91Ó°ÊÓ

Discuss the permitted angular momentum and parity states in the reaction \(\pi^{-}+d \rightarrow n+n+\pi^{0}\), given that the pion has intrinsic spin of zero and negative intrinsic parity. Assume very low energy incident \(\pi^{-}\).

Find which of the following reactions are forbidden by one or more conservation laws. Give all violated laws in each case. : (a) \(\mathrm{K}^{+}+\mathrm{n} \rightarrow \Sigma^{+}+\pi^{0}\) (d) \(\pi^{-}+\mathrm{p} \rightarrow \Sigma^{+}+\mathrm{K}^{-}\) (b) \(\pi^{-}+\mathrm{n} \rightarrow \mathrm{K}^{+}+\Lambda^{0}\) (e) \(\pi^{-}+\mathrm{p} \rightarrow \Xi^{-}+\mathrm{K}^{+}+\overline{\mathrm{K}}^{0}\) (c) \(\mathrm{K}^{-}+\mathrm{p} \rightarrow \mathrm{n}+\Lambda^{0}\) (f) \(\mathrm{d}+\mathrm{d} \rightarrow{ }^{4} \mathrm{He}+\tau^{0}\)

Show how the decays \(\omega \rightarrow 3 \pi^{0}\) and \(\omega \rightarrow \pi^{+} \pi^{-}\)are forbidden by isospin conservation from proceeding through the strong interaction.

Explain why the decay \(\rho \rightarrow \eta+\pi\) is forbidden.

(a) Show how the decay \(\eta \rightarrow 2 \pi\) is forbidden by conservation of angular momentum and parity. (b) Discuss how the decay \(\eta \rightarrow 3 \pi^{4}\) violates isospin conservation. (Hint: Find the possible values of the total isospin of two pions. and then couple the third to obtain the resultant.) (c) Discuss the decay \(\eta \rightarrow 4 \pi\). Why is this decay not observed?

(a) It is desired to produce the \(\Omega^{-}\)particle in proton-proton collisions. Find the reaction satisfying all strong-interaction conservation laws and requiring the smallest possible threshold energy. (b) Find the reaction and the threshold energy for production of \(\Omega^{-}\)by negative kaons incident on protons.