(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

Consider the event ## p + \gamma \to p + \pi ##, where ##p## is a cosmic ray of a proton, ##\gamma## is a microwave background photon, and ##\pi## is a generated meson. What is the minimum energy of the proton for such an event to happen? Proton has a rest mass of 1 GeV/c2, π particle has a rest mass of 100 MeV/c2, and microwave background photon has an energy of 2.5*10^-4 eV.

2. Relevant equations

Conservation of energy and momentum equations.

$$ E = mc^2 $$

3. The attempt at a solution

From conservation of energy, we get the equation:

$$

\begin{align*}

E_i &= E_f \\

E_{p_i} + E_{\gamma} &= E_{p_f} + E_{\pi} \\

E_{p_i} + 2.5 \times 10^{-4} &= \gamma_{p_f}(1 \times 10^6) + \gamma_{\pi}(1 \times 10^5)

\end{align*}

$$

In order to minimize the energy of the initial proton, is it reasonable to simply set the gammas on the right side equal to 1 (i.e. let them be at rest)?

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# Special relativity with particles

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