1000 Solved Problems in Modern Physics

564 10 Particle Physics – II Therefore,σ 1 =C|M 3 |^2 whereC=constant For reaction (2) we have the mixture ofI= 1 /2 andI= 3 /2 ...

10.3 Solutions 565 10.20 The nucleon hasT = 1 /2 and pionT =1. TheΔ+hasT = 3 /2 and T 3 =+ 1 /2. Using the C.G.C. for 1× 1 /2 (T ...

566 10 Particle Physics – II 10.25 (a) From Problem 10.18, we have the result ∣ ∣a 3 / 2 ∣ ∣^2 ∝190 mb { 1 √ 3 ∣ ∣a 3 / 2 + 2 a ...

10.3 Solutions 567 The ratio of cross sections is σ− σ^0 = |a 3 + 2 a 1 |^2 ∣ ∣ ∣ √ 2 (a 3 −a 1 ) ∣ ∣∣^2 Puta 3 =a 1 eiΦwithΦ=± ...

568 10 Particle Physics – II 10.30 In the initial stateT(K)=^1 / 2 andT(p)=^1 / 2 , so thatI =0or1.Inthe first two reactionsI=2, ...

10.3 Solutions 569 Assuming that the decay proceeds via strong interaction, the parity PB=PωPπ=(−1)(−1)(−1)^0 =+ 1 Jω= 1 + 0 =1 ...

570 10 Particle Physics – II 10.36 Fig. 10.6Y−I 3 plot for baryon octet 10.37 Fig. 10.7Y−I 3 plot for baryon decuplet 10.38 (a) ...

10.3 Solutions 571 K^0 +p→K++n allowed K^0 +p→Σ++π^0 K^0 +n→K−+p } forbidden because of strangeness non-conservation K^0 +p→Σ++π ...

572 10 Particle Physics – II While the p–p system is a pureI=1 state the p-n system is a linear super- position with equal stati ...

10.3 Solutions 573 10.45 Fig. 10.8Chain decay of B-meson The decays are weak at each stage as the quantum numbersb, candS change ...

574 10 Particle Physics – II The sum of the squares of the quark charges refer to those quark pairs which can possibly contribut ...

10.3 Solutions 575 10.51 (a)Δ−:ddd,Δ^0 :ddu,Δ+:uud,Δ++:uuu (b) The fundamental difficulty is that Pauli’s principle is violated. ...

576 10 Particle Physics – II Fig. 10.9 Actually the value of Rwill be slightly greater than 2 because of an increased value ofαs ...

10.3 Solutions 577 The ground state energy is obtained by minimizingE,∂∂Ea =0; − ^2 μa^3 + 3 2 B= 0 →a= ( 2 ^2 3 μB )^1 / 3 (2 ...

578 10 Particle Physics – II 10.61 Neithere+nore−is an eigen state ofC. However, the systeme+e−in a definite (l, s) state is an ...

10.3 Solutions 579 10.64σ∝ 1 [ q^2 +m^2 ] 2 At low energiesq→ 0 σ σ 0 = 80 100 = [ m^2 302 +m^2 ] 2 m=87 GeV/c^2 10.65 Number of ...

580 10 Particle Physics – II Reaction (3) has relative weightage of 3 because of three colours. Thus the branching fraction of ( ...

10.3 Solutions 581 The initial state is a mixture ofI=0 andI=1 states. The final state can exist only inI=1. |Λ,π^0 >= 1 √ 2 ...

582 10 Particle Physics – II |N,π, 1 / 2 ,− 1 / 2 〉=− √ 2 3 ∣ ∣pπ− 〉 + √ 1 3 ∣ ∣nπ^0 〉 Therefore, ω ( Λ→pπ− ) ω ( Λ→nπ^0 ) = (√ ...

10.3 Solutions 583 (h) Massmx≥ ( mπ+mμ+mυ ) /c^2 =( 135 + 106 + (^0) )/c^2 =241 MeV/c^2 (i)Xis identified asK+-meson. 10.77 The ...