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Lesson 9 - Photon interactions

In this lesson we will pick up what we need to know about photon interactions in the energy range that we are primary interested in -- 1 keV to 20 MeV.  The top end of this range covers the highest energy gamma rays that we normally see from reactor or radioisotope decay source; the lower end is below the lowest energy gamma rays that can typically penetrate material in significant numbers.

We will cover the material in three categories:

  1. As part of our general nuclear engineering education, we will learn the terminology for photon interaction types that we are not going to study in great detail.
  2. We will learn the mechanisms, dominant energy ranges, and general characteristics for the three dominant photon attenuation mechanisms in the 1 keV-20 MeV energy range.
  3. We will develop the "energy absorption" coefficients lurking within the attenuation coefficients developed in (2), which will be of use to us later in the course.

 

General terminology for areas of the subject we will not study in detail

From the part of the reading that we will NOT concentrate on, you should be able to :

  1. Contrast incoherent vs. coherent scattering.
  2. Explain the meaning and importance of Thomson scattering.
  3. Explain what the Klein-Nishina formula is used for and be able to interpret Figure 3.3.
  4. Explain why coherent (Rayleigh) scattering is generally ignored.

 

Three predominant photon attenuation mechanisms in 1 keV < E < 20 MeV

The three predominant photon attenuation mechanisms are photoelectric effect, Compton scattering, and pair production.

The photoelectric effect -- which you should remember from your physics studies -- is described in Section 3.4.5 of the text. You should understand the underlying physics for this reaction. For photon shielding studies, this effect serves as a low-energy photon absorption mechanism; as demonstrated in Figure 3.4, the cross section associated with this mechanism increases so dramatically as energy drops that it serves as a "floor" of photon energies we are concerned about. (A glance at Table C.5 will indicate that even for the lightest elements, by 10 keV -- 0.01 MeV on the table -- wpeF5.gif (992 bytes) is more than 4, which -- for water-like densities -- would give us a mean free path of less than a quarter of a centimeter.  The photoelectric effect generally dominates the attenuation coefficient up to about 50-100 keV. 


Note: When describing the physics of this reaction, do not forget the low energy gammas produced as fluorescent radiation.


Pair production, the second dominant mechanism for photon attenuation, is described in Section 3.4.6 of the text.  Again, you should understand the underlying physics for this reaction.  It is a threshold reaction that is impossible below 1.02 MeV and generally doesn't become significant until about 5 MeV; therefore, it is only important in the upper range of the energies that we are concerned about in this class.  For our purposes, it acts like a scattering mechanism that always produces the same yield and energies for the outcoming photons -- 2 photons of 0.511 MeV energy.  Pair production generally dominate the attenuation coefficient above about 2-5 MeV.


Note: Since the energy of the resultant photons is below the threshold, obviously pair production can happen only once for a photon.  You should view it as a high-probability first reaction for a multi-MeV source photon.


Compton scattering, the third dominant mechanism for photon attenuation, was described in Section 3.3.  It tends to dominate for energies between the energy regions dominated by the other two mechanisms -- from about 50-100 keV to about 2-5 MeV.

 

Energy-absorption coefficients

The text sections 3.4.8 through 3.4.11 talks about "energy-absorption" cross sections.  I find this discussion a little hard to follow for reasons that are mentioned briefly in a footnote on page 47: These are not true cross sections (in the since of representing unique interaction possibilities.  There is no analogy to these "energy-absorption" cross sections, so let's back up a bit and put them in perspective.

Up to now you have used cross sections for two different purposes in your nuclear engineering education:

1.  You have used them for attenuation determination (i.e., how a particle beam is decreased as it travels through a material).  For this purpose we use the total macroscopic cross section wpe11F.gif (891 bytes) (for neutrons) and the linear attenuation coefficient wpe102.gif (871 bytes) (for photons), which shows up in an equation like:

wpe12D.gif (1368 bytes)

2.  You have used them for reaction rate determination.  Here the cross sections show up in equations multiplied by the flux:

wpe12E.gif (1744 bytes)

For this purpose, we have often broken the total cross section down into parts:

wpe12F.gif (1492 bytes)

Total = Capture + Fission + Scattering

each of which represent different types of interactions, and then proceeded to use the parts to get "partial" reaction rates, for example:

wpe130.gif (1728 bytes)

For each of these, the

 

The use of "energy-absorption" coefficients described here fall into a category similar to the second -- they are used with flux to determine a physically measurable quantity -- but these quantities are not reaction rates.   They are fractional energy deposition rates.

 

Their use is best illustrated by an example that contrasts how the "neutron community" would calculate energy deposition rate vs. how the "photon community" would handle the same physical phenomenon.  Let us say that we have a particle flux rate of wpe131.gif (883 bytes) particle/cm-squared/sec -- where the particles all have an energy of 1 MeV -- and the only reaction is a scattering reaction that always results in a 0.1 MeV particle.  We can all agree that the energy deposition rate can be found from:

wpe133.gif (1692 bytes)

where

wpe134.gif (1800 bytes)

Both the "neutron community" and the "photon community" simplifies this relation, but they do it differently.  The neutron community would maintain the total reaction rate as an entity in the calculation and would combine the fraction and E like this:

wpe135.gif (2587 bytes)

The photon community chooses instead to keep the full energy E, but to combine the fraction and the interaction coefficient, like this:

wpe136.gif (2110 bytes)

 

They do it different ways because they have different primary interest:   For the neutron community, reaction rates form the basis for neutron balance, which is of prime importance in reactor design; therefore their interaction coefficients (cross sections) always can be combined with fluxes to get true reaction rates.  For the photon community, energy deposition is the important consideration in dose rates, so ease of calculating energy deposition is incorporated into their interaction coefficients.

Just remember -- like the footnote said -- the energy-absorption coefficient is NOT the same as an absorption cross section: it does NOT represent the probability of occurrence of an "absorption reaction".  It only has meaning when multiplied by flux and initial particle energy to get energy deposition rate.

 

 


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