# Energy of Two Gamma Rays Produced by Pion Decay

#### TheBigDig

Homework Statement
An experiment is designed to search for proton decay. A suggested possible pathway is:
$p \rightarrow \pi^0 + e^+$

a) Calculate the signature momenta of both products of this two-body decay in the rest frame of the proton.

b) The decay of a neutral pion subsequently occurs on a very short timescale and produces two gamma rays. Calculate the average value of the energies of these gamma rays as observed in the laboratory where the proton is at rest.
Homework Equations
$$E_1 = \frac{M^2+m_1^2-m_2^2}{2M}$$
$$E_2 = \frac{M^2+m_2^2-m_1^2}{2M}$$
$$p = \frac{\sqrt{(M^2-m_1^2-m_2^2)-4m_1^2m_2^2}}{2M}$$
$$s = m_1^2c^4 + m_2^2c^4 +2E_1E_2 - 2p_1p_2cos\theta_{12}c^2$$
So I worked out the first part and obtained $E_1 = 478.8MeV$, $E_2 = 459.4MeV$ and $p = 0.49 MeV/c$ but I can't quite wrap my head around the second part. Normally, I'd use the equation for s but I'm confused since I don't know the angle between the gamma rays.

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#### kuruman

Homework Helper
Gold Member
I don't know the angle between the gamma rays.
You know what it is in the rest frame of the pion, do you not?

Staff Emeritus