A particle of mass m1 is fired at a stationary particle of

Chapter 46, Problem 68

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A particle of mass m1 is fired at a stationary particle of mass m2, and a reaction takes place in which new particles are created out of the incident kinetic energy. Taken together, the product particles have total mass m3. The minimum kinetic energy the bombarding particle must have so as to induce the reaction is called the threshold energy. At this energy, the kinetic energy of the products is a minimum, so the fraction of the incident kinetic energy that is available to create new particles is a maximum. This condition is met when all the product particles have the same velocity and the particles have no kinetic energy of motion relative to one another. (a) By using conservation of relativistic energy and momentum and the relativistic energymomentum relation, show that the threshold kinetic energy is K min 5 3m3 2 2 1m1 1 m2 2 2 4c 2 2m2 Calculate the threshold kinetic energy for each of the following reactions: (b) p 1 p S p 1 p 1 p 1 p (one of the initial protons is at rest, and antiprotons are produced); (c)p2 1 p S K0 1 L0 (the proton is at rest, and strange particles are produced); (d) p 1 p S p 1 p 1 p0 (one of the initial protons is at rest, and pions are produced); and (e) p 1 p S Z0 (one of the initial particles is at rest, and Z0 particles of mass 91.2 GeV/c 2 are produced).

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