Solving Relativistic Momentum Problem: Pion Decays into Photons

mewmew
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I am having trouble with getting the right answer for this problem that is pretty simple and it is driving me insane.

You start out with a pion that decays into 2 photons that split at an angle theta in opposite directions from the original pion.

The velocity v of the pion is 2.977*10^8 m/s, with a mass m of 135 MeV.

If E is the pions energy and E1 and E2 are the photons energy then we have:
<br /> E=E1+E2=\gamma*m*v<br />
With E1=E1/c, E2=E2/c

and so for momentum we have(P1-P2)Sin[\theta]=0 so we get P1=P2 so E1=E2

So we can write 2(P1+P2)Cos[\theta]=Ppion

Now we can write 2E/C*Cos[\theta]=\gamma*m*v

Which reduces to Cos[\theta]=\gamma*m*v*c/2E but this does not give me the correct angle :( The correct angle should be 6.79 degrees for each photon but as you can see from my equation since v=2.977 I get Cos[\theta]=1/2(about), can anyone find my problem before I go insane? Thanks
 
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E=m\gamma, not mv\gamma.
Just write p/E=v/c=(2k\cos\theta)/(2k).
 
Thanks, the book does it similar to how you solve it, but I like to be able to solve things in a way that I will remember on a test just in case I can't find the easy way. Thanks, I figured it was something stupid like that.
 
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The easy way is easier to remember. Physics is finding the easy way.
 
To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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