Coherent scattering is an interaction between a photon (such as an X-ray) and an atom, where the photon’s path is altered without changing its energy. This process is also referred to as Rayleigh scattering, especially when dealing with visible light interacting with small atmospheric particles. The scattered photon retains the same energy, frequency, and wavelength as the incident photon, classifying the interaction as elastic. Coherent scattering is defined by the preservation of phase, meaning the scattered wave maintains a predictable, fixed relationship with the incoming wave. This preservation allows for constructive and destructive interference, which is key to its applications.
The Mechanism of Coherence
The process begins when an incident photon interacts with the entire electron cloud of an atom, rather than a single electron. Since the photon’s energy is relatively low, it is insufficient to remove an electron, and they remain tightly bound. This collective interaction causes the electrons to oscillate in response to the electric field of the incoming wave, vibrating at the same frequency as the incident photon.
These oscillating electrons act as secondary emitters, re-radiating the absorbed energy as a new photon. Because the atom remains in its initial ground state and no energy is transferred, the scattered photon’s energy remains unchanged.
The fixed phase relationship arises because the re-radiated wave is a direct and consistent response to the incident wave. The collective oscillation of the electron cloud ensures that the re-emitted waves are synchronized. This synchronization forms a scattered wave that maintains a predictable phase with the original incoming wave, enabling interference.
Contrasting Coherent and Incoherent Scattering
Coherent scattering is often contrasted with incoherent scattering, known as Compton scattering, as both change the photon’s direction. Coherent scattering is elastic, involving no energy loss, while Compton scattering is inelastic, involving energy transfer. This difference stems from the nature of the photon’s target within the atom.
In Compton scattering, the incident photon interacts with a single, loosely bound electron, similar to a collision. The photon transfers some energy and momentum directly to the electron, causing the electron to recoil and be ejected from the atom.
Consequently, the scattered photon has less energy, resulting in a longer wavelength. Compton scattering is incoherent because the phase relationship is not maintained, meaning the scattered waves cannot interfere predictably. The result is a loss of energy from the photon beam and the creation of a recoil electron, whereas coherent scattering only redirects the photon without energy loss or ionization.
Factors Influencing Coherent Scattering
The likelihood and intensity of coherent scattering depend on the target material and the energy of the incident photon. The probability of this interaction increases with the atomic number (\(Z\)) of the material. Heavier elements have a larger number of electrons, which presents a greater collective target area for the photon, enhancing the coherent effect.
The interaction is highly sensitive to photon energy, decreasing rapidly as energy increases. The cross-section is inversely proportional to the square of the photon energy, making it dominant at very low energies. For typical X-ray imaging, coherent scattering is most important below 10 to 50 kilo-electron volts (keV).
Coherent scattering is primarily a forward-directed phenomenon. Scattered photons tend to travel at small angles relative to the original path of the incident beam, and the intensity diminishes as the scattering angle increases.
Applications in Science and Medicine
The preserved phase relationship enables X-ray diffraction (XRD), a technique used to determine the atomic structure of crystalline materials. When a coherent X-ray beam strikes a crystal, the regularly arranged atoms scatter the X-rays. Since the scattered waves are coherent, they interfere with one another, creating a high-intensity pattern of spots on a detector called a diffraction pattern.
This interference pattern maps the material’s internal atomic structure. By analyzing the angles and intensities of the spots, scientists can mathematically reconstruct the arrangement of atoms and molecules within the crystal lattice, a process known as crystallography. Preserving phase allows researchers to obtain structural information at the atomic level, which is not possible through simple absorption imaging.
In medical imaging, coherent scattering contributes to X-ray phase-contrast imaging (XPCI). Conventional X-ray images rely on photon absorption, which provides poor contrast for soft tissues like cartilage or tumors due to similar absorption properties. XPCI exploits the subtle phase shifts caused by coherent scattering as X-rays pass through a material. Because the phase shift is sensitive to small variations in electron density, XPCI improves the contrast between different soft tissues. This technology is promising in areas like low-energy mammography, offering improved visualization of fine tissue structures with a potentially lower radiation dose.