National Physical Laboratory

Example of decay scheme correction: 111In

It is assumed that only one radionuclide is involved, the surface is non-absorbent and it is constructed from low density material.
The simplified decay scheme is shown below and indicates that there are 18 separate decay pathways to consider.

Decay scheme

Figure 5 111In decay scheme

111In decays through three separate stages:

Stage 1: transition from the ground state of 111In to the 416 keV excited state of 111Cd

This electron capture process results in  K X-rays being emitted  in 71.7% of the disintegrations and, in the other 28.3%, particles or photons which will not be detected in the photon probe are emitted.

Stage 2: transition from the 416 keV excited state of 111Cd to the 245 keV excited state

90.6% of these transitions emit a 171 keV gamma. In the other 9.4% of transitions, a conversion electron is produced and that is followed either by K X-rays (in 71.7% of cases) or by particles or photons which will not be detected (in 28.3% of times)

Stage 3: transition from the 245 keV excited state of 111Cd to the ground state

94.1% of these transitions emit a 245 keV gamma. In the other 5.9% of transitions, a conversion electron is produced and that is followed either by K X-rays (in 71.7% of cases) or by particles or photons which will not be detected (in 28.3% of cases)

Thus the total number of 171 keV gammas that are emitted per decay is 91% and the total number of 245 keV gammas that are emitted per decay is 94%. For the K-X-rays, there are 71.7% per decay arising from stage one, 6.7% per decay from stage 2 (i.e. 71.7% of 9.4%) and 4.2% per decay from stage 3 (i.e. 71.7% of 5.9%), giving a total of 83%.

All of the emissions, including those which will not be detected by the probe, are summarised in the table below. The type of probe used in this example is a NaI detector, 2mm thick, Al window 14 mg cm-2. The 2π efficiencies in Table 3 below are quoted from the graph in Figure 3, (red line). The particle emissions (Auger and conversion electrons) are not detected because the probe window absorbs them.

 

Emission Energy (keV)

Emissions per decay (%)

 2π Efficiency from Figure 3 Comment
L Auger electrons 3 - 4 100 0 Absorbed by probe window
K Auger electrons 19 - 26 16 0 Absorbed by probe window
Conversion electrons 140 - 250 15 0 Absorbed by probe window
K X-rays 23 - 27 83 0.9 Emissions of similar energies can be grouped for the purpose of this approx method
Gamma 171 91 0.4 In most cases, both the 171 and 245 keV gammas are emitted simultaneously
Gamma 245 94 0.15

Table 3. Summary of 111In emissions and 2π detection efficiencies

(A) Determination of instrument response - approximation method

The most abundant branch is indicated by the red coloured arrows in the decay scheme. The following emissions occur: 

Stage 1: K electron capture resulting in:                     K X-ray                       (~ 72% of decays)

Stage 2: gamma transition resulting in:                       171 keV photon          (~ 91% of decays)

Stage 3: gamma transition resulting in:                       245 keV photon          (~ 94% of decays) 

To simplify the process, only one of the 18 paths (the most abundant outlined above) will be used to estimate the instrument’s response. The other 17 paths will be considered later.

The fraction of decays which follow the most abundant path is 0.72 x 0.91 x 0.94 = 0.61 (i.e. 61% of decays).

The chances of detecting at least one of these emissions can be calculated as 1 minus the probability of missing all three. (Whether one or two or all three emissions are detected, only one event is registered by the instrument).The probability of missing all three is just the product of the probabilities of missing each one separately. For each decay, only half of the emissions start off towards the detector, so the probability of detection for an ideal source is the 2π efficiency divided by 2.

Therefore, the chance of detecting at least one of the emissions is given by: 

Emission equation

The next stage is to assume (this is a significant assumption but it errs on the side of caution) that this efficiency is representative of that for all of the other 17 paths. For every 100 Bq of

111In the instrument will produce a response of 59 counts. If a probe with a surface area of 100 cm2, monitors contamination of 1 Bq cm-2, then the IR(A) will be 59 cps/(Bq cm-2).    

Conversely, the activity being monitored (in Bq) will be 1.70 (i.e. 1/0.59) times the count rate registered by the instrument.

Greasy surface effect on instrument response

For a grimy source, the gammas are unaffected but it is assumed that the number of X-rays entering the probe was half that for the ideal source. Then the chance of detecting at least one emission is given by:  

Greasy surface equation

The IR(A) then becomes 43 cps/(Bq cm-2) and the activity being monitored (in Bq) will be 2.3 (i.e.1/0.43) times the count rate registered by the detector.

(B) Determination of instrument response - complex approach

This considers every decay path in total and sums their individual responses. The detailed analysis is presented elsewhere (IRMF reference) but the results of this for the 111In case show that for the ideal source the activity is given by 2.0 x instrument response whilst for the grimy source the corresponding value is 2.6 x instrument response.

It can be seen that the approximation method underestimates the activity by about 10-15%  but this is normally well within the uncertainties required for monitoring.

Provided there is a relatively dominant decay path, the surface effect factors are applied separately to individual emissions and the coincident summing is taken into account, the approximation method can be employed in many situations.

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