Chapter2_9 - = = ∑ final i p p p s In Lab-Frame In...

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PHY3063 R. D. Field Department of Physics Chapter2_9.doc University of Florida Center of Mass – Threshold Energy p 1 m 1 m 2 Center-of Mass Frame Before Collision p 2 p 1 + p 2 = 0 p 1 m 1 m 2 Laboratory Frame Before Collision p 2 = 0 Consider the collision of two particles from two frames of reference. In the “center-of-mass” frame the two particles have equal and opposite momentum and in the “Lab” frame particle 2 is at rest. Define s to be square of the sum of all 4-momenta before the collision (also equals the square of the sum of all 4-momenta after the collision since energy and momentum are conserved). Thus, 2 2 2 1 ~ ) ~ ~ (
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Unformatted text preview: = + = ∑ final i p p p s In Lab-Frame In CM-Frame 2 2 2 2 1 2 2 1 2 2 2 1 2 2 1 ) ( ) ( 2 ) ( ) ( ) ~ ~ ( 2 c m c m c m E cp E E p p s lab lab lab lab + + = − + = + = 2 2 2 1 2 2 1 ) ( ) ~ ~ ( cm cm cm E E E p p s = + = + = Thus, 2 2 2 2 2 2 2 1 1 2 ) ( ) ( c m c m c m s E lab − − = where 2 cm E s = . Threshold Energy: ( ) 2 2 2 2 2 2 2 1 min min 1 2 ) ( ) ( c m c m c m s E E lab threshold − − = = with ( ) 2 2 min 2 min = = ∑ final i cm c m E s . s is a Lorentz invariant! Particles produced at rest in the CM-frame! Sum of 4-momenta after collision!...
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