- #1

FaradayCage

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## Homework Statement

A (pi)0 meson whose rest mass is 135 MeV/c2 is moving with a kinetic energy of 1 GeV. It decays in flight into two photons whose paths are along the direction of motion of the meson. Find the energies of the two photons.

## Homework Equations

__Lab Frame:__

The invariant: [tex] E^2 = P^2c^2 + m^2c^4 [/tex]

Conservation of Energy: [tex] E = E_1 + E_2 = hf_1 + hf_2[/tex]

Conservation of Momentum: [tex] P = P_1 + P_2 = hf_1/c + hf_2/c[/tex]

__ZMF Frame:__

The invariant: [tex] E^2 = P'^2c^2 + m^2c^4[/tex]

Conservation of Energy(ZMF frame): [tex] m_0c^2 = E'_1 + E'_2 = hf'_1 + hf'_2[/tex]

Conservation of Momentum(ZMF frame): [tex] P' = P'_1 + P'_2 = 0[/tex]

## The Attempt at a Solution

Using invariant and [tex] E = E_1 + E_2 [/tex], [tex] P = P_1 + P_2 [/tex] (lab frame)

We have [tex] E_1^2 + E_2^2 + 2E_1E_2 = (P_1^2 + P_2^2 + 2P_1P_2)c^2 + m_o^2c^4 [/tex]

Not sure what other equations I can get from conditions given. Too many unknowns?? I get the feeling this should end up with a quadratic to give the two different energies...