The "threshold energy" for μ+
and μ-
production by annihilation of an electron positron pair in a head on
collision is 105 MeV. It is clear that, in this case, all the energy of
the colliding particles can be used to create the new particle pair. This
gives a threshold energy that is 400 times less than in the
stationary target case (105 MeV compared with 43 GeV !! In the stationary
target case most of the beam energy goes into conserving forward momentum
and very little is left over to create the pair). This makes
the colliding beams method the natural choice for particle accelerators,
as was the case for LEP.
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