10.2 Problems
545
(iv) μ
+
+ μ
−
→ τ
+
+ τ
−
(v) p → e
+
+ π
0
(vi) π
0
→ γ + γ
(vii) π
−
+ p → K
+
+ Σ
−
(viii) π
−
+ p → K
−
+ Σ
+
10.5 The ρ
0 meson is known to have an intrinsic spin of , and pions zero spin.
Show that the requirements of symmetry on the total wave function of the
final state permit the decay
ρ
0
→ π
+
π
− but not ρ
0
→ π
0
π
0
10.6 The baryon Ω
− has a mass 1,672 MeV/c
2 and strangeness s = −3. Which
of the following decay modes are possible?
(a) Ω
−
→ Ξ
−
+ π
0 (m Ξ − = 1,321 MeV/c
2
, S = −2, m π 0 = 135 MeV/c
2 )
(b) Ω
−
→ Σ
0
+ π
− (m Σ 0 = 1,192 MeV/c
2
, S = −1, m π − = 139 MeV/c
2 )
(c) Ω
−
→ Λ + K
−
m Λ = 1,115 MeV/c
2
, S = −1
m K − = 494 MeV/c
2
, S = −1
(d) Ω
−
→ n + K
−
+ K 0 (m K 0 = 498 MeV/c
2
, S = −1)
10.7 The following transitions have Q-values and mean lifetimes as indicated
Transition
Q-value
(MeV) Lifetimes(s)
(a)
Δ
++
→ p + π
+
120
10
−23
(b)
π
0
→ 2γ
135
10
−17
(c)
μ
+
→ e
+
+ ν e + ν μ
105
2.2 × 10
−6
(d)
μ
+
+
12 C →
12 B + ν μ
93
2 × 10
−6
State which interactions are responsible in each case and estimate the relative
coupling strengths.
10.8 Indicate how the following quantities will transform under the P (space
inversion) and T (time reversal) operation:
(a) Position coordinate
r
(b) Momentum vector
P
(c) Spin or angular momentum vector σ = r × P
(d) Electric field
E = −∇V
(e) Magnetic field
B = i × r
(f) Electric dipole moment
σ.E
(g) Magnetic dipole moment
σ.B
10.9 The deuteron is a bound state of neutron and proton and has spin 1 and positive parity. Prove that it can exist only in the
3 S 1 and
3 D 1 states.