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 statistical weight ofI=1 andI=0 states. Therefore if
isospin is conserved only theI=1 state can contribute since the final state
is a pureI=1 state. The expected ratio of cross-sections at a given energy isσ+
σ^0=
1
(
1
/√
2
) 2 =^2
The observed ratio 3. 15 / 1. 5 = 2 .1 is consistent with the expected ratio of
2.0.10.43 Pions obey Bose statistics and the system of pions must be symmetric upon
interchange of space and isospin coordinates of any two pions. For each pion
T=1 and for a system of two pions, total isospin,I= 2 , 1 ,0. The corre-
sponding states are
| 2 ,± 2 〉,| 2 ,± 1 〉,| 2 , 0 〉 (Symmetric)
| 1 ,± 1 〉,| 1 , 0 〉 (Anti symmetric)
| 0 , 0 〉 (Symmetric)Nowψ(total)=ψ(space)ψ(isospin)
Thus for the symmetric states like| 2 ,± 1 〉or| 0 , 0 〉,ψ(space) must be
symmetric because of Bose symmetry. But for two pions the interchange of
the spatial coordinates introduces a factor (−1)lso that only evenlstates
are allowed. Thus, (π^0 ,π^0 ),(π+,π+),(π−,π−) in (a), (b) and (f) will
be found in the statesL= 0 , 2 ,...However, the states| 1 ,± 1 〉,| 1 , 0 〉are
antisymmetric and this requires,L=odd, that isL= 1 , 3 ,...(c) being
antisymmetric can have odd values forL, that isL= 1 , 3 ,...(d) and (e)
can exist inI =1 regardless of theLvalues because of two particles in
these two cases are fermion and boson, so that the previous considerations
are inconsequential.10.3.3 Quarks...........................................
10.44 High energy collisions can cause the quarks within hadrons, or newly created
quark–antiquark pairs, to fly apart from each other with very high energies.
As the distance from the origin increases the colour force also increases,
and it is energetically more favourable for the quarks to be fragmented,
that is transformed into a jet of hadrons, mostly pions. Gluons may also
radiate a separate jet. However, the quarks can not be dislodged as free
particles.