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Front page of the NY Times on Friday February 24, 2017 Kim Jong Un Nuclear Physics question: What kind of bomb is this ? Midterm results were encouraging: average score was 85.6 Notes: Dx = gb ct since Dx=g vt + - e e ® ¡(4S) ® BB Question: What is the quark content of a B meson ? B0 = bd; B- = bu Midterm problem and one homework problem based on PEP-II accelerator Dx = gb ct since Dx=g vt Hard to flip the helicity of an electron than a muon Leptons are left-handed in the V-A weak interaction. Anti-leptons are right-handed. Flipping a helicity requires boosting to the rest frame of a particle. The electron is nearly massless. Re-read p.99-102 of Bettini M = ml fpfp l(1- g 5 )p g mn l m See the V-A coupling here Lamb shift (master energy level diagram) Review: The hydrogen atom: Schrodinger Equation Use this potential in the Schrodinger Equation 2 -1 e U(r) = 4pe 0 r Use the separation of variables technique and spherical coordinates y (r,q ,f ) = R(r)Q(q )F(f ) The hydrogen atom: 3-D Schrodinger Equation y (r,q ,f ) = R(r)Q(q )F(f ) Question; What three quantum numbers appear in the solution ? Ans: n, l, m Review Question: What are the energy levels ? -13.6eV En = n2 This result agrees with the Bohr model ! What happens to the l, m quantum numbers ? Here l=0,1,2,….n-1 This result does not agree with the Bohr model. Question: Why ? What happens for n =1 ? Here m=0,±1, ±2,…. ±l The energies of the l, ml levels are degenerate ! Magnetic moments (from the Bohr model to QM) Let’s calculate the magnetic dipole moment in the Bohr model (assume electron moves with velocity v at a radius r around the nucleus) 2p r q ev T= ;I = = v T 2p r ev evr 2 m = IA = pr = 2p r 2 evr emvr e m= = = L 2 2m 2m This is the “Bohr magneton” mB = 5.788 ´10-5 eV / T = 9.274 ´10 -24 J / T Magnetic moments from orbital ang. momentum Now let’s put aside the Bohr model and get the precise results from QM U = - mz B -e mz = Lz 2m Here ml=0,±1,±2…±l This result explains the Zeeman effect. mB = 5.788 ´10-5 eV / T = 9.274 ´10 -24 J / T • Hierarchy of effects: • Fine structure (spin-orbit coupling): this involves the interaction of orbital magnetic moment and the spin magnetic moment of the electron. Need the Dirac equation. • Hyperfine structure: Interaction of nuclear spin magnetic moment and electron spin magnetic moment. Question: Can you give a simple argument for the relative size of these effects ? Ans: Key is the mass term in the nuclear magnetic moment. The Lamb shift is somewhat smaller. The 21 cm line of hydrogen in Radio Astronomy Question: What is the physical origin of the famous 21cm line ? (first detected in 1951) The spins of the nucleus and electron are shown. A “spin flip” transition is the origin of the 21cm photon (5.87μ eV) Lamb shift (master energy level diagram) What happens to atomic energy levels in a B field ? For l>0, the levels are split according to the ml value. This is called the Zeeman effect. Block diagram of the Lamb shift experiment Note a deficit of 2S1/2 electrons is detected. Oven to dissociate single H atoms. Bombard with electrons to excite a few atons to the 2S1/2 state Separation of ml levels by B field. (2S1/2, m=+1/2) state is metastable (10-4s). Pumping by RF to excite it to the (2P3/2, m=-1/2, +1/2. +3/2) states, which are not stable. Lamb used a metal to detect the 2S1/2 states; these dexcite and produce a conduction electron Data from the Lamb shift experiment. Adapted from Lamb, W. E. Jr. & Retherford, R.C. (1947); Phys. Rev. 72 241 Willis E. Lamb, 1955 Nobel Prize in Physics (shared with Polykarp Kusch (g-2 for the electron)) E(2S1/2 ) - E(2P1/2 ) = 0 This expectation is not confirmed. E(2S1/2 ) - E(2P1/2 ) = 1057,8 ± 0.1 MHz Question: What is the significance of the deviation of red points (data) from atomic physic expectations (black dashed lines) ? QED Feynman (x vs t) diagrams Question: Are we done ? Question: Are we done ? Question: How is the diagram on the right compatible with energy conservation ? Isn’t it forbidden ? Question: Are we done ? Question: Are we done now ? Ans: No. There is an infinite series of finite diagrams to sum-up. Nobel Prize in 1965, Feynman, Tomonga and Schwinger for QED Feynman Diagrams for other fundamental interactions Components of Feynman diagrams.