Available energy (particle collision)

From Wikipedia, the free encyclopedia
Jump to: navigation, search
For a discussion about the meaning of the term in classical thermodynamics, see Exergy.

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:

 E_a = \sqrt{2 E_t E_k + (m_t c^2)^2 + (m_k c^2)^2}

where

 E_t is the total energy of the target particle,
 E_k is the total energy of the moving particle,
 m_t is the mass of the stationary target particle,
 m_k is the mass of the moving particle, and
 c is the speed of light.

Derivation[edit]

Suppose the following:

 E_a = E_k + E_t

We know that since

 E = m c^2

must hold, then

 E_k = m_k c^2

and

 E_t = m_t c^2

should both hold. From here, we can see that

 E_a = m_k c^2 + m_t c^2

Squaring both sides, we get

 (E_a)^2 = (m_k c^2 + m_t c^2)^2

Expanding, we can see that

 (E_a)^2 = ((m_k c^2)^2 + (m_t c^2)^2 + 2 (m_t c^2) (m_k c^2))

Taking the square root of both sides,

 E_a = \sqrt{(m_k c^2)^2 + (m_t c^2)^2 + 2 (m_t c^2) (m_k c^2)}

Evaluating the inside of the square root, we see that

 E_a = \sqrt{(m_k c^2)^2 + (m_t c^2)^2 + 2 E_k E_t}

Which can be rearranged to form the original equation,

 E_a = \sqrt{2 E_t E_k + (m_t c^2)^2 + (m_k c^2)^2}

See also[edit]

References[edit]

External links[edit]