Issued Wed Mar 19 Due Wed, Apr 2

Required reading: F+H Ch. 9 and 10

1a) F+H 9.6

b) F+H 9.11. ("Find the parity selection rule" means: decide what the relative parity of the initial and final states must be, if you get from one to the other by way of the electric dipole formula given)

2a) F+H 9.15 (Note the typo: Use Fig 7.2 (not 7.1). Figs. 9.4 as well as 9.6 are also useful.)

b) In beta decays, you either see an electron spit out, or a positron spit out. The helicity of electrons formed in such beta decays is always negative. The helicity of positrons in such beta decays is positive.

Explain (using words, pictures, or formulas) how this implies that P (parity) is violated in such beta decays, and also that C (charge conjugation) is violated. (By the way, it turns out that CP (combined) is preserved as a decent symmetry)

3a) Show that a scalar meson cannot decay to three pseudoscalar mesons in a parity conserving process. ("Scalar" means a particle with no spin, but positive parity. A pseudoscalar also has no spin, but has negative parity, like the pion)

b) Capture of negative kaons in helium sometimes leads to the formation of a hypernucleus (a nucleus in which a nucleon is replaced by a Lambda hyperon) according to the reaction . Study of the decay branching ratios of , and the isotropy of decay products establishes that J( )=0.

i) If He is a "ppnn" system, what is ?

ii) Use this reaction to deduce the intrinsic parity of the kaon. (Show that it is independent of the orbital angular momentum of the state from which the K is captured)

Hints: F+H Eq. 9.22 is useful here. Assume, as usual, that a J=0 ground state (even a hypernucleus) will find a state with no orbital angular momentum of any kind. You can check your final answer for the kaon's parity in the appendix.

4a) F+H 9.33a only.

b) The reaction is observed in nature. (Strangeness is not conserved, what does that tell you?) Show that this reaction violates parity.

5a) F+H 9.18

b) F+H 9.37