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Search for 3 signals from the alpha decay chain: ²²⁴Ra → ²²⁰Rn → ²¹⁶Po → ²¹²Pb

by Silvia

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: 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 41000-45000. I select the events in this interval, and for each event I plot the time difference dT with the previous alpha event, versus the ADC value of the previous alpha event.

Note that since the mean life of this decay is much smaller than the mean time dT between two events, if one selects the pairs of events with dT < 3 τ (0.63 s), the two events are, with high probability, due to the ²²⁰Rn → ²¹⁶Po decay and the subsequent ²¹⁶Po decay. A very small background is expected in such a short time. Indeed, in the scatter plot a decay signal (decreasing with dT) is well visible in the range 36000 < ADC < 41000, with very few signals outside. To further reduce the background, I select the events in this ADC interval and then I plot the dT distribution.

I expect an exponential behavior, since the background should be almost absent, but I found that the dT distribution is actually a combination of TWO exponentials. I fit the histogram with a function which is the sum of two exponentials.

F(x) = exp(p0+p1x)+exp(p2+p3x)

The best-fit parameters obtained can be seen in the statistics box of the plot. The slope of one exponential gives a half-life = 0.142 +- 0.002 s, in agreement with the decay of ²¹⁶Po. The slope of the second exponential (the flatter one) gives a half-life of 3.32 s +- 0.15. The origin of this second component is unknown, since is too large to be due to the residual background.

(Possible interpretation: it could be the decay of ²¹⁹Rn → ²¹⁵Po of the ²³⁵U chain, with half-life=3.96 s? The Q value of this decay is 6946 keV , very similar to 6906 keV of the ²¹⁶Po decay, but the Q values of the parent decays are 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 (9793 events), I search further back, looking for the previous decay, ²²⁴Ra → ²²⁰Rn. The half-life (55.6 s) is of the same order of magnitude of the average time difference between two consecutive events. Therefore, to find the parent decay, I consider not only the previous event, but all events within a suitable time window. 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 = 32000, where there is a decrease of events with increasing dT. To reduce the background, I select the alpha events in the band 31000 < ADC < 35500, and I plot the dT distribution:

An exponential behavior is well visible over a flat background. Note that in this case, the background should be flat because I considered all events inside a time window, and not just the previous event. I fit the histogram with a function which is the sum of an exponential with slope p1 plus a constant value p2:

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

The found best-fit parameters are shown in the statistics box. The slope gives a half-life time of 56.0 +- 1.4, which agrees with the expected value of τ = 55.6 s. Integrating the exponential to 1000 s gives 8932 events, compared to the 9773 events found previously in the chain. This difference is probably due to the fact that the ADC selection causes a loss of events.

Step 3: ADC calibration

To calibrate the ADC in energy, I select the events of Fig. 4 with dT < 1 τ = 80 s to have a small background. Out of 7908 events selected, about 2270 are background (almost 29% of the signal). I have tried to reduce this high background both reducing the ADC interval to 32000-35000 and the dT interval to 50 s, but the background remains larger than 24% of the signal in any case, and the final result does not change substantially. Therefore, I report here the results using the first selections.

For each event, I plot the corresponding ADC value, together with the ADC values of the two events that follow it 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 = 33312

Q = 6405 keV — ADC = 38517

Q = 6906 keV — ADC = 42862

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 = 440 + 0.194 * A - 1.01 e-6 *A*A

where A is the ADC value.