Solving Relativistic Momentum Problem: Pion Decays into Photons

[mewmew]

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:
$$E=E1+E2=\gamma*m*v$$
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

 

[Meir Achuz]

E=m\gamma, not mv\gamma.
Just write p/E=v/c=(2k\cos\theta)/(2k).

 

[mewmew]

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.

 

[Meir Achuz]

The easy way is easier to remember. Physics is finding the easy way.