Uncharged particle interactions notes

HPS/RAD 102 Radiation Science - Lecture 6: Uncharged (Neutral) Particle Interactions

Instructor Information

Instructor: Raynard K Fong, MS CHP
Role: Medical Health Physicist, specializing in radiation safety and dosimetry.

Course Overview: Uncharged Particle Interactions

Topics Covered: This lecture delves into the fundamental principles of how different types of radiation interact with matter, focusing on:
- Charged Particles: Review of their direct interaction mechanisms.
- Photon Interactions: Detailed exploration of various photon interaction processes.
- Attenuation & Shielding: Principles governing the reduction of radiation intensity and the design of protective barriers.
- Neutron Sources & Interactions: Understanding neutron behavior and their unique interaction pathways.

Fundamental Concepts:

What is Radiation?

Definition: Radiation is the emission and propagation of energy through space or a material medium, often transmitted by a particle (e.g., alpha, beta particle, photon, neutron).
Energy Transfer:
- During an interaction, energy is transferred from the incident particle (the radiation) to the atomic electrons within the target material (the medium it passes through).
- Resulting Effects of Energy Transfer:
- Ionization: Occurs when the transferred energy (E) is sufficient to completely eject an electron from its atomic orbit, creating an ion pair (e.g., E > 13.6 \text{ eV} for hydrogen). This process changes the chemical nature of the atom.
- Excitation: Occurs when energy (E) is transferred to an atomic electron, causing it to jump to a higher energy level (an excited state) without being ejected (e.g., E < 13.6 \text{ eV} for hydrogen). The atom later returns to its ground state, often emitting a photon.

What is Matter?

Definition: Matter is anything that has mass and takes up space, fundamentally composed of a vast collection of atoms.
Structure: Each atom is comprised of:
- A tiny, dense, positively charged nucleus located at its center, containing protons and neutrons (nucleons).
- A much larger, low-density atomic electron cloud surrounding the nucleus, where negatively charged electrons orbit in specific energy shells or orbitals.

Uncharged vs. Charged Particle Interactions

Perspective of Charged Particles:
- Charged particles (e.g., electrons, protons, alpha particles) interact continuously with the electromagnetic fields of atomic electrons and nuclei via Coulomb forces.
- They experience numerous small-angle deflections and energy losses as they pass through the electron cloud.
Perspective of Uncharged (Neutral) Particles:
- Uncharged particles (e.g., photons, neutrons) do not possess a net electrical charge and therefore are not influenced by Coulomb (electromagnetic) interactions.
- They perceive matter as largely empty space and only interact when they make a direct collision with either an entire atom, an atomic electron, or the nucleus itself.

Charged Particle Interactions

Capabilities: Charged particles are capable of interacting directly and frequently with electrons via Coulomb interactions, continuously transferring small amounts of energy.
Energy Loss Mechanisms for Electrons:
- Collisional Loss (Ionization and Excitation): The primary mode of energy loss, where electrons transfer kinetic energy to atomic electrons of the medium, causing ionization or excitation. This is dominant at lower electron energies.
- Radiative Loss (Bremsstrahlung x-rays): When a high-energy electron is decelerated by the electric field of an atomic nucleus, it emits electromagnetic radiation (Bremsstrahlung or "breaking radiation"). This mechanism becomes increasingly significant at higher electron energies and with higher atomic number (Z) materials.

Uncharged (Neutral) Particle Interactions:

Types of Neutral Particles: The primary neutral particles in radiation science are Photons (gamma rays and x-rays) and Neutrons.
Characteristics:
- Photons and Neutrons are not influenced by Coulomb interactions due to their lack of charge, consequently, they do not experience continuous energy loss.
- They interact with matter through discrete, often energetic, collisions (physical bumping) with atomic nuclei or electrons, creating secondary charged particles that then induce ionization and excitation.

