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Modern Physics IV Lecture 6

Fromm Institute for Lifelong Learning University of San Francisco. Modern Physics for Frommies IV The Universe - Small to Large Lecture 6. 22 February 2012. Modern Physics IV Lecture 6. Modern Physics IV Lecture 5. 1. 1. Agenda. Administrative matters Superconductors (con.)

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Modern Physics IV Lecture 6

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  1. Fromm Institute for Lifelong Learning University of San Francisco Modern Physics for Frommies IV The Universe - Small to Large Lecture 6 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 Modern Physics IV Lecture 5 1 1

  2. Agenda • Administrative matters • Superconductors (con.) • BCS Theory of Superconductors • “High” Temperature Superconductors • Nuclear Physics • The Nucleus • Nuclear forces • Radioactive Decay 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 Modern Physics IV Lecture 5 2 2

  3. Gorter and Casimir • 2-fluid model • Normal electrons and super electrons • Model is ad hoc but does explain some things 1939 London Brothers Fritz and Heinz Meisner effect is a more fundamental property of superconductors than zero resistivity The electrons in a superconductor are acting in concer (coherence) which is not the case for the normal state. Instead of using applied voltage try to write an equation connecting current with B (actually A, the magnetic vector potential. Current exists by itself, wrapped in its own magnetic field. 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 Modern Physics IV Lecture 5 3 3

  4. External magnetic field penetrates short distance into superconductor, the London penetration depth. It is determined by the mass, charge and number of the superconducting charge carriers. Wave functions of individual electrons are phase locked together. Property of rigidity. Rigid collection not much affected by scattering. Macroscopic quantum mechanics: Superconductor acts like giant atom in stationary state. Superconductor could display quantum behavior on macro scale. 1948 Fritz London predicts that magnetic flux through a superconducting loop should be quantized. Flux quantum is very small and was not detected experimentally until the 1960’s 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 4

  5. Post WWII Herbert Frőlich Try to include effect of lattice vibrations Does TCdepend on atomic mass? Look at superconductor isotopes. Experiment → The lattice is involved, not just the electrons (pre WWII) • John Bardeen, Leon Cooper, Robert Schreifer • 1972 Nobel Prize • How to get coherence amongst electrons despite their Coulomb repulsion. Enter the lattice again 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 5

  6. Consider 2 electrons. An arbitrarily small attraction between them makes it energetically favorable for them to “pair up” rather than go it “alone” Cooper pair. Attraction arises from electron-phonon interaction, interaction between electrons and vibrations of the crystal lattice. m(+) ion >> melectron Distortion persists long enough to attract 2nd electron Distortion is described by a phonon “Water bed effect” 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 6

  7. 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 7

  8. In good normal conductors the electron phpnon interaction is weak so normal conduction is not strogly hindered by scattering. Too weak for Cooper pairs so no superconductivity. In bad normal conductors the electron phonon interaction is strong so normal conduction is strogly hindered by scattering. At low temperatures, Cooper pairs may form and superconductivity can occur. Electrons are fermions and hence must occupy different states. Cooper pairs may be considered pseudo particles and are bosons. Bosons at low temperatures can and will pile up in the lowest state. Bose - Einstein condensate. Cooper pairs cannot lose energy in scattering. They have nothing to give up. 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 8

  9. For T > TC, thermal agitation breaks up the Cooper pairs and superconductivity disappears. The Meissner effect with its exclusion of magnetic flux, F, => a finite range for B=> the existence of a “massive photon”. The mass may be generated by a Higgs type mechanism. In this case the Higgs bosons are the Cooper pairs. 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 Modern Physics IV Lecture 5 9 9

  10. High Temperature Superconductors Highest known TC is Nb3Ge at 23.2 K. (1973) In the 1980’s a new class of superconductors (ceramic or perovskite copper oxides) was discovered. TC > 77 K YBCO actually YBa2Cu3O7 22 February 2012 Modern Physics IV Lecture 6 Modern Physics IV Lecture 6 10

  11. Red = O Green = Y Purple = Ba Blue = Cu BCS theory does not explain this superconductivity, Cooper pairs cannot form for T above about 30 K. Mechanism is not well understood but there is lots of speculation and lots of work going on. Modern Physics IV Lecture 6

  12. Spin Fluctuation Model : Extremely similar to conventional BCS mechanism except lattice distortion waves are replaced by spin density waves. e moving in say YBCO. Its spin → SDW → spin depression around e Nearby e can fall into the spin depression forming a Cooper like pair Leading candidate but experimental tests have been ambiguous. Modern Physics IV Lecture 6

