Lectures 1

1
Lectures 1

• Introduction and Overview
• Nuclear sizes and isotope shifts

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1.0 Overview

• 1.1 User guide to these lectures
• 1.2 Why study nuclear physics
• 1.3 Why nuclear physics is diff(eren)??(icul)t
• 1.4 Course synopsis
• 1.5 Notation Units
• 1.6 Nuclear Masses and Sizes
• Mass measurements
• Isotope Shifts

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1.1 How to use these lectures

• Definition of a classical lecture
• A lecture is 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.
• Disadvantages
• obvious
• Conclusion to make lectures useful YOU have to
  participate
• annotate the notes
• notes are not a replacement for text book(s!).
• Without your comments writtend during and after
  the lectures they are of very little use to all
  but the lecturer
• take your own notes As if you were never given
  these pages
• exception might be good to write your notes onto
  the sides of these
• ask questions
• If you dont understand something the chances are
  gt50 of the audience doesnt either, so dont be
  shy !

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1.1 Corrections

• To err is human and I am giving half of this
  course for the first time ? 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!).

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1.2 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 to understand
  nucleosynthesis ? experimental nuclear
  astrophysics is a hot topic.

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1.2 Energy Applications

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

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1.2 Medical Applications

• Radiotherapy for cancer
• Kill cancer cells.
• Used for 100 years but can be improved by better
  delivery and dosimetry
• Heavy ion beams can give more localised energy
  deposition.
• Medical Imaging
• MRI (Magnetic Resonance Imaging) uses nuclear
  magnetic resonances
• X-rays (better detectors ? lower doses)
• PET (Positron Emission Tomography)
• Many otherssee Medical Environmental short
  option.

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1.2 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
• Forensic (eg date As in hair).
• Biology (eg elements in blood cells)
• Archaeology (eg provenance via isotope ratios).

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1.3 Why is Nuclear Physics diff(eren)??(icul)t?

• We have QCD as an exact theory of strong
  interactions ? just solve the equations
• Thats fine at short distances ltlt size of proton
• i.e. at large momentum transfers collisions
  with high CM energies gtgt mproton (HEP)
• ? coupling constant is small (asymptotic freedom)
• ? perturbation theory works
• But it fails at large distances O(size of
  proton)
• coupling constant becomes big
• ? perturbation theory fails
• ? we dont know how to solve the equations

Boo !
Not on syllabus !
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1.3 Nuclear Physics (Super) Models

• Progress with understanding nuclear physics from
  QCD0
• ? use simple, approximate, phenomenological
  models
• inspired by analogies to other system
• Semi Empirical Mass Formula (SEMF)
• SEMF Liquid Drop Model Fermi Gas Model
  phenomenology QM EM.
• Shell Model look at quantum states of individual
  nucleons to understand ground and low lying
  excited states
• spin, parity
• magnetic moments (not on syllabus)
• deviations from SEMF predictions for binding
  energy.

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1.4 Overview of Lectures (I)

• Introduction
• Fri. Week 1, Lindemann (L)
• Why do we study Nuclear Physics
• What will this course cover
• Shape and density of the nuclei
• 2. The Semi Empirical Mass Formula (SEMF)
• Thu. Week 2, Martin Wood (MW)
• The liquid drop model
• The Fermi Gas Model
• Experimental verification
• 3./4./5. Using the SEMF and transition to Shell
  Model
• Fri. (L) Week 2 Thu. (MW), Fri (L) Week 3
• The valley of nuclear stability
• Nuclear decays (a, b, fission, others)
• Natural radioactivity
• The end of SEMF Evidence of magic numbers
• The Shell Model

Note lectures in the Martin Wood lecture theatre
starting 1205 lectures in the
Lindemann lecture theatre starting 1405
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1.4 Overview of Lectures (II)

• 6./7. Crossections
• Thu. (MW), Frid (L) Week 4,
• Experiments, natural units, conventions and
  definitions
• Fermis Golden Rule
• Rutherford Scattering
• Breit-Wigner resonances and partial decay widths
• Note No nuclear physics lectures in week 5 !
• 8./9. Theory of Decays
• Thu. Fri. Week 6, (MW)
• Tunnelling model of a-decay
• Selection rules and decay rates in g-decay
• Fermi theory of b-decay

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1.4 Overview of Lectures (III)

• 10./11. Particle Interactions with Matter
• Thu. Fri. Week 7, (MW)
• dE/dx by ionisation and the Bethe-Bloch formula
  (9)
• Photoeffect, Compton Scattering, Bremsstrahlung,
  Pair Production
• Cherenkov radiation
• 12./13. Applications of Nuclear Physics
• Thy. Fri. Week 8, (MW)
• Particle Detectors
• Fission Reactors
• Bombs
• Fusion reactors
• Radioactive dating (notes only)

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The Minister of Science

• This is a true story honest.
• Once upon a time the UK science minister visited
  the Rutherford Lab (UK national lab. near Didcot)
  and after a days visit of the lab was discussing
  his visit with the lab director and he said
  ltcensoredgt
• Your answer should at least have been as good as
  air!

