A neutral pion of mass is at rest in the laboratory

PHYSICS · Multi-part · Fermi University Physics · Relativity & Gravitation · Relativistic dynamics and fields in flat spacetime · Relativistic dynamics and fields in flat spacetime

Relativity and Gravitation, Ch Relativistic momentum, energy and collisions

Problem

A neutral pion

\pi^0

of mass

134.98\ \mathrm{MeV}/c^2

is at rest in the laboratory. It decays into two photons. Treat the pion as isolated, so that four-momentum is conserved, and take

c = 2.998\times 10^8\ \mathrm{m\,s^{-1}}

. ((a)) Find the energy of each photon in the frame in which the pion is at rest. ((b)) Using the total energy and total momentum of the pair, find the invariant mass of the two-photon system in that frame. ((c)) A second

\pi^0

travels along the

+x

axis of the laboratory at

0.600c

. Write its four-momentum

\mathbf{P} = (E/c, \vec p)

by giving its energy

E

in MeV and its momentum

p

\mathrm{MeV}/c

, both measured in the laboratory.

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