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Threshold energy : ウィキペディア英語版
Threshold energy
In particle physics, the threshold energy for production of a particle is the minimum kinetic energy a pair of traveling particles must have when they collide. The threshold energy is always greater than or equal to the rest energy of the desired particle. In most cases, since momentum is also conserved, the threshold energy is significantly greater than the rest energy of the desired particle - and thus there will still be considerable kinetic energy in the final particles.
==Example==
Consider the collision of a mobile proton with a stationary proton, s.t. a ^0 meson is produced: p^+ + p^+ \to p^+ + p^+ + \pi^0
By transforming into the ZMF (Zero Momentum Frame, aka the Centre of Mass Frame), and assuming the outgoing particles have no KE (Kinetic Energy) when viewed in the ZMF the conservation of energy equation is:
E = 2\gamma m_pc^2 = 2 m_pc^2+ m_\pi c^2
Rearranged to give
\gamma = \frac
By assuming that the outgoing particles have no KE in the ZMF, we have effectively considered an inelastic collision, whereby the product particles move with a combined momentum equal to that of the incoming proton in the Lab Frame.
Our c^2 terms in our expression will cancel, leaving us with:
\beta^2 = 1-(\frac)^2 \approx 0.130
\beta \approx 0.360
Using relativistic velocity additions:
v_\text = \frac}/c^2}
We know that V_ is equal to the speed of one proton as viewed in the ZMF, hence we can re-write with u_ = V_:
v_\text = \frac^2/c^2} \approx 0.64c
So the energy of the proton must be E = \gamma m_p c^2 = \frac} = 1221\, MeV.
And Hence, it's Kinetic Energy must be T = E - \approx 280 MeV

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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