Photon Interactions:

Definition of a Photon

Expression: A photon is a quantum of electromagnetic radiation, often conceptualized as a particle with no rest mass, traveling at the speed of light.
Energy: The energy of a photon is directly proportional to its frequency and is given by the equation: $E = h\nu$
- Where:
- h: Planck's constant ( $6.626 \times 10^{-34} \text{ J}\cdot\text{s}$ or $4.136 \times 10^{-15} \text{ eV}\cdot\text{s}$ ), a fundamental proportionality constant in quantum mechanics.
- $\nu$ : Frequency of the electromagnetic wave (in s $^{-1}$ or Hz).

Energy Relation to Wavelength

Formula: The speed of light (c) is related to frequency ( $\nu$ ) and wavelength ( $\lambda$ ) by the equation: $c = \lambda\nu$
- Substituting $\nu = c/\lambda$ into the energy equation, we get:
  $E = \frac{hc}{\lambda}$
Interpretation: This formula shows that energy is inversely related to wavelength ( $\lambda$ ):
- Higher energy photons correspond to shorter wavelengths.
- Conversely, lower energy photons have longer wavelengths.

Energy Transfer Mechanism

Photons primarily interact with atomic electrons to induce ionization, but they do so indirectly.
When a photon collides with an atomic electron, it transfers energy, which results in the electron being ejected or gaining significant kinetic energy.
This ejected or energized electron then acts like a beta particle (a charged particle) and subsequently causes ionization and excitation in the surrounding medium (indirect ionization).

Mechanisms of Photon Interactions in Matter

Photoelectric Effect (PE):
- In this interaction, an incident photon transfers all of its energy to a tightly bound atomic electron, typically an inner-shell (e.g., K-shell) electron, often ejecting it from the atom.
- The ejected electron is called a photoelectron, which then causes ionization and excitation as it travels through the material.
- The vacancy left behind is filled by an outer-shell electron, emitting characteristic X-rays or an Auger electron.
- The photoelectric effect predominates at lower photon energies and in materials with higher atomic numbers (Z).
Compton Scattering (CS):
- This is an elastic scattering interaction where an incident photon collides with a loosely bound (or free) atomic electron.
- The photon transfers only a portion of its energy to the electron, ejecting it (the Compton electron), and the scattered photon continues in a different direction with reduced energy and longer wavelength.
- The energy distribution is given by the formula: $E{\nu} = Te + E_{\nu'} + BE$
 - Where:
 - $E_{\nu}$ : Incident photon energy
 - $T_e$ : Kinetic energy of the Compton electron
 - $E_{\nu'}$ : Energy of the scattered photon
 - $BE$ : Binding energy of the electron (often negligible for outer-shell electrons, making $E{\nu} \approx Te + E_{\nu'}$ ).
- Compton scattering is the dominant interaction for photons in the intermediate energy range (e.g., 100 keV to 10 MeV for tissue).
Coherent Scattering (Rayleigh/Thomson Scattering):
- This is an elastic scattering process where the photon interacts with the atom as a whole, causing no energy change in the photon. The photon's direction is changed (scattered).
- It occurs predominantly at very low photon energies (E < 10 \text{ keV}) and is more significant in high-Z materials.
- Examples include Thompson Scattering (interaction with a free electron) and Rayleigh Scattering (interaction with bound electrons in an atom).
- While it does not transfer energy for ionization, it can contribute to dose by changing the photon direction within the body.
Pair Production (PP):
- A high-energy photon, under the influence of the strong electric field of an atomic nucleus, converts its energy into mass, producing an electron-positron pair.
- This interaction has a threshold energy: the incident photon must have an energy greater than twice the rest mass energy of an electron ( $2 \times 0.511 \text{ MeV} = 1.022 \text{ MeV}$ ).
- The energy conservation equation for pair production is:
 $h\nu = 2mc^2 + T+ + T-$
- Where:
 - $h\nu$ : Incident photon energy
 - $2mc^2$ : Energy equivalent of the rest mass of the electron-positron pair ( $1.022 \text{ MeV}$ )
 - $T_+$ : Kinetic energy of the positron
 - $T_-$ : Kinetic energy of the electron
- The positron eventually annihilates with an electron, producing two 0.511 MeV annihilation photons emitted in opposite directions.
- This interaction dominates at very high photon energies (> 10 \text{ MeV}).
Photonuclear Interaction ( $(\gamma,n)$ /Photo-disintegration):
- In this rare interaction, a very high-energy photon (typically > 7 \text{ MeV} for biological materials, or up to many tens of MeV depending on the nucleus) is absorbed by the target nucleus.
- This absorption leads to a nuclear reaction where the nucleus becomes unstable and emits secondary particles, most commonly a neutron (hence $\gamma,n$ ).
- Example:
 ${}^{206}{82}Pb + \gamma \rightarrow {}^{205}{82}Pb + n$
- This can induce radioactivity in the material and produce additional radiation hazards, like neutron exposure.

