Particle Decay I
A particle of mass M at rest in the laboratory frame decays into two identical particles of mass m=m1=m2 and speeds |β|=0.866024.
(a) What is the speed and 4momentum of m2 as seen in the m1 frame?
Use the addition law β' = (0.866+0.866)/(1+0.866*0.866) = 0.9897
Then γ'=7, γ'β'=6.9282 and
Pμ = (mγ'c,mγ'v') = (7mc,6.9282mc).
(b) What is the mass ratio M/m?
The reaction is before = after: (γ=2 for β=0.866)
(Mc,0) = (mγc,mγv) + (mγc,-mγv)
Simply take (Mc,0)=(2mγc,0). ie, Mc = 2mγc = 4mc
M/m = 4.
This problem is too simple! You can just say energy before = energy after
(Mc2 = mγc2 + mγc2)
You could have squared the above to get the same rusult....
...simple, because particles were not created or destroyed.