Relativistic theory to Compton effect for spectroscopic detector

Abstract

We report here a theoretical proof of the limiting value of the velocity of target/particle responsible for various photon–electron interactions in the Compton scattering experiment which may be carried out in various applications such as gamma-ray spectroscopy. Compton scattering deals with the collision of photons with a target particle where both energy and momentum are transferred to the particle while the photon moves with reduced energy and a change of momentum. Here, the changed energy of a photon depends on the angle between the incident axis and scattered photon (θ), the rest mass of the electron, and the frequency of the photon before the collision. However, when some initial velocity is provided to an electron that is at rest initially, then in such cases, the particle obeys limiting value on velocity for a particular energetic photon to follow Compton scattering. In such cases, the changed frequency of photons also depends on the initial and final velocity of nonstationary electrons during a collision, including the angle (φ′) between the recoil electron and incident axis. Here, we have presented the derivations to calculate the recoil velocity of the nonstationary electron. These terms are the accurate solution of the Compton shift. We have tried to calculate the upper limit or limiting values of the initial velocity of the target particle in Compton scattering. Further, we have computationally demonstrated that there is a dependence of scattered photon frequency on initial velocity of target particle (u) and mass of the target particle (m) at a higher scattering angle. Finally, numerical simulations were carried out with particles such as an electron, pion (+/-, 0) to verify the greater degree of accuracy of the particles in spectroscopic detectors such as gamma-ray spectroscopy and other high energy spectroscopic techniques.