[Q] What is derivation of total available energy formula for one way collisions?

[Eric]

I'm familiar with the formula

Ea^2 = 2Mc^2Em + (2Mc^2)^2 + mc^2)^2

 

where

Ea is total energy available for particle production in centre of momentum or mass frame of reference for the two particles

Em is total energy of bombarding particle in lab/ earth frame

M is target particle rest mass

m is bombarding particle rest mass

 

I'm aware that this is based on calculating the total kinetic energy in the frame of reference of the centre of momentum frame of both particles, but I haven't been able to find or work out - how this formula is derived.

 

Can you help?