Compton scattering is a crucial quantum phenomenon where a photon collides with a charged particle, typically a loosely bound outer-shell electron, resulting in the photon losing some of its energy and momentum to the electron. This interaction leads to the photon being scattered at a reduced energy and a longer wavelength. It is one of the three primary ways that gamma rays and X-rays interact with matter, alongside the photoelectric effect and pair production, and plays a significant role in radiation detection, dosimetry, and shielding applications.
Discovered by Arthur Compton in 1923, the Compton effect provided compelling evidence for the particle-like nature of light, confirming that photons possess momentum as well as energy. His experiments demonstrated that X-rays scattered by electrons undergo a change in wavelength that depends on the scattering angle, a result that could not be explained by classical wave theory but was perfectly consistent with the concept of photons as discrete quanta of energy and momentum.
In a Compton scattering event, an incident photon, with energy and momentum , interacts with an electron at rest (or moving slowly compared to the photon's speed). The photon imparts some of its energy to the electron, causing the electron to recoil with kinetic energy. The scattered photon, now with lower energy () and longer wavelength (), is deflected from its original path at a scattering angle . Both energy and momentum are conserved during this relativistic collision.
The change in the photon's wavelength, known as the Compton shift, is described by the Compton formula:
Where:
is the change in wavelength.
is the wavelength of the scattered photon.
is the wavelength of the incident photon.
is Planck's constant ( J\cdot s).
is the rest mass of the electron ( kg).
is the speed of light in a vacuum ( m/s).
is the scattering angle of the photon relative to its initial direction.
The term
is known as the Compton wavelength of the electron (denoted as ), which has a value of approximately metres or pm. The maximum wavelength shift occurs at (backscattering), where , resulting in a shift of .
The energy of the scattered photon, , can be calculated using the incident photon energy and the scattering angle :
Compton scattering is a dominant interaction mechanism for photons in the intermediate energy range (typically MeV to MeV) across a wide range of materials, especially those with a low atomic number (Z). This makes it profoundly important in nuclear safety for several reasons: