I* + p+r* + p Width 100 MeV 200 400 600 800 KE of r (MeV) Figure 33.26 This graph shows the probability of an interaction between a n and a proton as a function of energy. The bump is interpreted as Number of interactions
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 is
π+ + 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 this
reaction annihilates and then re-creates a d quark and a d
antiquark by writing the reaction and decay in terms of
quarks.
(c) Draw a Feynman diagram of the production and decay of
the Δ++ showing the individual quarks involved.
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