  13. The nucleus 1911 Ernest Rutherford (1871-1937) et al. concluded a study of a particle scattering from metal foils. An excess of events at large scattering angles lead him to the conclusion that the positive charge in atoms is concentrated in a small, massive charged core, the nucleus. Atomic size ~ 10-10 m = 1 Å Nuclear size ~ 10-15 m = 1 fm Modern Physics IV Lecture 6

  14. Nucleus has (+) charge => protons Nuclei with same amount of nuclear charge but different masses (isotopes) => there are components besides protons in the nucleus. Electrons?? Modern Physics IV Lecture 6

  15. Lowest p is least uncertainty >> mc2 => unlikely to be bound in nucleus Other arguments involving spin and magnetic moments 1932, James Chadwick discovers the neutron Modern Physics IV Lecture 6

  16. Particle roughly same mass as proton but with zero charge Modern Physics IV Lecture 6

  17. Proton-neutron model of nucleus: Z protons, Z is the atomic number (A-Z) neutrons, A is the mass number Total charge = Ze Total mass  A mp Notation:X is chemical symbol for element Modern Physics IV Lecture 6

  18. Nuclear size: Experiment => nuclear density is uniform and independent of A Modern Physics IV Lecture 6

  19. Nuclear forces Binding energy: Consider components brought together to form a system. e.g. p+e  1H atom Same for nuclei, e.g. p+n  D Modern Physics IV Lecture 6

  20. An aside on units: 1 amu or 1 u = 1/12 mass of 12C atom (including electrons) This is what is listed in the Periodic Table and tables of nuclides. Modern Physics IV Lecture 6

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  23. The nuclear force: Overcomes the coulomb repulsion of protons in nucleus =>strong force Nuclear density is roughly constant as nucleons are added => each nucleon sees only its nearest neighbors. Also B/A is roughly constant for large A. => short range force Nuclear force does not distinguish neutrons from protons. => charge independent force Isotopic spin Modern Physics IV Lecture 6

  24. Kindergarten quantum field theory: 2nd quantization, fields as well as “matter” Coulomb interaction under wave-particle duality is either EM field due to one charged particle and felt by the other, or the exchange of photons between them Modern Physics IV Lecture 6

  25. g gis emitted and reabsorbed. Virtual, not observable. Mediates the EM force Photon is zero mass and EM interaction has infinite range Modern Physics IV Lecture 6

  26. There ought to be a similar exchange picture for the strong nuclear force. Meson has m  0, how do we conserve energy? H.U.P. says OK if DE Dt  ħ Meson cannot exceed c so max. Dt = d / c Modern Physics IV Lecture 6

  27. m  130 Mev/c2 C. F. Powell and G. Occhialini (1947) discover pion in cosmic rays. m(p0) = 135.0 MeV/c2 m(p) = 139.6 MeV/c2 Again in exchange picture these are virtual pions. Real pions can be made e.g. in accelerators p p  p p p0 p p  p n p+ Incident p must have enough E to conservemomentum and produce mp Modern Physics IV Lecture 6

  28. Radioactive decay Nuclear stability: Deviation from N  Z for Z  20 is due to stronger Coulomb force Modern Physics IV Lecture 6

  29. Alpha (a) decay: Q-value or disintegration energy: Q = (mX – mD – ma) c2 > 0 for decay to occur Modern Physics IV Lecture 6

  30. a –decay theory: Recall tunneling: Lifetime dependent on height and width of barrier. 100 nsec – 1010 yrs a rather than p or n because tight binding of a makes it energetically more favorable Modern Physics IV Lecture 6

  31. Beta (b) decay: b are e± The e± are created within the nucleus itself, hence b particles The neutrino: Postulated by Wolfgang Pauli in 1930, not observed until 1956 by Frederick Reines and Clyde Cowan. Early b –decay measurements appeared to violate conservation of energy, momentum and angular momentum Modern Physics IV Lecture 6

  32. If b-decay were a 2-body decay like a-decay The electron K. E. spectrum should be monoenergetic. Instead it is continuous from 0 up to a maximum. C is spin 0, N is spin 1 and e is spin ½. Spin 1 and spin ½ cannot be added to yield spin 0. Postulate the existence of a massless, spin ½ particle which interacts only weakly, i.e. via the weak nuclear force, the neutrino. Modern Physics IV Lecture 6

