Abstract
Energy-momentum conservation laws in Compton scattering are analyzed. The conservation of total angular momentum is applied to a general formula that describes the variation of the light angular momentum. The Compton scattering model of a vortex beam is generalized to describe the momentum exchange beyond the well-known photon wave number shift. The illustrated analysis indicates that the light angular momentum may vary due to Compton scattering.
Highlights
Compton Scattering satisfies conservation both energy and momentum in inelastic collision between a photon and an electron
Our analysis focuses on three main cases for the vortex light beam: first when it possesses well define orbital angular momentum states, when it possesses both spin and orbital angular momentum that are separately conserved during free propagation
Their coupling is associated with the ratio of total angular momentum to linear momentum that is Compton Scattering of this case is supposed to be described by total angular momentum (Jc) which associates with the coupling of spin and orbital momenta states:
Summary
Compton Scattering satisfies conservation both energy and momentum in inelastic collision between a photon and an electron. ; Compton scattering can be generalized to include the conservation of angular momentum too. Of a single photon, is quantized by an integer number called the topological charge of the vortex beam [3]. Vortex light beam carry spin angular momentum that associates with polarization states. Several studies have been recently described variation in light angular momentum at Compton scattering in ultra-relativistic considerations [4, 5]. This study describes the Compton effect of a vortex light beam which carries both angular and spin angular momentum in form of two components: orbital and spin. Our analysis is important to understand angular momentum transfer between a photon and an electron or any massive particle
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