Subatomic Physics

274 P , C, CP, andT
9.17. Electrons emitted in nuclear beta decay are found to have negative helicity,
whereas positrons show positive helicity. What can be deduced from this
observation?
9.18. Consider a system consisting of a positive and a negative pion, with orbital
angular momentum l in their c.m.
(a) Determine the C parity of this (π + π − )system.
(b) If l = 1, can the system decay into two photons? Justify your answer.
9.19. Show that Maxwell’s equations are invariant under time reversal.
9.20. Assume
ψ =
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ψ1
ψ2
to be a two-component Pauli spinor, satisfying the Pauli equation. Find the
wave function Tψ that satisfies the Pauli equation.
9.21. Discuss one test of time-reversal invariance in the hadronic and one in the
electromagnetic interaction.
9.22. Show that the helicity J · ˆp is invariant under the time-reversal operation.
9.23. A very small violation of parity invariance has been observed in nuclear decays
(FP ≈ 10 −7 ). How can this violation be explained without giving up parity
conservation in the hadronic interaction?
9.24. Sketch the application of the two-well model to ammonia. How big is the
total splitting 2∆E between states |a〉 and |s〉? Which state lies higher?
Are transitions between states |a〉 and |s〉 observed? If yes, where are these
transitions important?
9.25. (a) Find the general solution of Eqs. (9.71).
(b) Verify that Eq. (9.72) is the special solution of Eq. (9.71) with the initial
conditions α(0) = 1 and β(0) = 0.
9.26. Neutron and antineutron are neutral antiparticles, just as K 0 and K 0 are.
Why is it not meaningful to introduce linear combinations N1 and N2, similar
to K 0 1 and K0 2 ?
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