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On a stainless steel part that was removed from a spent fuel pool of a pressurized water reactor, we found (among the usual contamination with activated corrosion products, fission products, and activation products from the fuel) some contamination with Ba-133.

I can see the two most important lines of Ba-133 in the gamma spectrum (356 keV and 81 keV); therefore, I assume it really is Ba-133. The activity was significantly reduced after decontamination with alkaline and acidic water in ultrasonic baths; therefore, I am sure that it's only contamination and not activation of the part.

Typical spent fuel doesn't contain much Ba-133 (the activity ratio of Cs-137 to Ba-133 is about $10^7$). So where could it come from? Could it be an activation product of concrete?

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Looks like it can be an activation product of concrete indeed (92-0-103198-X):

133Ba This radionuclide is produced by the 132Ba(n,$\gamma$)133Ba reaction in the 0.097% abundant isotope… 133Ba is mainly found in the heavy concrete of biological shields based on the use of BaSO4 to increase the density. The Ba content in such concrete can amount to 30–40% by weight. The main $\gamma$ emitter in concrete will then be 133Ba, which can be directly measured by $\gamma$ spectrometry.

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Now that the decommissioning of the plant has progressed further, the spent fuel pool mentioned in my question is finally dry (for the first time since its commissioning in the 1970s).

In addition, we are now dismantling the biological shield, which obviously contains the most activated concrete in the entire plant.

Indeed, we occasionally find traces of Ba-133 in the activated concrete. However, the activated concrete always contains a much higher specific activity of Eu-152 (which is very easy to detect). The contaminated stainless steel part from the pool, however, showed no Eu-152 activity. Even in the entire spent fuel pool we did not find any significant activity of Eu-152. Since there is also no conceivable mechanism for how this particular part in the pool could have been contaminated with traces of concrete; therefore, I no longer assume that the source could be activated concrete.

The most likely culprit seems to be barium complex grease that could have been used for screw connections of the part or for the lubrication during CNC manufacturing of the part.

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