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Mathematics for Physics

187 Particle Creation

The process in which high-energy collisions or fields convert kinetic energy into new particles with rest mass, conserving total energy and momentum.

Mass-energy transmutation. Kinetic energy or radiant energy can convert into the rest mass of new particles. Particle creation is that conversion of incoming energy into rest mass. This principle is used to compute the energy needed to produce new particles in an accelerator.

Fixed-target threshold energy. A projectile hitting a stationary target must carry more kinetic energy than the rest energy of the new particles, because leftover kinetic energy is required by momentum conservation. Threshold energy is the minimum laboratory energy that allows the reaction. This principle is used to find the extra energy needed in a fixed-target collision.

Kinematic forbiddenness of vacuum pair production. An isolated photon in vacuum cannot become a massive pair, because energy and momentum cannot both be conserved. Pair production is the conversion of a photon into a particle and its antiparticle. This principle is used to show that pair production needs a nearby nucleus to take recoil momentum.

Center-of-momentum efficiency. In a head-on collision of equal speeds, all of the kinetic energy is available for creating mass. The center-of-momentum frame is the frame in which the total spatial momentum is zero. This principle is used to prefer colliding beams over a stationary target.

187.1 References

  1. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — source for the heading explanation.
  2. Knight, R. D. Physics for Scientists and Engineers: A Strategic Approach with Modern Physics. Pearson, 2023. — kinetic energy into rest mass; colliding beams.
  3. Griffiths, D. J. Introduction to Electrodynamics. Cambridge University Press, 2024. — pair production near a nucleus; threshold energy; colliding beams.
  4. Shankar, R. Fundamentals of Physics I. Yale University Press, 2019. — particle creation; fixed-target threshold; colliding-beam efficiency.
  5. Carroll, S. M. Spacetime and Geometry. Cambridge University Press. — vacuum pair production forbidden; four-momentum conservation.