1. 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

2. 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= W
M= kg
R= m
Tony Weidberg
Nuclear Physics Lectures

3. 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

4. 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

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.
Tony Weidberg
Nuclear Physics Lectures

6. Nuclear Physics Lectures
Example aC
Tony Weidberg
Nuclear Physics Lectures

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

8. 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

9. 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

10. 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

11. 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

12. 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

13. Nuclear Physics Lectures
Jet
Tony Weidberg
Nuclear Physics Lectures

14. Nuclear Physics Lectures
Tony Weidberg
Nuclear Physics Lectures

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

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

17. Inertial Confinement Fusion
Tony Weidberg
Nuclear Physics Lectures

18. 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

19. 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

20. Carbon Dating Calibration
Tony Weidberg
Nuclear Physics Lectures

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

22. 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

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

24. 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

25. 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

26. 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

27. 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

28. 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

29. 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

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

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

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

33. 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

34. Rutherford Scattering 1
Tony Weidberg
Nuclear Physics Lectures

35. Rutherford Scattering 2
Tony Weidberg
Nuclear Physics Lectures

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

37. 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

38. 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