495 Lectures 1-6

• Interaction cross sections represent the area that an interaction centre presents to the incident photon and are measured in units of cm^2 or barns (1 barn = 10^-28 m^2).
• For a fluence Φ of photons crossing a unit volume containing one scattering centre, the number of interactions expected is 𝑛 ≈ 𝜎Φ.
• The expected number of interactions in a unit volume in which there are 𝜌 scattering centres is 𝑁 ≈ 𝜌 𝜎Φ.
• This also gives the number of interactions when Φ photons incident on an area cross a unit path length.
• Charged particle interactions with matter involve types of charged particle interactions, stopping power, restricted stopping power, radiative yield, Metcalfe chapter, pg 90-98.
• Charged particles travelling in matter are constantly interacting via Coulomb forces with all atoms (electrons and nuclei), undergo elastic and inelastic interactions, and lose kinetic energy with each inelastic collision until they eventually stop.
• Sources of charged particles in matter include photoelectric pair production, Compton imaging/therapy machines, and e-beam treatment.
• Electrons interact with atomic nuclei via Coulomb forces, resulting in trajectory deflection without energy loss, and acquire negligible energy.
• Multiple Coulomb Scattering theory can be used to predict the net angular deflection of an electron traversing a given thickness of material.
• Electrons are the main contributor to the tortuous path of light particles in medium compared to heavy particles, which travel effectively straight.
• Inelastic interactions involve collisions with atomic electrons (collision energy loss) and interactions with nuclear electric fields (radiative energy loss/Bremsstrahlung).
• Collision energy loss by charged particles leads to the ionization and excitation processes that cause biological damage in cells.
• The most common inelastic interaction is Hard Collisions, where a particle passes close to an atom, interacting with a single bound electron, resulting in an electron being ejected with considerable kinetic energy (10s – 100s of keV), these are referred to as delta rays or “knock-on electrons”.
• Soft and hard collisions are approximately equivalent in terms of their contribution to kinetic energy loss.
• Eventually, the particle will lose all its kinetic energy and stop, the rate of energy lost by the charged particle per unit distance travelled is referred to as the stopping power.
• In interactions with the nuclear field, an electron interacts with the coulomb field of the nucleus, leading to approximately 98% of cases resulting in elastic scattering, causing the trajectory of particles to change and being the primary cause of tortuous electron paths in the medium.
• Derivations of the stopping power require relativistic and quantum mechanical corrections, refer to textbooks (Podgorsak, etc.) for the gory details.
• In approximately 2% of cases, the electron is decelerated in the process of radiative (Bremsstrahlung) interaction, losing kinetic energy as a photon, this process is referred to as “braking radiation”.
• The process by which medical x-rays are produced is the radiative (Bremsstrahlung) interaction.
• Characteristic x-rays or Auger electrons are also produced due to the vacancy left in the atom.
• The energy loss of charged particles as they pass through media (per unit length) is called stopping power, represented by the equation 𝑆 ൌ െ 𝑑𝐸 𝑑𝑙 or in terms of a mass stopping power, ௌ ఘ ଵ ఘ ௗா ௗ௟ (MeV cm 2 /g).
• For light charged particles (electrons), stopping power can be broken down into the energy loss to radiation (Bremsstrahlung) and the energy loss to the medium (ionization + excitation).
• Soft collisions involve a particle interacting at a relatively large distance, where through Coulomb interactions, the kinetic energy lost by the particle is absorbed by the atom, leading to the excitation or ionization of a valence shell electron.
• Soft collisions are overwhelmingly the main contributor to the tortuous path of electrons in medium compared to heavy particles, which travel effectively straight.
• Mass Collisional Stopping Power is inversely proportional to 𝐸 ௄ up to about 1 MeV, then leveling off and gradually increasing.
• Range R is the mean distance travelled for electrons of a given energy in a given medium.
• X-rays are produced by bombarding a substance (target) with high-speed electrons.
• The density correction term is represented as �� ௥௔ௗ 𝜌 ൌ 𝑆 ௥௔ௗ 𝜌.
• Restricted stopping power 𝐿 ୼ is the fraction of the mass collision stopping power that includes all soft collisions and only those hard collisions which result in delta rays with energy less than Δ.
• The mean ionizing potential of the atom is represented as �� ௄.
• Radiation Yield is the fraction of an initial electron’s kinetic energy that is converted into heat.
• For clinically relevant electron energies (1 – 20 MeV), the total stopping power for liquid water is around 2 MeV / cm.
• It can be calculated by integration over the increasing rate of energy loss (inverse of stopping power) as the electron comes to a stop.
• Particles deposit more energy towards the end of their track in medium (Bragg peak).
• This is called the continuous slowing down approximation (CSDA).
• As charged particles travel through the medium and lose energy, stopping power is increasing.
• For electrons in a medium, the kinetic energy is represented as 𝑆 ௖௢௟ 𝜌.
• Mass Radiative Stopping Power is not very energy dependent below 𝐸 ௄ ~ 1 MeV, then approximately proportional to 𝐸 ௄ above 1 MeV.
• Proportional to 𝑍/𝐴 of the medium.
• In the Metcalfe chapter, the stopping powers for various materials have been tabulated.