SAMPLE SELF-ABSORPTION

The reference notes: "Detector Count Rate Normalization and Calibration" describe a simple analytical model which may be used to estimate the self-shielding of a sample having a uniformly distributed radioactive source. The counts expected due to uncollided gamma-rays is related to the counts associated with the same source strength with no intervening material to attenuate the rays:

where: C is count with absorption C_{o i} is the count rate with no absorption and: r, m, and h describe the source and its geometry.

Recall that the model employed a very simple physical model. We can "adjust" the answer given by that model by including a factor H which we understand will be a complex function of source geometry, detector geometry, materials, and perhaps other factors:

By carefully constructing a set of samples, all components of the above equation can be measured or found in reference material, permitting evaluation of H as a function of sample height. By using a multi-channel analyzer, we can work with the unscattered gamma-rays directly.

Select a high-purity powder or fine granular material, one which has a reasonable half-life (in the order of days), and which (preferably) will produce a single gamma-ray following irradiation. Take a clean polyethylene container with a screw-top lid, weigh it to determine the tare weight for later measurements. Weigh enough of the material to provide a thin layer on the flat bottom inside the container.

The material must be much less than 1 mean free path thick for the gamma rays anticipated.

1. Wipe the outside of the container after closing the lid.
2. Weigh the assembly.
3. Calculate the irradiation parameters which will produce a source strength in the material that will yield reasonable statistics on the detector set-up chosen.
4. Irradiate the sample.

   Note the clock time here and at each step that follows.

5. Place the sample on the detector, taking care to tap the container to ensure a uniform distribution of source over the bottom of the container.
6. Take a reading for an appropriate live time.
7. On a clean, absorbent paper work surface, carefully open the container top and add a measured quantity of the material under study.

   Gloves must be worn during the following procedures. The amount added should fill the bottom tenth of the container. Be careful: the radioactive material must not be allowed to migrate from the container.

8. Replace the cover and shake the container to fully mix the contents.
9. Wipe the outside of the container with a filter element saturated with solvent.
10. Survey the wipe and your hands before proceeding.
11. Tap the container to produce a flat top surface on the material in the container.
12. Return the sample to the same location in the detector and count again.
13. Weigh the assembly, and record the height of material.
14. Repeat, until the container is about 75% full (a void is necessary in order to adequately mix the contents by shaking.

If there is more than 1 gamma ray involved in the material used, repeat the following for each of the peak energies involved.

• Normalize to the end of irradiation all counts taken, correcting for wait times and for clock times during counting.
• Consult reference data to determine the mass attenuation coefficient of the sample material.
• Calculate the density of the sample material, using the data collected.
• Calculate the factor.
• Using the data from the first run, calculate C_o.
• Calculate the value of H for each of the thicknesses.
• Plot H versus h.
• Explain your results.