the neutron events. To check this I selected the gamma events in the region [3,10] MeV where we know for certain that the events above 5 MeV are neutrons. There are 23 of such events in 77.5 days of data, corresponding on average to an event every 3.23 days. Applying the procedure described above we get the following for 5t_1/2 (left) and 10t_1/2 (right):

We can see that in both cases we are eliminating too many neutrons, and this should not happen when searching for coincidences. The reason for this is easily found, in fact I am searching for the alpha coincidence in the range [35400, 38600], corresponding to 8663 events. This means that on average there is an alpha event every 13 minutes, and in the case of 5t_1/2 the time window is roughly 15 minutes, while for 10t_1/2 it's 30 minutes. The conclusion is that in the case of 5t_1/2 there is a really high probability that the neutron events fall in the time windows, even tough the events are not correlated. This is almost certain if we use 10t_1/2.

The problem is given by the high counting rate of the GAGG crystal, and so the straighforward way to solve this would simply be to use a less contaminated crystal. Another approach would be to tighten the ADC range of the ²¹²Bi, but if we do this clearly the coincidence analysis would be less effective. A compromise has to be found.

One thing that can also be done is to add the alpha from ²¹²Bi in the calibration curve. In this case to perform the gaussian fit I use the ADC range [35500, 39500]. The fit is done using a gaussian with a constant background and an error function.

So I can now associate the mean obtained by the gaussian fit with the Q value of the alpha decay:

Q = 6207 keV → ADC = 37320

This value is 1.7 % greater that the one predicted by the alpha calibration curve. I now use this new point to update the calibration curve:

As I have already noted the new point is a little bit off the line, nevertheless the result from the fit are compatible with the ones obtained by Silvia without using ²¹²Bi. If we decide to keep this point the formula to convert ADC into alpha energy is:

E (keV) = 513 + 0.185 * ADC - 8.34e-7 * ADC*ADC