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Lesson 7: Interaction coefficients

In this lesson, we take concepts that you have already familiar from your previous study of  neutron cross sections and relate them to the slightly different notation that is predominant in describing photon interactions.  For this course, we need to be familiar with both nomenclatures.  In addition, this lesson describes the scattering interaction coefficients in terms of distributions in energy and direction for the particle after the scattering event.

 

Interaction coefficient = Macroscopic cross-section

In previous courses, you have learned the concept of the macroscopic cross section, wpe54.gif (868 bytes), for a material as the probability of interaction per unit path, with units of wpe55.gif (933 bytes).  For photons, the traditional symbol for this is wpe54.gif (871 bytes); same idea, same unit.

Other variations that your are used to carry over to the new notation:

  • wpe5C.gif (995 bytes)= linear absorption coefficient (Not QUITE equivalent, but we will cover the different in a later lesson)
  • wpe7A.gif (980 bytes)= linear scattering coefficient
  • wpe81.gif (927 bytes) gives a collision rate in interactions/cc/sec just like wpe82.gif (926 bytes)
  • a given wpe54.gif (871 bytes) is associated with a particle type and a particular material
  • wpe54.gif (871 bytes) is usually dependent on the energy of the particle, which is denoted as wpe83.gif (989 bytes)

Note:  One notational convention that does not carry over is that we do not use the subscript "t" on wpe54.gif (871 bytes) for "total".  Instead, the "bare" wpe83.gif (989 bytes) corresponds to the neutron notation of macroscopic total cross section wpeAA.gif (1005 bytes)

wpe83.gif (989 bytes) is referred to as the linear attenuation coefficient, since it is the coefficient by which a photon population decreases ("attenuates") as it penetrates a material (i.e., wpeAC.gif (962 bytes)).


 

Use of mass interaction and attenuation coefficients

One other convention that we will have to get used to is that the photon interaction coefficients themselves are not usually tabulated (i.e., presented in data tables or problem descriptions) as the wpe54.gif (871 bytes) values we have discussed, but instead as this value divided by the material density, wpeAD.gif (937 bytes), which has units of wpeAE.gif (997 bytes) and is referred to as the mass interaction (or attenuation) coefficients.  (i.e.,The word "linear" is replaced with the word "mass".) 

 

This has been found to be useful for a number of reasons:

  • Where, as we have seen, the product of flux and linear interaction coefficient, wpe81.gif (927 bytes),  gives us interaction rate per unit volume, the product of flux and mass interaction coefficient, wpeAF.gif (1107 bytes), gives us interaction rate per unit mass.

  • As we will see in Chapter 5, the concept of dose, in units of rad, is a measure of energy deposition per unit mass, which fits this unit better..

  • The energy dependence of wpeAD.gif (937 bytes) tends to be fairly uniform for many different materials.   As we will see, photon interactions tend to be driven by the presence of electrons.   Since materials with similar masses tend to have similar numbers of electrons, this uniformity results.


Note: It is somewhat surprising (to me, at least) to compare the data in Tables C.5 on pages 451 and 452.  It shows that the mass interaction coefficients for air and water are very similar.  (The principal difference is that water has a substantial hydrogen content.  Hydrogen delivers more electrons per unit mass than any other element.)


  • Since it is per unit mass, it applies just as well to elements as to materials.  The neutron community uses a microscopic cross section for individual isotopes and builds macroscopic cross sections from them using isotope densities:

wpeB1.gif (1212 bytes)

where I = number of isotopes

wpeB3.gif (906 bytes)= number density of isotope i (nuclei/barn/cm)

wpeB4.gif (892 bytes)= microscopic total cross section of isotope i (barns) 

 

        No such juggling of units is needed if we stay on a per mass basis, since:

wpeB5.gif (1599 bytes)

where wpeB6.gif (892 bytes)=mass fraction of isotope i in the material

 

 

 


Return to Course Outline                                                                                               İRonald E. Pevey.  All rights reserved.