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

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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. Tony Weidberg Nuclear Physics Lectures

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

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. Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures Example aC Tony Weidberg Nuclear Physics Lectures

Reaction Rates & Coulomb Barrier From definition of s Main contribution around min f Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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. Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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? Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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 . Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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. Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures Jet Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures Tony Weidberg Nuclear Physics Lectures

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

Inertial Confinement Fusion Mirrors Very Big Laser D-T Pellet Tony Weidberg Nuclear Physics Lectures

Inertial Confinement Fusion Tony Weidberg Nuclear Physics Lectures

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

Nuclear Physics Lectures 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? Tony Weidberg Nuclear Physics Lectures

Carbon Dating Calibration Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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. Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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. Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures Rb87/Sr86

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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/(Nb s) Beam a Na dx Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

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

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

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

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

Breit-Wigner Cross Section Combine rate, flux & density states  Tony Weidberg Nuclear Physics Lectures

Breit-Wigner Cross Section n + 16O 17O Tony Weidberg Nuclear Physics Lectures

Nuclear Physics Lectures 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 Tony Weidberg Nuclear Physics Lectures

Rutherford Scattering 1 Tony Weidberg Nuclear Physics Lectures

Rutherford Scattering 2 Tony Weidberg Nuclear Physics Lectures

Rutherford Scattering 3 Use Fermi Golden Rule: Tony Weidberg Nuclear Physics Lectures

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

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