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1291_Physics ProblemsTechnical Physics

# 1291_Physics ProblemsTechnical Physics - 632*P46.28...

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632 Particle Physics and Cosmology *P46.28 (a) Let E min be the minimum total energy of the bombarding particle that is needed to induce the reaction. At this energy the product particles all move with the same velocity. The product particles are then equivalent to a single particle having mass equal to the total mass of the product particles, moving with the same velocity as each product particle. By conservation of energy: E m c m c p c min + = + 2 2 3 2 2 3 2 e j b g . (1) By conservation of momentum: p p 3 1 = = = p c p c E m c 3 2 1 2 2 1 2 2 b g b g e j min . (2) Substitute (2) in (1): E m c m c E m c min min + = + 2 2 3 2 2 2 1 2 2 e j e j . Square both sides: E E m c m c m c E m c E m m m c m K E m c m m m m m c m m m m c m min min min min min min 2 2 2 2 2 2 3 2 2 2 1 2 2 3 2 1 2 2 2 2 2 1 2 3 2 1 2 2 2 1 2 2 2 3 2 1 2 2 2 2 2 2 2 2 2 + + = + =
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