Today

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Todays Menu

• Why study nuclear physics
• Why nuclear physics is difficult
• Course synopsis.
• Notation Units

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What is the use of lectures

• Definition of a lecture a process whereby notes
  are transferred from the pages of a lecturer to
  the pages of the student without passing through
  the head of either.
• Conclusion to make lectures useful YOU have to
  participate, ask questions ! If you dont
  understand something the chances are gt50 of the
  audience doesnt as well, so dont be shy !

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Why Study Nuclear Physics?

• Understand origin of different nuclei
• Big bang H, He and Li
• Stars elements up to Fe
• Supernova heavy elements
• We are all made of stardust
• Need to know nuclear cross sections ?
  experimental nuclear astrophysics is a hot topic.

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Practical Applications

• Nuclear fission for energy generation.
• No greenhouse gasses
• Safety and storage of radioactive material.
• Nuclear fusion
• No safety issue (not a bomb)
• Less radioactive material but still some.
• Nuclear transmutation of radioactive waste with
  neutrons.
• Turn long lived isotopes ? stable or short lived.
• Every physicist should have an informed opinion
  on these important issues!

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Medical Applications

• Radiotherapy for cancer
• Kill cancer cells.
• Used for 100 years but can be improved by better
  delivery and dosimetery
• Heavy ion beams can give more localised energy
  deposition.
• Medical Imaging
• MRI (Nuclear magnetic resonance)
• X-rays (better detectors ? lower doses)
• PET
• Many otherssee Medical Environmental short
  option.

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Other Applications

• Radioactive Dating
• C14/C12 gives ages for dead plants/animals/people.
  
• Rb/Sr gives age of earth as 4.5 Gyr.
• Element analysis
• Forenesic (eg date As in hair).
• Biology (eg elements in blood cells)
• Archaeology (eg provenance via isotope ratios).

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Why is Nuclear Physics Hard?

• QCD theory of strong interactions ? just solve
  the equations
• At short distance/large Q coupling constant small
  ? perturbation theory ok but long distance/small
  Q, q ? large

Not on syllabus !
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Nuclear Physics Models

• Progress with understanding nuclear physics from
  QCD0 ? use simple, approximate, phenomenological
  models.
• Liquid Drop Model phenomenology QM EM.
• Shell Model look at quantum states of individual
  nucleons ? understand spin/parity magnetic
  moments and deviations from SEMF for binding
  energy.

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Course Synopsis - 1

• Liquid Drop Model and SEMF.
• Applications of SEMF
• Valley of stability.
• abg decays.
• Fission fusion.
• Limits of validity of liquid drop model (shell
  model effects)

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Course Synopsis - 2

• Cross Sections
• Experimental definition
• FGR theory
• Rutherford scattering
• Breit-Wigner resonances
• Theory of abg decays.
• Particle interactions in matter
• Simple detectors for nuclear/particle physics.

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Corrections

• To err is human and this is a new course ? lots
  of mistakes.
• Please tell me about any mistakes you find in the
  notes (I will donate a bottle of wine to the
  person who finds the most mistakes!).

13
The Minister of Science

• This is a true story honest.
• Once upon a time the government science minister
  visited the Rutherford Lab (UK national lab) and
  after a days visit of the lab was discussing his
  visit with the lab director and he said
• I hope that you all have a slightly better grasp
  of the subject by the end!

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Notation

• Nuclei are labelled where El is the
  chemical symbol of the element, mass number A
  number of neutrons N number of protons Z. eg
• Excited states labelled by or m if they are
  metastable (long lived).

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Units

• SI units are fine for macroscopic objects like
  footballs but are very inconvenient for nuclei
  and particles ? use natural units.
• Energy 1 eV energy gained by electron in being
  accelerated by 1V.
• 1 eV e J.
• Mass MeV/c2 (or GeV/c2)
• 1 eV/c2 e/c2 kg.
• Or use AMU defined by mass of 12C 12 u
• Momentum MeV/c (or GeV/c)
• 1 eV/c e/c kg m s-1
• Cross sections (as big as a barn door)
• 1 barn 10-28 m2
• Length fermi 1 fm 10-15 m.

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Nuclear Masses and Sizes

• Masses and binding energies
• Absolute values measured with mass spectrometers.
• Relative values from reactions and decays.
• Nuclear Sizes
• Measured with scattering experiments (leave
  discussion until after we have looked at
  Rutherford scattering).
• Isotope shifts

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Nuclear Mass Measurements

• Measure relative masses by energy released in
  decays or reactions.
• X ? Y Z DE
• Mass difference between X and YZ is DE/c2.
• Absolute mass by mass spectrometers (next
  transparency).
• Mass and Binding energy
• B Z MH N Mn M(A,Z)/c2

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Mass Spectrometer

• Ion Source
• Velocity selector ? electric and magnetic forces
  equal and opposite
• qEqvB ? vE/B
• Momentum selector, circular orbit satisfies
• MvqBr
• Measurement r gives M.

Detector
Velocity selector
Ion Source
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Binding Energy vs A

• B increases with A up to 56Fe and then slowly
  decreases. Why?
• Lower values and not smooth at small A.

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Nuclear Sizes Isotope Shift

• Coulomb field modified by finite size of nucleus.
  
