632 Particle Physics and Cosmology*P46.28(a)Let Eminbe the minimum total energy of the bombarding particle that is needed to inducethe reaction. At this energy the product particles all move with the same velocity. Theproduct particles are then equivalent to a single particle having mass equal to the total massof the product particles, moving with the same velocity as each product particle. Byconservation of energy:Em cm cp cmin+=+2232232ejbg.(1)By conservation of momentum:pp31=∴==−p cp cEm c32122122bgbgejmin.(2)Substitute (2) in (1):Em cm cEm cminmin+=+−223222122ejej.Square both sides:EEm cm cm cEm cEmmmcmKEm cmmmm mcmmmmcmminminminminminmin222222322212232122222123212221222321222222222++=+−∴=−−∴
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