Classical Electrodynamics · Problem 11.24

Radiating Systems, Multipole Fields and Radiation — John David Jackson

Physics — E&M · threshold-kinetic-energy-reactions

Problem

The threshold kinetic energy

T_{\rm th}

in the laboratory for a given reaction is the kinetic energy of the incident particle on a stationary target just sufficient to make the center of mass energy

W

equal to the sum of the rest energies of the particles in the final state. Calculate the threshold kinetic energies for the following processes. Express your answers in MeV or GeV and also in units of the rest energy of the incident particle (unless it is a massless particle). (a) Pi-meson photoproduction,

\gamma p \to \pi^0 p

(m_p = 938.5 \text{ MeV}, \quad m_{\pi^0} = 135.0 \text{ MeV})

(b) Nucleon-antinucleon pair production in nucleon-nucleon collisions, for example,

pp \to ppp\bar{p}

. (c) Nucleon-antinucleon pair production in electron-electron collisions,

e^-e^- \to e^-e^-p\bar{p}

and

e^+e^- \to p\bar{p}

(m_e = 0.511 \text{ MeV})

Related theory

Work And Kinetic Energy Work Energy Theorem

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