Calculate Efficiency of Particle Production

[Nusc]

Homework Statement

Derive the efficiency for production of a particle of rest mass m made by colliding a 'bullet' particle of mass M with a stationary target particle mass N.

Homework Equations

ans is k^-1 =1 + (m+2M)/2N

The Attempt at a Solution

$$\bf{P_1} + \bf{P_2} = \bf{P}$$

$$\bf{P}^2 = \bf{P_1}^2 + \bf{P_2}^2 + 2\bf{P_1}\cdot \bf{P_2}$$

$$\bf{P_1}\cdot \bf{P_2} = c^2 M N \gamma(v)$$

$$\bf{P}^2 = m^2 c^2 - p^2$$

 

[gabbagabbahey]

The Attempt at a Solution

$$\bf{P_1} + \bf{P_2} = \bf{P}$$

$$\bf{P}^2 = \bf{P_1}^2 + \bf{P_2}^2 + 2\bf{P_1}\cdot \bf{P_2}$$

$$\bf{P_1}\cdot \bf{P_2} = c^2 M N \gamma(v)$$

$$\bf{P}^2 = m^2 c^2 - p^2$$

All you've done here is write down a bunch of equations (none of which has the definition of efficiency in it) without defining any of the variables you are using (except for the ones given in the problem statement), telling us why these equations are true (for example, "Conservation of momentum tells us..."), or even telling us which reference frame you are working in, or where you are stuck...Do you really expect people to able to provide help under these circumstances?