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 (becausel=0)
I= 0 + 1 = 1
For theB+meson,Jp= 1 +andI= 1
In case of weak decay, the spin would still be 1 but it would not be mean-
ingful to talk aboutIorP.10.33 The nucleon hasT = 1 /2 and pionT =1. TheΔ^0 hasT = 3 /2 and
T 3 =− 1 /2. Using Clebsch – Gordon coefficients (C.G.C) for 1× 1 / 2
(Table 3.3 of Chap. 3), we have
∣
∣
∣
∣
3
2
,−
1
2
〉
=
√
2
3
| 1 , 0 〉
∣
∣
∣
∣
1
2
,−
1
2
〉
+
√
1
3
| 1 ,− 1 〉
∣
∣
∣
∣
1
2
,
1
2
〉
Δ^0 π^0 n π− pThe ratio of the amplitudes for the decaysΔ^0 →π−pandΔ^0 →π^0 n
is given by the ratio of the corresponding C.G.C. and the ratio of the cross
sections by the squares of the C.G.C. Thus, the branching ratio would be
(√
2
3) 2 /(√
1
3
) 2
= 2
10.34
Fig. 10.4S−I 3 plot for
pseudoscalar meson octet
10.35
Fig. 10.5S−I 3 plot for
vector meson nonet