- #1

Forco

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## Homework Statement

A particle of mass M and 4-moment P decays into two particles of masses m

_{1}and m

_{2}

1) Find the total energy of each particle (lab frame).

2) Show that the kinetic energy T

_{1}of the first particle in the same reference frame is given by

$$T_1= \Delta M (1 - \frac{m_1}{M} - \frac{\Delta M}{2M}) $$

3) A pion (M= 139.6 MeV) decays into a muon (m=105,7 MeV) and a neutrino (m=0). Find the kinetic energy of the muon and the neutrino (pion rest frame and lab frame).

## Homework Equations

$$ E_1+E_2 = Mc^2$$

$$E_{1}^{2} +\frac{p^2}{c^2} = m_{1}^{2} c^4$$

$$E_{2}^{2} +\frac{p^2}{c^2} = m_{2}^{2} c^4$$

## The Attempt at a Solution

I was able to do the first one, since it was really simple, I only needed to set

$$E_{1}^{2} - m_{1}^{2} c^4 = E_{2}^{2} - m_{2}^{2} c^4$$

And since $$ E_1+E_2 = Mc^2$$, it was easy to find that

$$E_1 = \frac{M^2+m_{1}^{2}-m_{2}^{2}}{2M}$$

Which is the correct expression for the energy. I'm having some trouble with the other two though. Especially the second one.

Any help is appreciated.