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Applications of Nuclear Physics

Applications of Nuclear Physics. Fusion How the sun works Fusion reactor Radioactive dating C dating Rb/Sr  age of the Earth. Fusion in the Sun. Where nuclear physics meets astrophysics and has a big surprise for particle physics. Neutrinos Heavier Elements Up to Fe Beyond Fe

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Applications of Nuclear Physics

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  1. Applications of Nuclear Physics • Fusion • How the sun works • Fusion reactor • Radioactive dating • C dating • Rb/Sr  age of the Earth Nuclear Physics Lectures

  2. Fusion in the Sun • Where nuclear physics meets astrophysics and has a big surprise for particle physics. • Neutrinos • Heavier Elements • Up to Fe • Beyond Fe • Sun by Numbers: L=3.86 1026 W M=1.99 1030 kg R=6.96 108 m Nuclear Physics Lectures

  3. How to power the sun • Try gravity • Too short! • By elimination must be nuclear fusion. • Energy per particle (nuclei/electron) • Gives plasma, ionised H and He. Nuclear Physics Lectures

  4. PP Chain • Very long range weather forecast very cold • But only ~ 10% H atoms converted to He Nuclear Physics Lectures

  5. Physics of Nuclear Fusion • All reactions at low energy are suppressed by Coulomb barrier (cf a decay). • Reaction rate: convolution of MB distribution and barrier penetration (EG= Gamow Energy) • Problem: s(0) too small to measure! Extrapolated from higher energy or from n scattering. Nuclear Physics Lectures

  6. Example aC Nuclear Physics Lectures

  7. Reaction Rates & Coulomb Barrier • From definition of s • Main contribution around min f Nuclear Physics Lectures

  8. Cross Sections and W.I. • Consider first reaction pp chain • Cross section small even above Coulomb barrier because this is a weak interaction • Order of magnitude estimate • At 1 MeV ss=36b; tnuclear~10-23s; tdecay~900s • s~10-25b • This reaction is the bottleneck  explains long time scales for nuclear fusion to consume all the H in the core of the sun. Nuclear Physics Lectures

  9. Heavier Elements • He to Si: • 8Be unstable! Resonance in C12 enhances rate. • Heavier elements up to Fe • Photo-disintegration  n,p and a. These can be absorbed by other nuclei to build up heavier nuclei up to Fe. • Fe most stable nucleus, how do we make heavier nuclei? Nuclear Physics Lectures

  10. Fusion Reactors • Use deuterium + tritium: • Large energy release • Large cross-section at low energy • Deuterium abundant (0.015% of H). • Breed Tritium in Lithium blanket • . Nuclear Physics Lectures

  11. Fusion Reactors • Energy out > Energy in • Lawson criteria (assume kBT=20 keV). • number density D ions : r • Cross-section: s • Confinement time for plasma: tc • Energy released per fusion: Efusion Nuclear Physics Lectures

  12. Magnetic Confinement • Confine plasma with magnetic fields. • Toroidal field: ions spiral around field lines. • Poloidal fields: focus ions away from walls. • Heating: • RF power accelerates electrons • Current pulse causes further heating. Nuclear Physics Lectures

  13. Jet Nuclear Physics Lectures

  14. Nuclear Physics Lectures

  15. Magnetic Confinement Fusion • JET passed break-even (ie achieved Lawson criteria). Nuclear Physics Lectures

  16. Inertial Confinement Fusion Mirrors Very Big Laser D-T Pellet Nuclear Physics Lectures

  17. Inertial Confinement Fusion Nuclear Physics Lectures

  18. Radioactive Dating • C14/C12 for organic matter  age of dead trees etc. • Rb/Sr in rocks  age of earth. Nuclear Physics Lectures

  19. Carbon Dating • C14 produced by Cosmic rays (mainly neutrons) at the top of the atmosphere. • C14 mixes in atmosphere and absorbed by plants/trees  constant ratio C14 / C12 . Ratio decreases when plant dies. t1/2=5700 years. • Either • Rate of C14 radioactive decays • Count C14 atoms in sample by Accelerator Mass Spectrometer. • Which is better? • Why won’t this work in the future? Nuclear Physics Lectures

  20. Carbon Dating Calibration Nuclear Physics Lectures

  21. How Old Is The Earth? • Rb87 Sr87: b decay t1/2=4.8 1010 yr • Assume no initial daughter nuclei  get age from ratio of daughter/parent now. Nuclear Physics Lectures

  22. Improved Calculation • Allow for initial daughters to be present. • Need another isotope of the daughter D’ which is stable and not a product of a radioactive decay chain. • Plot vs straight line fit  age and initial ratio. Nuclear Physics Lectures

  23. Age of Earth • Rb/Sr method • Stable isotope of daughter is Sr86 • Fit gives age of earth=4.53 109 years. Sr87/Sr86 1.0 4.0 Nuclear Physics Lectures Rb87/Sr86

  24. Cross-Sections • Why concept is important • Learn about dynamics of interaction and/or constituents (cf Feynman’s watches). • Needed for practical calculations. • Experimental Definition • How to calculate s • Fermi Golden Rule • Breit-Wigner Resonances • QM calculation of Rutherford Scattering Nuclear Physics Lectures

  25. Definition of s • a+bx • Effective area or reaction to occur is s Na(0) particles type a/unit time hit target b Nb atoms b/unit volume Number /unit area= Nb dx Probability interaction = s Nbdx dNa=-Na Nb dx s Na(x)=Na(0) exp(-x/l) ; l=1/(Nbs) Beam a Na dx Nuclear Physics Lectures

  26. Reaction Rates • Na beam particles/unit volume, speed v • Flux F= Na v • Rate/target b atom R=Fs • Thin target x<<l: R=(NaT) F sTotal • This is total cross section. Can also define differential cross sections, as a function of reaction product, energy, transverse momentum, angle etc. • dR(a+bc+d)/dE=(NaT) F ds(a+bc+d)/dE Nuclear Physics Lectures

  27. Cross Section Calculations • Use NRQM to calculate cross sections: • Calculation (blackboard) gives Breit-Wigner resonance for decay of excited state Nuclear Physics Lectures

  28. Breit-Wigner Resonance • Important in atomic, nuclear and particle physics. • Uncertainty relationship • Determine lifetimes of states from width. • t=1/G G=FWHM; Nuclear Physics Lectures

  29. Fermi Golden Rule • Decays to a channel i (range of states n). Density of states ni(E). Assume narrow resonance Nuclear Physics Lectures

  30. Cross Section • Breit Wigner cross section. • Definition of s and flux F: Nuclear Physics Lectures

  31. Breit-Wigner Cross Section • Combine rate, flux & density states  Nuclear Physics Lectures

  32. Breit-Wigner Cross Section n + 16O 17O Nuclear Physics Lectures

  33. Low Energy Resonances • n + Cd total cross section. • Cross section scales s ~ 1/E1/2 at low E. • B-W: 1/k2 and G~n(E)~k Nuclear Physics Lectures

  34. Rutherford Scattering 1 Nuclear Physics Lectures

  35. Rutherford Scattering 2 Nuclear Physics Lectures

  36. Rutherford Scattering 3 • Use Fermi Golden Rule: Nuclear Physics Lectures

  37. Low Energy Experiment • Scattering of a on Au & Ag  agree with calculation assuming point nucleus dN/dcosq Sin4(q/2) Nuclear Physics Lectures

  38. Higher Energy • Deviation from Rutherford scattering at higher energy  determine charge distribution in the nucleus. • Form factors is F.T. of charge distribution. Nuclear Physics Lectures

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