• Assume a uniform charge distribution in the
  nucleus. Gausss law ?
• integrate and apply boundary conditions
• Difference between actual potential and Coulomb
• Use 1st order perturbation theory

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Isotope Shifts
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Isotope Shifts

• Isotope shift for optical spectra
• Isotope shift for X-ray spectra (bigger effect
  because electrons closer to nucleus)
• Isotope shift for X-ray spectra for muonic atoms.
  Effect greatly enhanced because mm 207 me and
  a01/m.
• All data consistent with RR0 A1/3 with
  R01.25fm.

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Isotope Shift in Optical Spectra
Frequency shift of an optical transition in Hg at
?253.7nm for different A relative to A198. Data
obtained by laser spectroscopy. The effect is
about 1 in 107. (Note the even/odd structure.)
Bonn et al Z Phys A 276, 203 (1976)
DE/h (GHz)
A2/3
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Data on the isotope shift of K X ray lines in Hg.
The effect is about 1 in 106. Again the data show
the R2 A2/3 dependence and the even/odd effect.
Lee et al, Phys Rev C 17, 1859 (1978)
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58Fe
Data on Isotope Shift of K Xrays from muonic
atoms in which a muon with m207me takes the
place of the atomic electron. Because a0 1/m
the effect is 0.4, much larger than for an
electron. The large peak is 2p3/2 to 1s1/2. The
small peak is 2p1/2 to 1s1/2. The size comes from
the 2j1 statistical weight. Shera et al Phys
Rev C 14, 731 (1976)
56Fe
54Fe
Energy (keV)
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SEMF

• Aim phenomenological understanding of nuclear
  binding energies as function of A Z.
• Nuclear density constant (see lecture 1).
• Model effect of short range attraction due to
  strong interaction by liquid drop model.
• Coulomb corrections.
• Fermi gas model ? asymmetry term.
• QM ?pairing term.
• Compare with experiment success failure!

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Liquid Drop Model Nucleus

• Phenomenological model to understand binding
  energies.
• Consider a liquid drop
• Ignore gravity and assume no rotation
• Intermolecular force repulsive at short
  distances, attractive at intermediate distances
  and negligible at large distances ? constant
  density.
• E-an 4pR2T ?Ban-bn2/3
• Analogy with nucleus
• Nucleus has constant density
• From nucleon nucleon scattering experiments
  Nuclear force has short range repulsion and
  attractive at intermediate distances.
• Assume charge independence of nuclear force,
  neutrons and protons have same strong
  interactions ?check with experiment!

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Mirror Nuclei

• Compare binding energies of mirror nuclei (nuclei
  n ??p). Eg 73Li and 74Be.
• Mass difference due to n/p mass and Coulomb
  energy.

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nn and pp interaction same (apart from
Coulomb) Charge symmetry
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Charge Symmetry and Charge Independence

• Mirror nuclei showed that strong interaction is
  the same for nn and pp.
• What about np ?
• Compare energy levels in triplets with same A,
  different number of n and p. e.g.
• Same energy levels for the same spin states ? SI
  same for np as nn and pp.

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Charge Independence
2311Na
2312 Mg

• Is np force is same as nn and pp?
• Compare energy levels in nuclei with same A.
• Same spin/parity states have same energy.
• npnnpp

2212Mg
2210Ne
2211Na
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Charge Independence of Strong Interaction

• If we correct for n/p mass difference and Coulomb
  interaction, then energy levels same under n ??p.
• Conclusion strong interaction same for pp, pn
  and nn if nucleons are in the same quantum state.
• Beware of Pauli exclusion principle! eg why do we
  have bound state of pn but not pp or nn?

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Asymmetry Term

• Neutrons and protons are spin ½ fermions ? obey
  Pauli exclusion principle.
• If other factors were equal ? ground state would
  have equal numbers of n p.

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Asymmetry Term

• From stat. mech. density of states in 6d phase
  space 1/h3
• Integrate to get total number of protons Z,
  Fermi Energy (all states filled up to this energy
  level).
• Change variables p ? E

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Asymmetry Term

• Binomial expansion keep lowest term in y/A
• Correct functional form but too small by factor
  of 2. Why?

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Pairing Term

• Nuclei with even number of n or even number of p
  more tightly bound ?fig.
• Only 4 stable o-o nuclei cf 153 e-e.
• p and n have different energy levels ? small
  overlap of wave functions. Two p(n) in same level
  with opposite values of jz have AS spin state ?
  sym spatial w.f. ?maximum overlap ?maximum
  binding energy because of short range attraction.

Neutron separation energy in Ba
Neutron number
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Pairing Term

• Phenomenological fit to A dependence
• Effect smaller for larger A

d
e-e ive
e-o 0
o-o -ive
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Semi Empirical Mass Formula

• Put everything together
• Fit to measured binding energy.
• Fit not too bad (good to lt1).
• Deviations are interesting ? shell effects.
• Coulomb term agrees with calculation.
• Asymmetry term larger ?
• Explain valley of stability.
• Explains energetics of radioactive decays,
  fission and fusion.

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The Binding Energy per nucleon of beta-stable
(odd A) nuclei. Fit values in MeV
9.0
a 15.56
b 17.23
c 23.285
d 0.697
d 12 (o-o)
d 0 (o-e)
d -12 (e-e)
B/A (MeV)
7.5
A
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Valley of Stability

• SEMF allows us to understand valley of stability.
• Low Z, asymmetry term ? ZN
• Higher Z, Coulomb term ? NgtZ.