Why do photons/electrons scatter at angles in compton scattering?

[nlsherrill]

This is something that I always just took for granted, but I have no idea how a photon scatters off of an electron at an angle other than 0 or 180 degrees. I haven't seen this mentioned in a modern physics or nuclear engineering textbook either, so I assuming its a pretty complicated reason?

 

[Dickfore]

An incident photon has a well-defined momentum. According to the Heisenberg's Uncertainty principle, its position is unknown. Particularly, the impact parameter, as defined in classical scattering theory, is not defined and may take any value. But, different impact parameters correspond to different scattering angles, so you get a whole spectrum of scattering angles.

More formally, the scattering matrix element between two plane-wave states is non-zero. The square of the modulus, multiplied by the available phase space around the final state, gives the scattering cross section.

 

[nlsherrill]

Dickfore,

Thanks for the quick reply! So essentially all comes down to the uncertainty principle? I understand classical scattering and understood the connection you made to an impact parameter.

 

[Bob S]

The inelastic scattering of a photon off of a free stationary electron is described classically by Thomson scattering, and relativistically by Compton scattering. The two solutions agree for photon energies up to roughly 100 keV.
The kinematics requires conservation of energy, and conservation of momentum in both longitudinal and transverse planes (3 unknowns, and 3 equations total). This is very similar to billiard ball kinematics.

See Section 4 in http://farside.ph.utexas.edu/teaching/em/lectures/node92.html for a discussion of Thomson scattering.

 

[sardar]

Compton scattering is a phenomenon that occurs when a photon interacts with an electron, resulting in the photon losing some of its energy and changing direction. This process was first described by Arthur Compton in 1923 and has since been extensively studied and explained by modern physics theories.

The reason why photons and electrons scatter at angles in Compton scattering can be explained by the principles of quantum mechanics. In this theory, particles such as photons and electrons are described as wave-like entities that have both particle and wave-like properties. When a photon interacts with an electron, it behaves like a wave and can be described by a mathematical function known as a wavefunction.

The wavefunction of the photon determines the probability of where it will interact with the electron. This probability is not uniform, meaning that there are certain areas where the photon is more likely to interact with the electron than others. This is known as the scattering cross-section.

The scattering cross-section is influenced by several factors, such as the energy of the photon and the properties of the electron, including its mass and charge. These factors determine the strength of the interaction between the photon and the electron, which ultimately affects the angle at which the photon will scatter.

Additionally, the spin of the electron also plays a role in Compton scattering. The electron's spin can either be aligned or anti-aligned with its motion, and this affects the probability of the photon interacting with it. This leads to a preference for certain scattering angles, which can be observed in experiments.

In summary, the reason why photons and electrons scatter at angles in Compton scattering is due to the wave-like nature of these particles and the probability of their interaction, which is influenced by various factors such as energy, mass, charge, and spin. This phenomenon is well-understood and has been extensively studied in modern physics, providing a deeper understanding of the interactions between particles at the quantum level.