548 10 Particle Physics – II
10.26 Consider the formation of the resonanceΔ(1,236) due to the incidence of
π+andπ−onp. Assuming that at the resonance energy theI= 1 /2 contri-
butiontotheπ−+pinteraction is negligible show that at the resonance peak
σ(π++p→Δ)
σ(π−+p→Δ)
= 3
10.27 Consider the reactions at the same energy
π++p→Σ++K+
π−+p→Σ−+K+
π−+p→Σ^0 +K^0
Assuming that the isospin amplitudea 1 / 2 a 3 / 2 , show that the cross
sections for the reactions will be in the ratio 9:1:210.28 Calculate the ratio of the cross sections for the reactionπ−p→π−pand
π−p→π^0 non the assumption that the two I spin amplitudes are equal in
magnitude but differ in phase by 30◦.
10.29 Negative pions almost at rest are absorbed by deuterium atoms and undergo
the following reaction
π−+d→n+n
which is established by the direct observation of the neutrons which have
a unique energy for this process. Assuming that the parity of neutron and
deuteron is positive, show how the existence of the above reaction affords
the determination of parity of negative pion.
10.30 The cross-section forK−+pshows a resonance atPK≈400MeV/c. This
resonance appears in the reactions
K−+p→Σ+π
→Λ+π+π
But not in the reaction
K−+p→Λ+π^0
What conclusion can you draw on the isospin value of the resonance?
10.31 K−mesons are incident with equal frequency on protons and neutrons and
the following reactions are observed:
K−+p→Σ++π−
→Σ^0 +π^0
→Σ−+π+
K−+n→Σ−+π^0
→Σ^0 +π−