- #1
TheBigDig
- 65
- 2
- 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.
- Relevant Equations
- [tex]E_1 = \frac{M^2+m_1^2-m_2^2}{2M}[/tex]
[tex]E_2 = \frac{M^2+m_2^2-m_1^2}{2M}[/tex]
[tex]p = \frac{\sqrt{(M^2-m_1^2-m_2^2)-4m_1^2m_2^2}}{2M}[/tex]
[tex]s = m_1^2c^4 + m_2^2c^4 +2E_1E_2 - 2p_1p_2cos\theta_{12}c^2[/tex]
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.