1000 Solved Problems in Modern Physics

562 10 Particle Physics – II

(c) Decay via strong or electromagnetic interaction is forbidden because of

violation of cp invariance. Forρ^0 ,cp=−1. Butcη=cπ 0 =+1 because

both decay to two gamma rays.

(d) The decay is allowed via electromagnetic interaction.

10.13 Parity of deuteronπd=πpπn.(−1)l.Asπp=πn=+1 for s or d state

l=0or2.

πd=+ 1

The intrinsic parity of quarks is assumed to be positive because the intrinsic

parity of a nucleon (+) comes from the parities of three quarks andl=0.

10.14 Decay (a) is forbidden by theΔS=ΔQ rule for the semi – leptonic decays

and (b) is forbidden by theΔS= 0 ,±1 rule for the hadronic weak decays.

(c) and (d) are allowed and both have been experimentally observed.

10.15 Since strange particles are always produced in pairs, as in the reactionπ−+

p→Λ+K^0 , the intrinsic parity of a strange particle can only be determined

relative to that of another. Thus, for example, one can determine the kaon

parity relative to that ofΛ, which by convention is assigned a positive parity.

Consider the reaction

K−+He^4 →ΛHe^4 +π−

→ΛH^4 +π^0

These reactions are known to occur in a helium bubble chamber. Now, the

Λis bound in an s-state relative to the nuclear core He^3 or H^3 which have

positive parity. Furthermore, all the participants in the reaction are spinless.

Linitial =Lfinal. The orbital angular momentum does not contribute to the

parity because of s-state. The only relevant parities in the above reaction are

PK=PΛ.Pπ−=−PΛ,asPπ−=− 1

The validity of the argument obviously hinges on the hyper-nuclei having

zero spin. If the spin were 1, for example, angular momentum conservation

would requirel =1 in the final state, thus reversing the conclusion. The

spin ofΛH^4 has also been experimentally determined to be indeed zero. It is

concluded that the relative parity of K−is negative.

10.16(a) (i) Hadronis an elementary particle which participates in strong interac-
tions, examples being neutron and pion.
(ii) Leptonparticipates in weak interaction and if charged in em interac-
tion as well, examples being electron and muon. Lepton number is
universally conserved.
(iii) Baryoncomprises nucleons and hyperons which participate in strong
interaction, examples being proton and Σ-hyperon. Baryons are
fermions and baryon number is universally conserved.
(iv) Mesonsare the carrier of strong forces, examples being pion and kaon.