Indirect Ionization Effects of Secondary Electrons

All photon interactions (PE, CS, PP) create secondary electrons (photoelectrons, Compton electrons, pair electrons/positrons) that possess kinetic energy.
These secondary charged particles then directly cause:
- Ionization: Ejecting other electrons from atoms.
- Excitation: Raising electrons to higher energy levels.
This cascade of secondary electrons ensures that while photons are indirectly ionizing, they are still highly effective at depositing energy and causing biological damage through these subsequent charged-particle interactions.

Photon Interaction Probability

The total probability of a photon interacting with matter is dependent on the relative likelihood of the individual interaction mechanisms: Photoelectric Effect, Compton Scattering, and Pair Production.
Total linear attenuation coefficient ( $\mu$ ) representing the total probability of interaction is given by: $\mu = \mu{PE} + \mu{CS} + \mu_{PP}$
- Each component ( $\mu{PE}$ , $\mu{CS}$ , $\mu_{PP}$ ) varies with photon energy and the atomic number (Z) of the absorbing material, illustrating the energy and Z-dependence of each process.

Attenuation Coefficient

The linear attenuation coefficient ( $\mu$ ) is a measure of the fraction of photons removed from a beam per unit thickness of material. It quantifies the probability of photon interactions in a given material.
For a small thickness, the probability of interaction (P) can be approximated as: $P \approx \mu x$
- Where:
- $P$ : Probability of interaction
- $x$ : Material thickness (e.g., in cm or m)
- More accurately, the intensity (I) of a monoenergetic photon beam decreases exponentially as it passes through a material of thickness x, described by Beer-Lambert Law:
  $I = I_0 e^{-\mu x}$
- Where:
  - $I_0$ : Initial intensity of the photon beam
  - $I$ : Intensity after passing through thickness $x$
The mass attenuation coefficient ( $\mu/\rho$ ) (where $\rho$ is density) is often used as it is less dependent on the physical state of the material.

Half-Value Layer (HVL)

The Half-Value Layer (HVL) is the thickness of a specific material required to reduce the intensity of an incident photon beam by exactly half.
For every additional HVL of material, the intensity decreases by a factor of $1/2$ . Thus, after n HVLs, the intensity ( $In$ ) is: $In = I_0 \left(\frac{1}{2}\right)^n$
The HVL can be calculated using the linear attenuation coefficient ($\mu) as:
$HVL = \frac{\ln(2)}{\mu} \approx \frac{0.693}{\mu}$
The HVL is a critical parameter for radiation shielding, as it directly indicates the effectiveness of a material in attenuating radiation for a given photon energy. It is relevant for materials and the energy of the photons involved; typical material properties discussed frame the understanding of radiation interactions in imaging and radiation protection.

Neutron Interactions:

General Characteristics

Neutrons, being electrically neutral, like photons, interact with matter as if it's empty space.
They are termed 'indirectly ionizing' because they do not directly ionize atoms.
Instead, neutrons interact with atomic nuclei, producing other charged particles (e.g., recoil protons, alpha particles, gamma rays from capture) that then induce ionization and excitation in the surrounding material.

