Conservation Laws in the Particles’ Decays

          A  particle with mass M decays at rest. Two particles, having the rest masses  and , result from this process. Compute each particle’s total energy immediately after the event.

Solution

In the frame of reference where the complex particle is initially at rest, one can write two equations:

        (2.1)      (conservation of energy)

   (2.2)   (conservation of  momentum)

where E₁ and E₂ are the total energies of the resulted particles and are their relativistic linear momenta.

Each linear momentum may be written according to the particle total energy:

       (2.3)

where c is the velocity of light and  are the rest masses of the final particles.

Plugging (2.3) into (2.2) gives:

      (2.4)

From (2.1), we get . This expression may be replaced in (2.4), and we get:

           (2.5)

Therefore:

and     (2.6)

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