91Ó°ÊÓ

A free neutron decays into a proton and an electron (and an anti-neutrino). A free proton has never been observed to decay into anything. Why then do we consider the neutron to be as "fundamental" (at the nuclear level) a particle as the proton? Why do we not consider a neutron to be a proton-electron composite?

The text describes and sketches the basic Feynman diagram for the fundamental process involved in the decay of the free neutron: One of the neutron's \(d\) -quarks converts to a \(u\) -quark, emitting a virtual \(W^{-}\) boson, which decays into an electron and an electron anti-neutrino (the only decay energetically possible). Similarly describe and sketch the basic (tree-level) Feynman diagram for the fundamental process involved in each of the following decays: a) \(\mu^{-} \rightarrow e^{-}+\nu_{\mu}+\bar{\nu}_{e}\) b) \(\tau^{-} \rightarrow \pi^{-}+\nu_{\tau}\) c) \(\Delta^{++} \rightarrow p+\pi^{+}\) d) \(K^{+} \rightarrow \mu^{+}+\nu_{\mu}\) e) \(\Lambda \rightarrow p+\pi\)

Draw possible Feynman diagrams for the following phenomena: a) protons scattering off each other b) neutron beta decays to a proton: \(n \rightarrow p+e^{-}+\bar{\nu}_{e}\).

Draw a quark-level Feynman diagram for the decay of a neutral kaon into two charged pions, \(K^{0} \rightarrow \pi^{+}+\pi^{-}\).

A Geiger-Marsden experiment, where \(\alpha\) particles are scattered off of a thin gold film, yields an intensity of particles of \(I\left(90^{\circ}\right)=100 .\) counts/s at a scattering angle of \(90^{\circ} \pm 1^{\circ} .\) What will be the intensity of particles at a scattering angle of \(60^{\circ} \pm 1^{\circ}\) if the scattering obeys the Rutherford formula?