Interaction Mechanisms

Scattering:
- Neutrons collide with nuclei, transferring kinetic energy. This process is analogous to billiard balls colliding.
- Elastic Scattering: The total kinetic energy of the neutron and nucleus is conserved. Maximum energy transfer occurs when the neutron collides with a nucleus of similar mass (e.g., hydrogen, which has effectively the same mass). This is the primary mechanism for slowing down fast neutrons.
- Inelastic Scattering: The neutron's kinetic energy is not fully conserved; some energy is used to excite the target nucleus to a higher energy state. The excited nucleus then de-excites by emitting gamma rays. This occurs predominantly with high-energy neutrons and heavy nuclei.
Capture (Absorption):
- In this process, a neutron is absorbed by a nucleus, forming a compound nucleus that is often unstable.
- Radiative Capture ( $(n,\gamma)$ ): The most common capture reaction. The compound nucleus immediately emits a gamma ray to de-excite, for example: ${}^{10}{5}B + n \rightarrow {}^{11}{5}B^* \rightarrow {}^{11}_{5}B + \gamma$
- Charged Particle Capture ( $(n,p)$ , $(n,\alpha)$ ): The compound nucleus might emit a charged particle (proton or alpha particle), for example: ${}^{14}{7}N + n \rightarrow {}^{14}{6}C + p$
- These capture reactions often result in the formation of radioactive isotopes (activation products) and the emission of secondary radiation (gamma rays, protons, alpha particles) that contribute to dose.

Biological Implications

Scatter interactions are highly effective for slowing down neutrons, especially elastic scattering with light nuclei.
This is particularly important for biological systems because the body is largely water, which contains a high concentration of hydrogen atoms.
Hydrogen nuclei (protons) are very efficient at absorbing kinetic energy from neutrons due to their similar mass, effectively slowing down fast neutrons to thermal energies.
The recoil protons produced from these interactions are directly ionizing and are a major contributor to the biological dose from neutron exposure.

Summary of Interactions

Charged vs. Neutral

Charged Particles:
- Examples: Heavy charged particles (alpha particles, protons) and electrons (beta particles).
- Interact continuously via Coulomb interactions with atomic electrons and nuclei.
- Lose energy gradually and follow tortuous paths.
Neutral Particles:
- Examples: Photons (gamma rays, X-rays) and neutrons.
- Utilize discrete mechanisms for interactions (collisions with electrons or nuclei) due to lack of charge and are not subject to Coulomb forces.
- Lose energy in relatively large, infrequent steps, leading to longer mean free paths.

Directly vs. Indirectly Ionizing

Directly Ionizing:
- All charged particles interact directly with atomic electrons, transferring energy to cause ionization and excitation along their path.
Indirectly Ionizing:
- Neutral particles (photons and neutrons) do not directly cause ionization.
- Instead, they create secondary charged particles (e.g., photoelectrons, Compton electrons, recoil protons) that then interact with matter to cause ionization and excitation.

Attenuation Capabilities

Different materials attenuate radiation differently based on the type and energy of the radiation and the material's atomic composition and density.
- Alpha particles: Easily stopped by a sheet of paper or skin due to their large charge and mass.
- Beta particles (Electrons): Require a few millimeters of low-Z material like aluminum or plastic for shielding.
- Gamma rays (Photons): Require dense, high-Z materials like lead or concrete for effective attenuation, primarily through photoelectric effect and Compton scattering.
- Neutrons: Require hydrogenous materials (e.g., water, paraffin, concrete with high water content) to slow them down (moderate them) via scattering, followed by materials like boron or cadmium for capture.

Review Questions

What mechanisms do photons utilize for interaction in matter, and how do their probabilities change with photon energy and atomic number (Z) of the absorber?
How do neutrons interact differently from charged particles, and what implications does this have for biological systems, especially concerning the role of hydrogen?
Discuss how the half-value layer (HVL) concept supports the understanding of radiation shielding, and explain its relationship to the linear attenuation coefficient.