In modern collider experiments the beam energy K has much greater energy than its rest energy (K >> mc2). If two particles each of mass m collide head-on with each having beam energy K, the energy in the center of mass Ecm = 2K. Show that two particles of the same mass m colliding head-on with each having kinetic energy K (K >> mc2 ) have the same center-of-mass energy as the same particle of energy Klab in a fi xed-target accelerator colliding with the same target particle, where Klab ≈ 2K2 /mc 2

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In modern collider experiments the beam energy K has much greater energy than its rest energy (K >> mc2). If two particles each of mass m collide head-on with each having beam energy K, the energy in the center of mass Ecm = 2K. Show that two particles of the same mass m colliding head-on with each having kinetic energy K (K >> mc2 ) have the same center-of-mass energy as the same particle of energy Klab in a fi xed-target accelerator colliding with the same target particle, where Klab ≈ 2K2 /mc 2

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