Question 9.3.Q1: Neutron interactions with absorber are classified into two m......

(a) Neutron interactions with nuclei of an attenuator are summarized in Table 9.2. The interactions fall into two main categories: neutron scattering and neutron absorption.
Neutron scattering is further subdivided into two categories: (1) elastic scattering and (2) inelastic scattering. In both types of scattering a portion of neutron’s kinetic energy is transferred to the recoiling nucleus of the attenuator.

(1) In elastic scattering the kinetic energy of the recoiling nucleus is equal to the kinetic energy that the neutron loses in the elastic scattering interaction, i.e., kinetic energy is conserved in the interaction.
(2) In inelastic scattering, on the other hand, in addition to transferring energy to kinetic energy of the recoil nucleus, some of the energy that the neutron loses in the interaction is used to excite the recoil nucleus into an available nuclear exciting state. Consequently, kinetic energy is not conserved in the inelastic interaction even though the total energy is. Since energy to excite a given nucleus is discrete, inelastic scattering is an interaction process characterized by threshold energy.
(3) An additional category of scattering termed non-elastic scattering is often added to the elastic and inelastic scattering categories. It refers to energetic neutron interaction with attenuator nucleus in which the energetic neutron is absorbed and a charged particle rather than a neutron is emitted. This type of interaction could also be categorized as neutron capture, however, the term “neutron capture” is usually reserved for absorption of thermal neutrons rather than energetic neutrons.

Neutron absorption is subdivided into five diverse categories that all have one common feature: penetration of the neutron into the attenuator nucleus, neutron disappearance from the neutron beam, emission of various particles, and transformation of the attenuator nucleus into a new, usually radioactive, nuclide. Often neutron absorption is referred to as neutron capture and the term implies absorption of a thermal neutron.
The five categories of neutron absorption are:

(1) Neutron activation (n, \mathcal{γ}) nuclear reaction also referred to as thermal neutron capture. This reaction is most commonly triggered with thermal neutrons in a nuclear reactor and produces a radioactive isotope of target nucleus.
(2) Neutron capture accompanied by release of nuclear charged particles, such as protons in (n, p) reaction, deuterons in (n, d) reaction, and α particles in (n,α) reaction. This reaction plays an important role in the calculation and measurement of kerma and absorbed dose in radiotherapy and radiation dosimetry. Neutron capture accompanied by emission of a γ ray rather than charged particle is also very common.
(3) Neutron absorption that releases more than one neutron. Emission of only one neutron is indistinguishable from a scattering event, so it falls under the scattering category. However, emission of more than one neutron multiplies the number of neutrons in the beam and affects the neutron fluence, so it is accounted for in this category.
(4) Spallation neutron reaction. At very high neutron energy the penetration of the nucleus by a neutron can add a sufficient amount of energy to the nucleus to cause nuclear fragmentation into many small residual components.
(5) Fission. Certain high atomic number Z target nuclei when bombarded with thermal or fast neutrons can split into two nuclei of smaller Z accompanied by release of several energetic neutrons that can be used for sustaining a fission chain reaction.

Nuclei of attenuator atoms are associated with cross sections that are proportional to the probability of specific interaction between incident neutron and nucleus of the attenuator and are measured in units of cm²/atom, m²/atom, or, most often in barns/atom (b/atom) where 1 b = 10^{−24}\ cm^2. A specific microscopic cross section σ_i can be associated with each one of the various neutron interactions with the nuclei of the attenuating medium, as indicated in Table 9.2.
Total microscopic cross section σ or reaction probability is given as the sum of partial cross sections σ_i applicable for the individual interactions. Often, a particular calculation of a given physical problem requires the application of a specific microscopic cross section σ_i only. Since the individual cross sections σ_i depend on neutron kinetic energy E_K and, consequently, on neutron velocity v as well as on composition of the target nucleus, there are large variations in total microscopic cross section σ from one target nucleus to another. At low E_K the elastic cross section σ_{n,n} is nearly constant with increasing kinetic energy E_K, whereas the inelastic cross section σ_{n,n^{\prime}} and all capture cross sections decrease with increasing E_K and are proportional to 1/v, where v is the neutron velocity.

