The pion for which it is easiest to be captured by a nucleus.

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Chapter 39, Problem 62PP

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The pion for which it is easiest to be captured by a nucleus.

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When a proton and an antiproton annihilate, the resulting energy can be used to create new particles. One possibility is the creation of electrically neutral particles called neutral pions. A neutral pion has a rest mass of 135 MeV/c2. How many neutral pions could be produced in the annihilation of a proton and an antiproton? Assume the proton and antiproton are moving very slowly as they collide.

Accelerators such as the Triangle Universities Meson Facility (TRIUMF) in British Columbia produce secondary beams of pions by having an intense primary proton beam strike a target. Such “meson factories” have been used for many years to study the interaction of pions with nuclei and,hence, the strong nuclear force. One reaction that occurs isπ+ + p → Δ++ → π+ + p , where the Δ++ is a very short-lived particle. The graph shows the probability of this reaction as a function of energy. The width of the bump is the uncertainty in energy due to the short lifetime of the Δ++ .(a) Find this lifetime.(b) Verify from the quark composition of the particles that thisreaction annihilates and then re-creates a d quark and a d antiquark by writing the reaction and decay in terms ofquarks.(c) Draw a Feynman diagram of the production and decay ofthe Δ++ showing the individual quarks involved.

Find this lifetime.