1000 Solved Problems in Modern Physics

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 Theρ^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 notρ^0 →π^0 π^0

10.6 The baryonΩ−has a mass 1,672 MeV/c^2 and strangenesss=−3. Which

of the following decay modes are possible?

(a)Ω−→Ξ−+π^0 (mΞ−=1,321 MeV/c^2 ,S=− 2 ,mπ^0 =135 MeV/c^2 )

(b)Ω−→Σ^0 +π−(mΣ^0 =1,192 MeV/c^2 ,S=−^1 ,mπ−=139 MeV/c^2 )

(c)Ω−→Λ+K−

(

mΛ= 1 ,115 MeV/c^2 ,S=− 1

mK−=494 MeV/c^2 ,S=− 1

)

(d)Ω−→n+K−+K^0 (mK 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 → 2 γ 135 10 −^17

(c) μ+→e++νe+νμ 105 2. 2 × 10 −^6

(d) μ++^12 C→^12 B+νμ 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 theP(space

inversion) andT(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 posi-

tive parity. Prove that it can exist only in the^3 S 1 and^3 D 1 states.