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
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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