Two equal-energy photons collide head-on and annihilate

Chapter 44, Problem 44.2

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Two equal-energy photons collide head-on and annihilate each other, producing a \(\mu^+\mu^-\) pair. The muon mass is given in terms of the electron mass in Section 44.1. (a) Calculate the maximum wavelength of the photons for this to occur. If the photons have this wavelength, describe the motion of the \(\mu^+\) and \(\mu^-\) immediately after they are produced. (b) If the wavelength of each photon is half the value calculated in part (a), what is the speed of each muon after they have moved apart? Use correct relativistic expressions for momentum and energy.

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