Nuclear Physics Fission and neutron crosssections Nuclear Physics

Nuclear Physics: Fission and neutron cross-sections

Nuclear Physics: Neutron cross-sections Ramsauer model: Crosssection depends on neutron de. Broglie wavelength and radius R of the nucleus Question: What are the implications of this graph for nuclear reactors ?

Need to slow down neutrons to achieve fission. Slow down neutrons higher fission probability As neutrons become too hot and go too fast, fission stops Water is a moderator for neutrons i. e. it thermalizes the neutrons (and provides cooling) Control rods contain cadmium, boron or other neutron absorbers These drop/move into the reactor when an emergency occurs and stop the fission.

Today’s plan Collect homework Weak interactions (Chapter 7 continued): Cabibbo mixing GIM mechanism CKM (Cabibbo Kobayashi Maskawa) matrix FCNC Friday: Quiz on QCD

Review ✔ Question: Which of these weak interaction couplings are allowed and exist ? Question: What does FCNC mean ? ✔ Ans: Flavor Changing Neutral Currents. (very important) Usually suppressed or forbidden.

Lorentz structure of the leptonic weak current Question: you fill in the other two expressions for the weak leptonic current ? Do you see why ?

Hadronic weak currents Vud Here the coupling is GF x Vij where the Vij are elements of the CKM (Cabibbo Kobayashi Maskawa) matrix. The values may be complex numbers ! Question: How do hadronic weak currents differ from leptonic or semileptonic weak currents ? Ans: in the leptonic current, the weak coupling is universal Question: How does the strangeness change in the two decays ? Ans: |ΔS|=1 and |ΔS|=0. The former is suppressed compared to the latter.

Eigenstates/Cabibbo mixing The rotation angle is the “Cabibbo angle”. Weak interaction quark eigenstates (d’-type) are rotated from strong interaction quark eigenstates (d-type). Cabibbo did not share in the 2008 Nobel Prize for Kobayashi and Maskawa

II III Naively, from phase space ratios, the kaon annihilation decay (II) should have a rate 8 times the pion annihilation decay (III) due to the larger mass of the kaon. Does not agree with experiment. Question: What are the coupling constants at each vertex ? Ans: g Vus g Vud ; g Vus g ; g Vud g Question: What are the relative rates of reaction II and III ? Ans: |Vus/Vud|2=sin 2 θc/cos 2 θc =0. 0484 (around 1/20)

This is the Cabibbo matrix, which is a 2 X 2 rotation matrix where θc =130 and sin θc~0. 22. Initially, Cabibbo only knew about u, d, s quarks and the first row of the matrix.

Glashow-Illiopoulos-Maiani (GIM) 1970 Weak isospin doublet Where did the (1 -γ 5) go ? This should be possible.

Glashow-Illiopoulos-Maiani (GIM) 1970 Weak isospin doublet Add another weak isospin doublet

GIM mechanism But at 2 nd order, there is a box diagram that would be much larger than the experimental limit. Note the sin factor is in the wrong place. Question: How can we solve this problem ?

GIM mechanism sinθc -sinθc Question: What are the Cabibbo factors in the two diagrams ? Ans: the two contributions have opposite sign and cancel out. In fact, cancellation works at all orders in perturbation theory. Beautiful. Importance of FCNC (Flavor Changing Neutral Currents)

Another example of the GIM mechanism: suppression of KL μμ Note relative signs of the Cabibbo factors.

Charm had to exist Later in 1974 Glashow was pushing scientists to find the charm. In doing so, he stated at a conference that there were three possibilities: "One, charm is not found, and I eat my hat. Two, charm is found by spectroscopists, and we celebrate. Three, charm is found by 'outlanders' (other kinds of physicists who did neutrino scattering or measured electronpositron collisions in storage rings), and you eat your hats. ” In 1976, charm was found by "outlanders", and a year later Glashow gave a rabble-rousing talk titled "Charm Is Not Enough. " Then they all had a big laugh as the spectroscopists present finally ate their hats – Mexican candy hats were supplied by the organizers. “I will eat my hat” Sheldon Glashow. Nobel Prize 1979

The full CKM (Cabibbo Kobayashi Maskawa matrix 3 X 3 unitary matrix But need three generations of quarks for this to work. When Kobayashi and Maskawa proposed this only the u, d, s quarks were known. So would need another generation of quarks (b, t) and a charm quark.

The full CKM (Cabibbo Kobayashi Maskawa matrix 3 X 3 unitary matrix with single irreducible complex phase Notice the pattern along and off the diagonal of the matrix.

The full CKM (Cabibbo Kobayashi Maskawa matrix 3 X 3 unitary matrix with single irreducible complex phase

Jumping generations is highly suppressed.

Question: What is the Taylor expansion of cos(λ) for small λ ? What about sin(λ) ? Ans: 1 -λ 2/2. Note that lambda is the Cabibbo angle !

CKM weak interaction example The first two are “singly Cabibbo suppressed”. The last one is “doubly Cabibbo suppressed. ”

CKM weak interaction example a Cabibbo favored: Vcs. Vud c Singly Cabibbo suppressed: Vcd. Vud b Singly Cabibbo suppressed: Vcs. Vus d Doubly Cabibbo suppressed: Vcd. Vus