Radiation Protection and Shielding
Lesson 17 - Neutron response functions
In this and the next lesson, we will be using cross sections (for neutrons) and linear interaction coefficients (for photons) to compute response functions. We need to keep in mind for both lessons that we are talking about kerma response functions for material that is present in the model by which we compute the flux that the response function is multiplied by to get the kerma. Another way of saying the same thing is:
We are building response functions to be used with fluxes that ARE influenced by the detector material.
This lesson, concerning neutron response functions, is the easier (and shorter) of the two because of the fact that the common notation in the "neutron community" follows the exact form given in the previous lesson:
where is the energy transferred to the material medium by secondary charged particles due to neutron reaction type j of isotope i.
The secondary charged particle of most concern for above-thermal neutron reactions is the recoiling nucleus itself. We assume is that the flux calculation itself takes care of the neutral particles -- the scattered neutrons and the gamma rays that are emitted from excited nuclei. For the case of elastic scatter, the recoiling nucleus contains all of the initial energy of the particle minus the energy carried off by the scattering neutron.
Isotropic elastic scattering
We learned earlier in the course that the average energy of the isotropically (in the COM system) elastic scattered neutron is halfway between the initial energy and the minimum energy of the scattered neutron, which means, of course, that the average energy of the recoil nucleus is one-half the energy lost, i.e.,
Anisotropic elastic scattering
If the collision is not isotropic, the deposited energy changes to:
where is the average cosine of the angle of scatter in the COM system. You must be sure to account for this anisotropy by using data (such as that found in Table 5.3).
( It makes sense that the deposited energy would decrease if the average scattering angle is forward, because -- as we learned in our study of kinematics of neutron collisions, the forward scatters are the ones in which the neutron loses the least energy.)
For inelastic scatter (which we will assume is isotropic), the deposited energy can be found from:
where, as before, we have:
On average, then, inelastic scattering reactions result in LESS energy being deposited in the material, but no lower than half as much (since ranges from -1 to 0).
Return to Course Outline © 1998 by Ronald E. Pevey. All rights reserved.