Results

The α-singles spectrum is shown in Figure. 2.26. Peaks corresponding to the short-lived nuclides ²²⁰Rn and ²¹⁶Po, and the long-lived ²¹²Bi were observed.

4500 5000 5500 6000 6500 7000 7500 0

1 2 3 4 5 6 7

Energy [keV]

Count ^Rn

Po

Bi

216

220 212

Figure 2.26: A singlesα-spectrum of measurement.

A conceptual diagram explaining the analysis of decay-correlated events is shown in Figure. 2.27. The analysis begins with identifying candidate events by selectingα-ray signals in the energy range consistent withα-decays for the candidate nuclide. A TOF spectrum is then constructed from TOF events occurring in a “coincidence time” prior to the α-decay signal. The coincidence time is chosen according to the half-life of the analyte nuclei. If there are two or more candidate time-of-flight signals in the same region of theα-ray, it is not possible to distinguish which is responsible for the decay signal. Therefore, in order to correlate decay in an event-by-event manner, the incoming ion rate must at least 5 times lower than the inverse half-life of the nucleus is required:

fion≤ 1

5·T_1/2 (2.2)

α signal ToF signal

coincidence time

t

t

Figure 2.27: Conceptual diagram of decay-correlated analysis. We exclude time-of-flight events which do not occur in the coincidence time prior to an α-decay event.

103

0 5 10 15 20 25 30 35 40 45 50

103

0 5 10 15 20 25 30 35 40 45 50

(a)

(c)

Counts / 12.8 ns

216PoCO⁺⁺

singles ToF

216Po gated ToF

112.5 113.5

111.5 112.0 113.0 114.0

111.0

Time-of-flight [ s]

220RnHF⁺⁺

220RnO⁺⁺

A/q

123 122

121 120

119 118

117

0 5 10 15 20 25 30 35 40 45 50

220Rn gated ToF (b)

Figure 2.28: TOF spectra in the range ofA/q= 117∼123after 12 hours of measurement. (a) Singles TOF spectrum, (b) TOF spectrum in coincidence with ²²⁰Rn α-decays, using a coincidence time gate of Tc = 180 s and (c) TOF spectrum in coincidence with²¹⁶Poα-decays, using a coincidence time gate ofTc= 450ms.

Figure 2.28 shows the results of a 12 hour measurement using the ²²⁴Ra radioisotope progenitor. TOF signals and α-decay signals were recorded event by event with absolute time stamps. The top panel of Fig. 2.28 shows the TOF-singles spectrum centered around the most intense peaks observed.

By the use of a coincidence time gate (T_c) prior to detection of a given α-decay energy signal it is possible to discriminate between TOF events corresponding to ²²⁰Rn and those corresponding to ²¹⁶Po, as shown in the middle and bottom panels, respectively. To identify peaks from ions consti-tuted from²¹⁶Po, a±150 keV gate was made onα-decay signals around 6.78 MeV withT_c= 450ms. To identify peaks from ions constituted from²²⁰Rn, a similar gate was made on 6.29 MeV α-decay signals withT_c= 180s.

Using correlated Eα-TOF measurements, it was possible to unambigu-ously determine that the TOF spectral peaks corresponding to A/q = 118 and 120 resulted from ions with a²²⁰Rn constituent, while the peak

corre-sponding toA/q= 122resulted from ions with a²¹⁶Po constituent. Unfortu-nately, the limited mass resolution of the wide mass bandwidth measurement precluded precise molecular identification. However, based on past experi-ence we have tentatively assigned the A/q = 118 and 120 TOF spectral peaks to be ²²⁰RnO⁺⁺ and ²²⁰RnHF⁺⁺, respectively, and the A/q = 122 spectral peak to be ²¹⁶PoCO⁺⁺.

T

[ T

(

Po) ]

Coun ts

Figure 2.29: Number of correlated TOF events for²¹⁶Po (black circle) and the missing TOF events (red triangle) as functions of the coincidence time in units of the half-life of ²¹⁶Po (T_1/2≈150 ms). The dotted lines indicate the fitted growth and decay curves. The asymptotic number of²¹⁶Po events indicates an effective α detection efficiency of 44(8)%, while the asymp-totic number of missing TOF events indicates a TOF detection efficiency of 84(9)%.

The data shown in Fig. 2.28 were used to determine the effective α-decay detection efficiency. Every TOF event from a radioactive ion should be followed by a subsequent α-decay. Comparing the TOF-singles counts with the Eα-TOF coincident counts in each TOF spectral peak we find that 44(8)% of TOF-singles corresponding to radioactive ions are followed by subsequent α-decays. This is consistent with the expectation of 50%

effective detection efficiency based on detector solid angle.

In order to determine the TOF detection efficiency, we must consider the inverse problem: how frequently is anα-decay signal detected without a preceding conjugate TOF signal. We use the²¹⁶Po for this as it is detected as a singular molecular ion and has a conveniently short half-life. Figure 2.29 shows the number ofE_α-TOF correlated events and the number of α-decay events with missing TOF events as functions of the coincidence time gate.

In this plot, the number of α-decay events with missing TOF events has been corrected to account for the ²¹⁶Po produced by decay of ²²⁰Rn on

the detector, resulting in the relatively large uncertainties shown. As an internal check on the validity of the background correction, the sum ofEα -TOF correlated events andα-decay events with missing TOF events is noted to be constant as a function of the coincidence time gate duration. The TOF detector efficiency can be taken to be the ratio of the asymptotic number of Eα-TOF correlated events to the total corrected ²¹⁶Po α-decay events, found to be 84(9)%. This is in good agreement with the value obtained in Sec. 2.4.1.

4 2

0 10 10 10

decay time [s]

Counts

-2 -1 0

Figure 2.30: Distribution of time between TOF signal from ²¹⁶PoCO⁺⁺

and subsequentα-decay signal, designated as “decay time” on the abscissa.

The red line indicates a distribution curve drawn with a literature value of T_1/2 = 145ms [96]. The green line indicates a distribution curve drawn with the experimentally obtained value ofT_1/2 = 123(22)ms.

Finally, by defining the decay time as the interval between the observa-tion of a TOF signal from a given radioactive ion and the subsequent de-tection of itsα-decay, we demonstrate the ability to measure half-lives with theα-TOF detector. Figure 2.30 shows a plot of measured decay times for

216PoCO⁺⁺ ions along with the expected decay time distribution function based on the literature value of the half-life [96]. The maximum likelihood value of the decay constant is well-determined by the mean value of the individual decay times [97]. In this case, the mean value was determined to be τ=177(31) ms, corresponding to T_1/2=123(22) ms, which is in good agreement with the literature value of 145(2) ms [96].