Unlocking the Mystery of Photon Emission Angle Calculation Through Relativistic Equations

How can we prove the equation for the angle θ that two equal energy photons will emit?

Given the energy of each photon as 1/2m₀c²(γ+1) and the relation cos(θ)=√(γ−1/γ+1), what approach should be taken to derive the equation and find the correct angle?

Final Answer:

To prove the equation for the angle θ that two equal energy photons will emit, we can use the relationship between photon momentum and energy and the relativistic total energy equation.

Explanation:

In the given scenario, where two equal energy photons are emitted from an axis after an antiparticle collides with a corresponding particle, we can utilize the principles of relativistic equations to derive the equation for the emission angle θ.

Starting with the energy of each photon expressed as 1/2m₀c²(γ+1), we can analyze the total energy before and after the collision to establish a relationship that leads to the desired equation for cos(θ)=√(γ−1/γ+1).

By applying the relativistic total energy equation E² = (pc)² + (mc)² and considering the conservation of energy, we can simplify the equation and derive the expression for the emission angle θ in terms of the Lorentz factor γ.

Through a detailed examination of the photon momentum-energy relationship and the relativistic energy equation, we can unravel the mystery behind the photon emission angle calculation and showcase the intricate connection between energy, momentum, and the emitted photons' direction.