Relativistic elastic scattering refers to the process in which two particles collide and exchange energy and momentum without any permanent change in their internal structures. In the case of electron-muon scattering in the presence of a linear polarized electromagnetic wave, several effects come into play, including the interaction with the electromagnetic field.
When an electron and a muon scatter elastically, their trajectories and momenta change due to the interaction between the particles. The presence of a linear polarized electromagnetic wave further complicates the dynamics of the scattering process.
The electromagnetic wave exerts a force on the charged particles, which influences their motion. This force depends on the charge and velocity of the particles, as well as the strength and polarization of the electromagnetic wave.
In the relativistic regime, where the speeds of the particles are close to the speed of light, special relativity must be considered to accurately describe the scattering. Relativistic effects, such as time dilation and length contraction, can affect the kinematics of the scattering process.
The exact details of the scattering process, including the differential cross-section (a measure of the probability of scattering in different directions) and the final state of the particles, depend on the specific properties of the particles, the incident electromagnetic wave, and the scattering angle.
To analyze such a scattering process in detail, one would typically employ a theoretical framework such as quantum electrodynamics (QED) or a more specialized model that takes into account the specific characteristics of the particles and the electromagnetic field.
It is worth noting that describing the full details of such a scattering process requires a more involved mathematical treatment and specific assumptions about the initial conditions and properties of the particles and the electromagnetic wave involved.