Available energy (particle collision)

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In particle physics, the available energy is the energy in a particle collision available to produce new matter from the kinetic energy of the colliding particles. Since the conservation of momentum must be held, a system of two particles with a net momentum may not convert all their kinetic energy into mass - and thus the available energy is always less than or equal to the kinetic energy of the colliding particles. The available energy for a system of one stationary particle and one moving particle is defined as:

where

is the total energy of the target particle,
is the total energy of the moving particle,
is the mass of the stationary target particle,
is the mass of the moving particle, and
is the speed of light.

Derivation[edit]

This derivation will use the fact that:

From the principle of the conservation of linear momentum:

Where and are the momentums of the created and the initially moving particle respectively. From the conservation of energy:

Where is the total energy of the created particle. We know that after the collision:

Denoting this last equation (1). But

and since the stationary particle has no momentum

Therefore from (1) we have

Square rooting both sides and we get

See also[edit]

References[edit]

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