The uncollided gamma-ray flux N at a point P which is located a distance R (cm) from a point source of strength S (photons/s), with an intervening thickness t (cm) of material is given by the relation:
Where s is a materials constant which describes the probability of removal of gammas from the beam per cm of path traveled through the material (s is called the linear attenuation coefficient).
If the beam is measured at point P by a detector system capable of measuring the gamma-ray flux with an efficiency k, the detector will record C (counts/s), where:
Now, if the distance from source to detector, R, is held constant and the shielding material removed, the count rate will become:
And we see that dividing C by Co yields:
This ratio is defined as the attenuating factor of the shield of thickness t and material constant s (1/cm).
Taking the natural log of both sides of the expression:
This shows that a plot of C/Co vs. t would be linear on semi-log paper (and have the value of 1 at t=0), provided:
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To measure the linear attenuation coefficient of some typical engineering materials.
Since the experimental determination of depends on recording only the uncollided gammas reaching the detector, great care must be taken to insure that scattered gammas will not be counted.
There are two techniques commonly used to accomplish this:
The first method employs a "narrow beam" geometry in which the test set-up produces the smallest beam divergence angles possible. If any scattering occurs, the scattered gamma-ray is forced to move through a considerable amount of shielding in order to reach the detector, effectively reducing the contribution of the scattered component to the measurement.
There are obvious drawbacks to this method. In order to reduce the included angle of the beam, long flight paths or small apertures, usually both, must be used. This reduces the count rate at the detector, necessitating long count times or strong sources to attain reasonable counting statistics.
The second method utilizes the ability of scintillation detector system to reject (not count) pulses which lie outside a set "energy window".
Pulses coming to the counter from the detector have the typical spectrum shown (for a monoenergetic gamma-ray source). Setting an electronic window as shown ensures that the counter does not record any low energy pulses, including those reaching the detector after scattering. The peak corresponds to the energy of the source, and is identified as a photopeak, as it is mainly due to deposition of the total photon energy in a photoelectric effect.
In practice, a combination of both techniques is used: collimators to manage the beam, including personnel protection, and rejection of pulses that are not at source energy.
Set up the test geometry on the test stand as shown for the narrow-beam test, using one of the Reactor Facility's larger gamma sources (mCi of monoenergetic 137Cs, 198Au, or the 2-gamma 60Co,). These are license-level sources: handle them properly, and have a survey meter available to monitor the radiation field around the experiment. The collimators reduce the radiation fields around the experiment, reducing personnel exposure and experiment background.
