10.2 Problems
549
Show that the number of charged Σ’s will be equal to twice the number of
neutral Σ’s.
10.32 In the rest system of the B
+ -meson, the products of the strong interaction
decay, B
+
→ ω
0
+ π
+ are found to be formed in an s-state. Deduce the spin,
parity and isospin of the B-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 the ω
0 ).
[University of Durham]
10.33 The Δ (1,232) is a resonance with I = 3/2. What is the predicted branching ratio for (Δ
0
→ pπ
− )/(Δ
0
→ nπ
0 )? What would be the ratio for a
resonance with I = 1/2?
10.34 Show the position of pseudo scalar mesons π
+
, π
−
, π
0
, K
0
, K 0 , K
+
, K
−
and η on the S − I 3 diagram.
10.35 Show the position of vector mesons ρ
−
, ρ
0
, ρ
+
, ϕ, ω, k
∗0
, k
∗+
, k
∗− and k
∗0
on S . I 3 diagram.
10.36 Show the position of Baryons p, n, Ξ
−
, Ξ
0
, Λ, Σ
+
, Σ
− , and Σ
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), while σ (K
−
+ p) = σ (K
+
+ n)
(b) How can the neutral K -mesons, K
0 and K 0 be distinguished?
10.39 A hyper nucleus is formed when a neutron is replaced by a Λ-hyperon. In
the reactions of K
− in a helium bubble chamber, the mirror hyper nuclei
4
Λ He and
4
Λ H are produced
K
−
+
4 He →
4
Λ He + π
−
→
4
Λ H + π
0
Determine the ratio of the cross sections.
10.40 In the reaction K
−
+
4 He →
4
Λ H + π
0 , the isotropy of the decay products
has established J (
4
Λ H) = 0. Show that this implies a negative parity for the
K
− - meson, regardless of the angular momentum state from which the K
− -
meson is captured.
10.41 Show that the reaction π
−
+ d → n + n + π
0 cannot occur for pions at rest.
10.42 At 600 MeV the cross sections for the reactions p + p → d + π
+ and
p + n → d + π
0 are σ
+
= 3.15 mb and σ
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
in I = 1 state
549
Show that the number of charged Σ’s will be equal to twice the number of
neutral Σ’s.
10.32 In the rest system of the B
+ -meson, the products of the strong interaction
decay, B
+
→ ω
0
+ π
+ are found to be formed in an s-state. Deduce the spin,
parity and isospin of the B-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 the ω
0 ).
[University of Durham]
10.33 The Δ (1,232) is a resonance with I = 3/2. What is the predicted branching ratio for (Δ
0
→ pπ
− )/(Δ
0
→ nπ
0 )? What would be the ratio for a
resonance with I = 1/2?
10.34 Show the position of pseudo scalar mesons π
+
, π
−
, π
0
, K
0
, K 0 , K
+
, K
−
and η on the S − I 3 diagram.
10.35 Show the position of vector mesons ρ
−
, ρ
0
, ρ
+
, ϕ, ω, k
∗0
, k
∗+
, k
∗− and k
∗0
on S . I 3 diagram.
10.36 Show the position of Baryons p, n, Ξ
−
, Ξ
0
, Λ, Σ
+
, Σ
− , and Σ
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), while σ (K
−
+ p) = σ (K
+
+ n)
(b) How can the neutral K -mesons, K
0 and K 0 be distinguished?
10.39 A hyper nucleus is formed when a neutron is replaced by a Λ-hyperon. In
the reactions of K
− in a helium bubble chamber, the mirror hyper nuclei
4
Λ He and
4
Λ H are produced
K
−
+
4 He →
4
Λ He + π
−
→
4
Λ H + π
0
Determine the ratio of the cross sections.
10.40 In the reaction K
−
+
4 He →
4
Λ H + π
0 , the isotropy of the decay products
has established J (
4
Λ H) = 0. Show that this implies a negative parity for the
K
− - meson, regardless of the angular momentum state from which the K
− -
meson is captured.
10.41 Show that the reaction π
−
+ d → n + n + π
0 cannot occur for pions at rest.
10.42 At 600 MeV the cross sections for the reactions p + p → d + π
+ and
p + n → d + π
0 are σ
+
= 3.15 mb and σ
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
in I = 1 state