  33. If b-decay were a 2-body decay like a-decay The electron K. E. spectrum should be monoenergetic. Instead it is continuous from 0 up to a maximum. C is spin 0, N is spin 1 and e is spin ½. Spin 1 and spin ½ cannot be added to yield spin 0. Postulate the existence of a massless, spin ½ particle which interacts only weakly, i.e. via the weak nuclear force, the neutrino. Modern Physics IV Lecture 6

  34. Again,  a Q-value. Q > 0 => decay is possible Use amu, Z of parent changes and number of electron masses is accounted for above Q = 0.156 MeV Excess neutron converted to proton. Unstable nuclides to left of line of stability Modern Physics IV Lecture 6

  35. Excess proton converted to neutron. Unstable nuclides to right of line of stability p  n + b ++ n (not infree space, only in nucleus) Modern Physics IV Lecture 6

  36. Electron capture: K or L shell orbital electron passes thru nucleus p + e- n + n Theoretical picture: • - decay of neutron. Weak nuclear force, mediated by exchange of W boson Modern Physics IV Lecture 6

  37. Gamma (g) decay: Decay of nuclear excited state with emission of a high energy photon. Nucleus left in excited state after a previous decay N*  N “forbidden” by a selection rule. Remains excited for some time. metastable or isomer Modern Physics IV Lecture 6

  38. Conservation laws: Energy, linear momentum, angular momentum and charge are conserved as in classical physics. 2 new laws: Baryon number (nucleon number) Lepton number Internal quantum numbers. There are a bunch more of these in particle physics. Modern Physics IV Lecture 6

  39. Rate of decay:Decay is a random process. Cannot predict when a given nucleus will decay only the probability of how many nuclei will decay over time. l is the decay or disintegration constant Modern Physics IV Lecture 6

  40. Radioactive dating: Carbon dating: 14C formed by cosmic rays in atmosphere Ratio 14C / 12C isroughly constant over many thousand years. Modern Physics IV Lecture 6

  41. Living organisms take in C with this isotopic ratio and maintain ratio in tissue. Organism dies, 14C decays, isotopic ratio decreases For 14C, T1/2 = 5730 yrs. => Carbon dating good for  about 80,000 yrs. Geological dating: 238U, T1/2 = 4.5 x 109 yrs Measurement of the 238U / daughters ratio => oldest rocks are about 4 x 109 years old. Modern Physics IV Lecture 6

  42. Nuclear reactions Ernest Rutherford (1919) Recall carbon dating Alternate notation: Conservation laws: charge, nucleon (baryon) number, energy, linear and angular momentum. Modern Physics IV Lecture 6

  43. Q-values: a +X  Y +b If Q > 0, reaction is exothermic If Q < 0, reaction is endothermic Threshold energy minimum projectile kinetic energy to make an endothermic reaction occur. p + p  p + p + p++ p- Modern Physics IV Lecture 6

  44. Cross section: Probability of reaction occuring, a.k.a. reaction rate n / A t = nuclei / volume each with cross sectional areas Total reaction target area: A’ = n A t s If R0 is the rate at which projectiles strike the target slab Modern Physics IV Lecture 6

  45. Total cross section: sT= sel+ sinel units: barns = 100 fm2 = 10-28 m2 Differential cross sections: Angular distributions Modern Physics IV Lecture 6

  46. Fission 1938 Otto Hahn and Fritz Strassmann Lise Meitner and Otto Frisch Modern Physics IV Lecture 6

  47. Fermi and others realized that the neutrons in the final state could beused to create a chain reaction Problem: only 235U fissions Natural Uranium is mostly 238U with ~ 0.7 % 235U Modern Physics IV Lecture 6

  48. Fermi’s CP-1 at Stagg field, University of Chicago: Modern Physics IV Lecture 6

  49. Critical mass Dependent on: Fuel, moderator, enrichment Enrichment, separate out the 235U Difficult, only 3 / 235 mass difference Electromagnetic separation Gaseous diffusion Oak Ridge, Tennessee Modern Physics IV Lecture 6

  50. Breeding in a reactor: e.g Plutonium Hanford, Washington Natural uranium containing mostly 238U and about 0.7% 235U. Fissioning235U supplies neutrons. Neutron absorption by 238U n + 238U  239U Beta decay of239U ( t1/2 = 23.5 min): 92239U  93239Np + e- + nbar Beta decay of239Np (t1/2 = 2.35 days): 93239Np  94239Pu + e- + nbar Modern Physics IV Lecture 6

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