NE406 Radiation Protection and Shielding
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NE406 Radiation Protection and Shielding
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Lesson 7: Interaction coefficientsIn 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-sectionIn previous courses, you have learned the concept of the macroscopic cross section, ,
for a material as the probability of interaction per unit path, with units
of  .
For photons, the traditional symbol for this is  ;
same idea, same unit.
Other variations that your are used to carry over to the new notation:
Distributions for scattering cross sectionsAnother notational similarity with the neutron idea of macroscopic cross section -- although you may not have seen it in your studies thus far -- is that for scattering interactions the variables that are used to describe the characteristics of the particle after the collision are expressed as distributions.For example, the linear scattering interaction rate for a given material
at a particular energy is denoted as This is interpreted in the usual way for a distribution:
with an energy between This means, of course, that:
since the particle must emerge with some energy.
The same is true for angular distributions, which are generally
written in terms of
with a deflection angle between and that:
Use of mass interaction and attenuation coefficientsOne 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
values we have discussed, but instead as this value divided by the material
density,  ,
which has units of 
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:
 ,
gives us interaction rate per unit volume, the product of flux and
mass interaction coefficient,  ,
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
where I = number of isotopes
No such juggling of units is needed if we stay on a per mass basis, since:
where
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Return to Course Outline © 1998 by Ronald E. Pevey. All rights reserved. |
= linear
absorption coefficient
= linear
scattering coefficient
.
This is a function of energy, not a distribution in energy
(the units are still 
.
).
,
with units of 
. Generally, for a given initial energy, there many different energies
are possible and we denote the probability distribution for the final energies
as 
,
with units of 
.
=
probability that particle emerges from the collision
and 
.
,
the angle of deflection of the particle, as in 
which is the angular deflection distribution for particles of energy E,
with units of 
.
As an illustration, you should be able to deduce that:
=
probability that particle emerges from the collision
and 
=
number density of isotope i (nuclei/barn/cm)
=
microscopic total cross section of isotope i (barns) 
=mass
fraction of isotope i in the material