(a) The proton and neutron are in the isospin

I=(1)/(2)

doublet with

I_(3)=(1)/(2)

and

I_(3)=-(1)/(2)

, respectively,\ while the pions are in the

I=1

, with

I_(3)=+1

for

\\\\pi ^(+),I_(3)=0

for

\\\\pi ^(0)

and

I_(3)=-1

for

\\\\pi ^(**)

. Determine the\ Clebsch-Gordan coefficients for:\ i.

\\\\pi ^(0)n

in the

I=(3)/(2),I_(3)=-(1)/(2)

state.\ \ ii.

\\\\pi ^(**)p

in the

I=(1)/(2),I_(3)=-(1)/(2)

state.\ \ iii.

\\\\pi ^(+)p

in the

I=(3)/(2),I_(3)=(1)/(2)

state.\

(a) The proton and neutron are in the isospin I=1/2 doublet with I3=1/2 and I3=1/2, respectively, while the pions are in the I=1, with I3=+1 for +,I3=0 for 0 and I3=1 for . Determine the Clebsch-Gordan coefficients for: i. 0n in the I=3/2,I3=1/2 state. ii. p in the I=1/2,I3=1/2 state. (4 marks) (4 marks) iii. +p in the I=3/2,I3=1/2 state. (4 marks)