10.2 Problems 549
Show that the number of chargedΣ’s will be equal to twice the number of
neutralΣ’s.10.32 In the rest system of theB+-meson, the products of the strong interaction
decay,B+→ω^0 +π+are found to be formed in ans-state. Deduce the spin,
parity and isospin of theB-meson. What difference would it make to your
conclusion if the decay took place by the week interaction (spin and parity
are respectively 0−for the charge triplet pion and 1−for theω^0 ).
[University of Durham]
10.33 TheΔ(1,232) is a resonance withI= 3 /2. What is the predicted branch-
ing ratio for (Δ^0 → pπ−)/(Δ^0 →nπ^0 )? What would be the ratio for a
resonance withI= 1 /2?
10.34 Show the position of pseudo scalar mesonsπ+,π−,π^0 ,K^0 ,K^0 ,K+,K−
andηon the S−I 3 diagram.
10.35 Show the position of vector mesonsρ−,ρ^0 ,ρ+,φ,ω,k∗^0 ,k∗+,k∗−andk∗^0
on S.I 3 diagram.
10.36 Show the position of Baryonsp,n,Ξ−,Ξ^0 ,Λ,Σ+,Σ−, andΣ^0 particles
with spin-parity
( 1
2)+
on the Y−I 3 diagram.10.37 Describe the (3
/
2)+baryon decuplet on Y−I 3 diagram.10.38 (a) Explain why at the same energy the total cross-sections
σ(π−+p)∼=σ(π++n),whileσ(K−+p) =σ(K++n)
(b) How can the neutralK-mesons,K^0 andK^0 be distinguished?10.39 A hyper nucleus is formed when a neutron is replaced by aΛ-hyperon. In
the reactions ofK−in a helium bubble chamber, the mirror hyper nuclei
4
ΛHe and
4
ΛH are produced
K−+^4 He→^4 ΛHe+π−
→^4 ΛH+π^0
Determine the ratio of the cross sections.
10.40 In the reactionK−+^4 He→^4 ΛH+π^0 , the isotropy of the decay products
has establishedJ(^4 ΛH)=0. Show that this implies a negative parity for the
K−- meson, regardless of the angular momentum state from which theK−-
meson is captured.
10.41 Show that the reactionπ−+d→n+n+π^0 cannot occur for pions at rest.
10.42 At 600 MeV the cross sections for the reactionsp+p→ d+π+and
p+n→d+π^0 areσ+=^3 .15 mb andσ^0 =^1 .5 mb. Show that the ratio of
the cross sections is in agreement with the iso-spin predictions.
[Osmania University]
10.43 Explain which of the following combination of particles can or cannot exist
inI=1 state