A photon of energy travelling along the -axis strikes a stationary proton head-on

PHYSICS · Subjective · Fermi University Physics · Relativity & Gravitation · Special relativity: spacetime and kinematics · Relativistic dynamics and fields in flat spacetime

Invariance, Ch General bases, the metric and tensors in spacetime

Problem

A photon of energy

E_\gamma

travelling along the

x

-axis strikes a stationary proton head-on, producing a proton and a neutral pion travelling together at threshold:

\gamma+p\to p+\pi^0.

The rest energies are

m_pc^2=938.3\,\mathrm{MeV}

and

m_{\pi^0}c^2=135.0\,\mathrm{MeV}

. Using the invariant

P^\mu P_\mu=-M^2c^2

for the total four-momentum

P^\mu

of the initial state, find the threshold photon energy

E_\gamma

, the minimum energy for the reaction to occur.

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