# X-ray Attenuation Mechanisms ## What is X-ray Attenuation?

The reduction in energy, or intensity, of a beam of X-rays due to their interaction with matter

- X-ray attenuation occurs as X-rays travel through materials - The beam loses energy through various interaction processes with atoms in the material ## The Four Main Attenuation Mechanisms - There are four principal ways X-rays can be attenuated: - Simple scattering - Photoelectric effect - Compton scattering - Pair production - All these mechanisms occur within the material the X-rays are travelling through - Each mechanism dominates at different X-ray energies ### Energy Dependence of Attenuation Mechanisms - The relative importance of each mechanism varies significantly with photon energy - Understanding which mechanism dominates at different energies is crucial for applications - The chart below shows how the probability of each mechanism changes with X-ray photon energy:

**Key observations from the chart:** - Photoelectric effect dominates at **low energies** (< 50 keV) - Compton scattering dominates at **medium energies** (50-1000 keV) - Pair production only occurs above **1022 keV** and dominates at very high energies - Simple scattering contributes minimally across all energies ## Simple Scattering ### What Happens - Simple scattering occurs when a low-energy X-ray photon encounters an electron in an atom - The photon is scattered (deflected) from its original path without any change in energy - 'Low-energy' in this context means the photon energy is insufficient to cause ionisation ### Key Characteristics - **No change in energy** of the X-ray photon - **No absorption** of the X-ray photon - The photon is merely redirected by interaction with atoms ### Effect on Medical Imaging - Simple scattering causes **blurring** or 'noise' in X-ray imaging - This is because scattered X-rays arrive at the detector from several different angles - Some arrive directly from the main beam - Others arrive after being scattered, coming from oblique angles - The scattered radiation degrades image quality by adding unwanted signal ## Photoelectric Effect ### What Happens - An X-ray photon is absorbed by an **inner shell electron** - The electron is ejected from the atom as a **photoelectron** - The X-ray photon is **completely absorbed** in this process

All of the X-ray photon's energy is transferred to the photoelectron when photoelectric absorption occurs

### Energy Conservation - Since energy is always conserved, the energy of an incident X-ray photon equals: - The work function + the maximum kinetic energy of the photoelectron ### The Photoelectric Equation - The energy within a photon is equal to $hf$ - This energy is transferred to the electron to: - Release it from the material (the work function $\phi$) - Give it kinetic energy $$E = hf = \phi + \frac{1}{2}mv^2_{max}$$ **Where:** - $h$ = Planck's constant (J s) - $f$ = the frequency of the incident radiation (Hz) - $\phi$ = the work function of the material (J) - $\frac{1}{2}mv^2_{max} = E_{k(max)}$ = the maximum kinetic energy of the photoelectrons (J) ## Compton Scattering ### What Happens - An X-ray photon is deflected by an interaction with an **orbital electron** - The photon's wavelength **increases** (energy decreases) - The electron is ejected from the atom at high speed ### Key Differences from Simple Scattering - Unlike simple scattering, the X-ray photon **imparts some of its energy** to the orbital electron - This is an intermediate-energy process (higher energy than simple scattering, lower than pair production) ### What Changes in Compton Scattering **The X-ray photon:** - Is deflected from its initial path - Has its wavelength increase (energy decreases) **The electron:** - Is ejected from the atom - Travels at high speed ### Conservation Principles - The electron and X-ray are deflected in different directions - This occurs due to **conservation of momentum** - Energy is shared between the scattered photon and the ejected electron ## Pair Production ### What Happens

Pair production only occurs with very high energy X-ray photons near an atomic nucleus

- A high energy X-ray photon passes close to the nucleus of an atom - The photon is converted into an **electron-positron pair** - Both particles are created simultaneously ### The Physics Behind Pair Production - This arises from Einstein's **mass-energy equivalence principle**: $$E = mc^2$$ **Where:** - $E$ = the energy of the X-ray photon (J) - $m$ = the mass of the electron and positron = $2m_e$ (kg) - $c$ = the speed of light (m s$^{-1}$) ### Energy Requirements - Pair production can only occur with **high energy X-rays** - The photon energy must be above a certain threshold value - This threshold is the total rest mass energy of the electron-positron pair ### Minimum Energy Calculation - The minimum energy $E_{min}$ for pair production is: $$E_{min} = hf_{min} = 2m_e c^2$$ **Where:** - $h$ = Planck's constant (J s) - $f_{min}$ = the minimum frequency for pair production (Hz) - $m_e$ = the rest mass of an electron (kg) - $c$ = the speed of light (m s$^{-1}$) ### What Happens to the Photon - As a result of pair production, the X-ray photon is **completely absorbed** - All its energy is imparted to the electron-positron pair - The created particles have kinetic energy equal to any excess energy beyond the threshold ## Summary Table | Mechanism | Energy Level | Photon Outcome | Electron Outcome | Products | |-----------|--------------|----------------|------------------|----------| | Simple Scattering | Low | Deflected, no energy change | Not ejected | Scattered photon (same energy) | | Photoelectric Effect | Medium | Completely absorbed | Ejected (photoelectron) | Photoelectron | | Compton Scattering | Medium-High | Deflected, energy decreases | Ejected at high speed | Scattered photon (lower energy) + electron | | Pair Production | Very High | Completely absorbed | Created (pair) | Electron + positron |