Values of partial cross sections σ_i are tabulated and usually given in units of cm²/atom; however, cross sections are usually combined first into one of the two major microscopic cross sections: scattering cross section σ_s (where σ_s = σ_{n,n} + σ_{n,n^{\prime}} ) and absorption cross section σ_a (where σ_a = σ_{n,γ} +σ_{n,xn^{\prime}} +σ_{n,cp} +σ_{n,s} +σ_{n,f}) for a given target nucleus and are then added to form the total microscopic cross section σ = σ_s + σ_a under the understanding that not all specific cross sections listed in Table 9.2 will be relevant for a given attenuating material at a given neutron energy.

(d) Kerma, an acronym for kinetic energy released in matter by indirectly ionizing radiation, is used in radiation dosimetry of photon and neutron beams. It is defined as energy that is transferred from neutral particles (photons or neutrons) to charged particles (CPs) per unit mass at a point-of-interest in the absorbing medium. In the case of photons the CPs released are electrons and positrons; in the case of neutrons they are protons and heavier ions.
Kerma is closely related to absorbed dose but the two quantities differ from each other because of radiation transport effects that manifest themselves through the finite range of the secondary charged particles released in the absorbing medium by indirectly ionizing radiation. Because of the very short range of heavy CPs released in absorbing medium by neutrons compared to the range of electrons and positrons released by photons, the charged particle equilibrium (CPE) is attained much faster in neutron beams than in photon beams.

(1) For mono-energetic photons of energy hν traversing an attenuating medium of atomic number Z and mass density ρ, kerma K at point-of-interest P in the attenuator is related to the photon energy fluence ψ at point P through the mass energy transfer coefficient \left(μ_{tr}/ρ\right) for given photon energy hν and attenuator atomic number Z. The mass energy transfer coefficient \left(μ_{tr}/ρ\right) is expressed as

\frac{\mu_{\mathrm{tr}}}{\rho}=\frac{\mu}{\rho} \frac{\bar{E}_{\mathrm{tr}}}{h \nu}=\frac{\mu}{\rho} \bar{f}_{\mathrm{tr}}            (9.52)

where

ρ    is the mass density of the attenuator.

μ    is the linear attenuation coefficient in units of cm^{−1}\ or\ m^{−1} for a given photon energy hν and attenuator atomic number Z.

μ_{tr}   is the linear energy transfer coefficient in units of cm^{−1}\ or\ m^{−1} for a given photon energy hν and attenuator atomic number Z.

\bar{E}_{\mathrm{tr}}   is mean energy transferred from photons of energy hν to charged particles (electrons and positrons) at point P in the attenuator of atomic number Z.

\bar{f}_{\mathrm{tr}}    is the mean energy transfer fraction for photons of energy hν and attenuating medium of atomic number Z.

Photon kerma K_γ at point P is thus expressed for mono-energetic photons as

K_\gamma=\psi \frac{\mu_{\mathrm{tr}}}{\rho}=\varphi h \nu \frac{\mu}{\rho} \frac{\bar{E}_{\mathrm{tr}}}{h \nu}=\varphi h \nu \frac{\mu}{\rho} \bar{f}_{\mathrm{tr}}=\varphi \frac{\mu}{\rho} \bar{E}_{\mathrm{tr}},            (9.53)

where

𝜙 is the photon fluence in cm^{−2}\ or\ m^{−2} expressing number of photons per area.
ψ is the photon energy fluence in MeV · cm^{−2}\ or\ J\ ·\ m^{−2}.

For a spectrum of photons energy fluence \psi^{\prime}(h \nu) at point-of-interest P and mass energy transfer coefficient \left(\mu_{\mathrm{tr}} / \rho\right)_{h \nu, Z} as a function of photon energy hν and attenuator atomic number Z, the kerma at point P is determined through the following integration

K=\int_{h \nu=0}^{h \nu_{\max }} \psi^{\prime}(h \nu)\left(\frac{\mu_{\mathrm{tr}}}{\rho}\right)_{h \nu, Z} \mathrm{~d} h \nu           (9.54)

where \psi^{\prime}(h \nu) is the differential distribution of photon energy fluence.

