I am having trouble with getting the right answer for this problem that is pretty simple and it is driving me insane.(adsbygoogle = window.adsbygoogle || []).push({});

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:

[tex]

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

[/tex]

With E1=E1/c, E2=E2/c

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

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

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

Which reduces to [tex]Cos[\theta]=\gamma[/tex]*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 [tex]Cos[\theta]=1/2(about)[/tex], can anyone find my problem before I go insane? Thanks

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# Relativistic momentum

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