Activity Calculation Issues

[sgt_bear]

Hi Guys,

I'm currently trying to calculate the activity (Bq/uCi) of certain sources, but I'm having issues here.

This is what I've done so far:

I ordered a few sources in the last years, these are all disk-type 1-inch Sources that have the same properties/geometries. For calibration of my HPGE Detector, I ordered an Eu-152 Source that was calibrated by the supplier and shipped with a calibration certificate.

The source was placed centered on my detector and a 5min. spectrum was collected. Then I calculated the efficiency of the detector

My calculations were as following:

Eu-152, 121.78keV
1.) 10'553 Emissions/sec at Calibration Date
2.) 10'438 Emissions/sec at Measure Date (Decayed for ~2 Months)
3.) 1095 Emission/sec measured with HPGE (Peak CPS with Interspec)
4.) Efficiency = 1095 / 10'438 = 0.149 = 10.49%
5.) Use the same formula for every other calibration peak

This gave me a reasonable and plausible efficiency curve, similar to visual curves online.

Now I wanted to calibrate my other sources and get to know their activities. For this, I placed the sources exactly at the same position and took 5min spectra.

Cs-137 0.25uCi Source:

Peak: 661.66keV, Measured Counts: 188cps, Detector Efficiency: 2.43%, Peak Branching (Ig%): 85.10%
Therefore: (188 / 2.43%) * 100% = 8'044.04cps -> (8'044.04 / 85.10% Ig) * 100 = 9'452 Bq (0.255uCi)
Which is a very plausible result, since its within the 20% Tolerance of the stated source activity!

Na-22 1.00uCi Source:

Peak: 1274.53keV, Measured Counts: 225.3cps, Detector Efficiency: 1.38%, Peak Branching (Ig%): 99.94%
Therefore: (225.3 / 1.38%) * 100% = 16'324cps -> (16'324 / 99.94% Ig) * 100 = 16'334 Bq (0.441uCi)
The result would be off the 20% of the stated tolerance of 1uC (0.8 ... 1.2 uCi)

Co-60 1.00uCi Source:

Peak: 1173.23keV, Measured Counts: 1198cps, Detector Efficiency: 1.44%, Peak Branching (Ig%): 99.97%
Therefore: (1198 / 1.44%) * 100% = 83'133cps -> ( 83'133/ 99.97% Ig) * 100 = 83'154 Bq (2.24uCi)
The result is way off the 20%, almost 5 times as the stated activity.

In conclusion, I don't believe that either Na-22 or Co-60 source is this way off the stated activity, and therefore I think that I've made a mistake somewhere.
The measurements were taken on the same day (except Eu-152) and all were 300s (+-5s) long.

Has anyone an idea what the problem in my calculations is?

[Sesselmann]

Jonathan,

How are you compensating for the difference in gamma energy?

[sgt_bear]

Hi Steven,

The Eu-152 calibration source has peaks all over the spectrum up to 1500kev. I used all of them to calculate the efficiency of the detector
For energies between the calibration peaks, i used a linear function

For example:
Co-60 has peak at 1173.23kev
Eu-152 has peaks at 1112 and 1212kev
So i calculated the linear difference from the eff% at 1112 and 1212kev, and applied to the 1173.23kev from Co-60

[GigaBecquerel]

Did you have the same measurement geometry every time?
Not only position, but also source shape etc.

Also, I heard that Eu152 is unfavorable as an efficiency calibration source, as it tends to have summing peaks.
But I don't have any, so I never looked further into that, it might just be something to look into.

[sgt_bear]

I used the same geometry, they are all these 2.5cm diameter disks that have a point source in the middle.

Eu-152 should be fine if you have a certification about initial calibration of the source was calibrated to 36'926Bq +-5% at the calibration date. So there were 5'037 emissions/sec @ 111.207kev and 524 emissions/sec @ 1212.95 keV, therefore it should be possible to calibrate / calculate against those two peaks.

What worries me more here is, that the numbers of Na-22 and Co-60 differ so much.
Co-60 has 99% peaks at 1'1732 and 1'3325
Na-22 has 99% peaks at 1'274

Therefore, in the worst case (Na-22 is -20% and Co-60 is +20%, or around), the count rate should be similar, for example, if Co-60 peaks are around 1200cps, Na-22 peak counts should be no lower than around 700cps (-40%), but they are way lower. This is what's interesting

[jneilson]

A few thoughts:

1. Efficiency curves are generally not linear, so linear interpolation is not ideal for finding your efficiencies at intermediate energies. The commercial gamma spec packages typically employ a quadratic or higher order efficiency fit on log-log or log-linear scales eg. eff = e^( a + b*ln(E) + c*(ln(E))^2). Your interpolative fit is probably quite close to your actual efficiencies near your calibration points, but they'll be increasing bias as the energy gets further away from your calibration points.
2. True coincidence summing (TCS) may be an issue as noted by GigaBecquerel, especially if your sources are very close or in contact with the detector. This could affect both your Eu-152 calibration and the Co-60 measurement. The effect of TCS is geometry and nuclide dependent, and drops as source-detector distance increases. I typically conduct calibration measurements at 30cm to minimise TCS - although I appreciate with weak sources and small crystals this will need massively longer acquisition times to get sufficient counting statistics.
3. Interference from NORM background is also possible - the 1408 peak has an interference with Bi-214 to be aware of - although given the short distance and acquisition times, I don't imagine this will be noticeable for your measurement.
4. You didn't mention the reverse decay correction of the sources you're measuring. They'll be close to 1uCi (or 0.25 or whatever) at manufacture, but depending how long since then you expect them to decay too - if you're aiming to compare with their nominal activity you should either back correct your result to (a rough) manufacture date, or forward decay correct from manufacture to your measurement date to compare your result with.