(2) The situation with neutron kerma is similar, yet not identical, to that of photons. For mono-energetic neutrons of kinetic energy E_{\mathrm{K}}^{\mathrm{n}} traversing an attenuating medium of mass density ρ and atomic number Z, the kerma at point P in the attenuating medium is related to neutron fluence φ through the neutron kerma factor \left(F_{\mathrm{n}}\right)_{h \nu, Z} that is characteristic of both hν and Z and expressed as follows

\left(F_{\mathrm{n}}\right)_{h \nu, Z}=\frac{\Sigma}{\rho} \overline{\Delta E_{\mathrm{K}}}=\frac{\Sigma}{\rho} \frac{\Delta E_{\mathrm{K}}}{E_{\mathrm{K}}^{\mathrm{n}}} E_{\mathrm{K}}^{\mathrm{n}}=\frac{\Sigma_{\mathrm{tr}}}{\rho} E_{\mathrm{K}}^{\mathrm{n}},          (9.55)

where

Σ    is the total macroscopic cross section in units of \mathrm{cm}^{-1} \text { or } \mathrm{m}^{-1} for neutron interaction in attenuating medium Z for neutrons of kinetic energy E_{\mathrm{K}}^{\mathrm{n}}.

\overline{\Delta E_{\mathrm{K}}}   is mean energy transferred from neutrons to charged particles (mainly protons) at point P in the attenuator.

\Sigma_{\mathrm{tr}} / \rho  is a parameter that plays a role of mass energy transfer coefficient and is for neutrons given by

\frac{\Sigma_{\mathrm{tr}}}{\rho}=\frac{\Sigma}{\rho} \frac{\Delta E_{\mathrm{K}}}{E_{\mathrm{K}}^{\mathrm{n}}} .            (9.56)

Kerma K_n for mono-energetic neutrons of kinetic energy E_{\mathrm{K}}^{\mathrm{n}} is thus expressed in terms of the neutron kerma factor F_n as follows

K_{\mathrm{n}}=F_{\mathrm{n}} \varphi=\frac{\Sigma}{\rho} \overline{\Delta E_{\mathrm{K}}}=\frac{n^{\square} \sigma}{\rho} \overline{\Delta E_{\mathrm{K}}}            (9.57)

where we used the standard relationship between the macroscopic interaction cross section Σ and microscopic cross section σ

\Sigma=n^{\square} \sigma          (9.58)

with n^{\square} the number of atoms (nuclei) per volume of the attenuating medium.
Kerma factors F_n are available from the literature in tabular format for various elements and compounds for a range of neutron kinetic energies E_{\mathrm{K}}^{\mathrm{n}} from thermal neutrons to fast neutrons (see, for example, the ICRU Report 26 or textbook by Attix).
For neutrons with an energy spectrum of neutron fluence \varphi^{\prime}\left(E_{\mathrm{K}}^{\mathrm{n}}\right) the following integral is used in calculation of neutron kerma

K_{\mathrm{n}}=\int_{E_{\mathrm{K}}^{\mathrm{n}}=0}^{\left(E_{\mathrm{K}}^{\mathrm{n}}\right)_{\max }} \varphi^{\prime}\left(E_{\mathrm{K}}^{\mathrm{n}}\right)\left(F_{\mathrm{n}}\right)_{E_{\mathrm{K}}^{\mathrm{n}}, \mathrm{Z}} \mathrm{d} E_{\mathrm{K}}^{\mathrm{n}}           (9.59)

where \left(F_{\mathrm{n}}\right)_{E_{\mathrm{K}}^{\mathrm{n}}, Z} represents neutron kerma factor as a function of E_{\mathrm{K}}^{\mathrm{n}} for a given attenuator medium Z.