560 10 Particle Physics – II
SubstitutingmK=498 MeV/c^2 and mπ=140 MeV/c^2 , we get
p 0 = 142 .8MeV/c^210.4 (i) Does not occur because energy is not conserved
(ii) Weak interaction because neutrinos are involved
(iii) Does not occur because lepton number is not conserved
(iv) Weak interaction because leptons are involved
(v) Does not occur because of non-conservation of baryon number and
lepton number
(vi) Electromagnetic interaction becauseγ-rays are involved, charge and
c-parity are conserved.
(vii) Occurs as strong interaction because strangeness is conserved
(viii) Does not occur because strangeness is not conserved.10.5ρ^0 hasJp= 1 −. The conservation of angular momentum requires that the
twoπ^0 ’s are inl=1 state of orbital angular momentum. This state is anti-
symmetric and is therefore forbidden for identical bosons which require the
state to be symmetric with respect to the exchange of two bosons.10.6 (a) This decay mode is allowed and is observed.ΔS=1 as required for the
weak decays of strange particles.
(b) The decay is forbidden asΔS= 2
(c) The decay is allowed asΔS=1. Further, the rest mass energy ofΩ−is
greater than the sum of the energies of decay products. AlsoQ/eandB
are conserved.
(d) The decay is forbidden althoughΔS=1 andQ/eandBare conserved.
ButEis violated.10.7 (a) Strong interaction
(b) Electromagnetic interaction
(c) Weak interaction
(d) Weak interaction
Relative strength:1 : 10−^2 :10−^7 :10−^710.8 (a)r→−runder P- operation as x→−x,y→−y and z→−zbutr→r
under T- operation.
(b)Preverses its sign under both P and T operation, P→−P. Bothrandp
are known as polar vectors.
(c)σorLare axial vectors.σ=r×p. Since bothrandpchange their
sign under P-operation,Ldoes not. However under T-operationrdoes
not change sign butpdoes and soσchanges its sign.
(d) E=−∂V/∂r for the above argument changes sign under P-operation asr
changes its sign and does not under T-operation asrdoes not.
(e) The magnetic field like angular momentum is an axial vectorB=i×r.
Under p-operationB→Bbecausei →−iandr →−rbut under
T-operation becauser→randi→−iso thatB→−B