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1.5 Notation

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

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1.5 Units

• SI units are fine for macroscopic objects like
  footballs but are very inconvenient for nuclei
  and particles ? use appropriate units.
• Energy 1 MeV kinetic energy gained by an
  electron in being accelerated by 1MV.
• 1 eV 106 x e/C x 1 J 1.602 x 10-19 J
• Mass MeV/c2 (or GeV/c2)
• 1 MeV/c2 106 x e/C / c2 x 1kg 1.783 x 10-30
  kg
• Or use Atomic Mass Unit (AMU or u) defined by
• mass of 12C 12 u
• 1 u 1.661 x 10-27 kg 0.93 GeV/c2
• Momentum MeV/c (or GeV/c)
• 1 MeV/c 106 x e/C / c x kg
• Length fermi 1 fm 10-15 m
• Cross sections barn as big as a barn door (to
  a particle physicists)
• 1 barn 10-28 m2 100 fm2

Note C Coulomb c speed of light
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1.6 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 in atomic spectra

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1.6 Nuclear Mass Measurements

• Lets collect all the experimental facts first !
• Measure relative masses by energy released in
  decays or reactions.
• X ? Y Z DE
• Mass difference between X and YZ is DE/c2.
• Absolute masses measured by mass spectrometers
  (next transparency).
• Relation between Mass and Binding energy
• B Z MH N Mn Matom(A,Z)/c2 or
• B Z Mp N Mn Mnucleus(A,Z)/c2
• (neglecting atomic binding energy of electrons)

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1.6 Mass Spectrometer

• Ion Source (e.g. strong laser takes out
  electrons)
• Velocity selector
• for electric and magnetic forces to be equal and
  opposite need
• Momentum selector, circular orbit satisfies
• Measurement of x gives rcurv
• rcurv and v gives M

xx(rcurv)
position sensitive detector
velocity selector
ion source
B
E
B
momentum selector
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1.6 Binding Energy per nucleon vs. A

• Typical way of representing mass measurements
• B increases with A up to 56Fe and then slowly
  decreases.
• B is very small and not smooth at small A.
• Why?
• See SEMF and Shell Modell.

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1.6 Nuclear Sizes and Isotope Shifts

• Measure size of nucleus by the effect of its
  charge distribution on the energy levels of
  atomic electrons
• Simple point like Coulomb field will be modified
  by finite size of nucleus.
• This should be felt most by electrons close to
  the nucleus i.e. k-shell L0
• And should be negligible for electrons with
  minimal overlap with the nucleus, i.e. Lgt0 (Yr
  L)
• ? study this assuming Hydrogenic ground state
  wave functions for the electrons
• thats justified even for large Z atoms since
  k-shell electron does not see much of outer
  electrons

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1.6 Nuclear Sizes Isotope Shifts

• Assume a uniform distribution of charge Ze in a
  spherical nucleus of radius R.
• Calculate potential inside nucleus Vinside
• Einside via Gausss law
• Vinside by integrating Einside and applying
  boundary conditions at rR to match Vinside to
  usual 1r2 potential
• Difference between actual potential and Coulomb

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1.6 Nuclear Sizes Isotope Shifts

• Use 1st order perturbation theory to calculate
  energy shift ?E

• Insert approximate Hydrogenic ground state wave
  function

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1.6 Nuclear Sizes Isotope Shifts

• Note ?E is proportional to Z4 and R2? most
  noticeable effect deep inside large Z nuclei
• a0 0.5 10-10 m

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1.6 Isotope Shifts

• Look at transitions from l1 (no isotope shift)
  to l0 (large isotope shift)
• Preferably look for transitions at low n.
• Types of isotope shifts in increasing shift
  order
• Isotope shift for optical spectra ?E O(meV)
• Isotope shift for X-ray spectra (bigger effect
  then optical because electrons closer to
  nucleus) ?E O(0.1 eV)
• Isotope shift for X-ray spectra for muonic atoms.
  Effect greatly enhanced because mm 207 me and
  a01/m. ?E O(keV)
• All data consistent with RR0 A1/3 using
  R01.25fm.

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1.6 Isotope Shift in Optical Spectra

• Need to use higher n wave functions to calculate
  this
• Use Zeff Z-n
• expect (Zeff/Z)4 dependence in ?E
• Why is ?E A2/3 ?
• ?E R2 (see before)
• and RR0A1/3

Energy shift of an optical transition in Hg at
?253.7nm for different A relative to A198. Data
obtained by Doppler free laser spectroscopy. The
effect is about 1 in 107. (Note the even/odd
structure.) Bonn et al Z Phys A 276, 203 (1976)
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1.6 Isotope Shift in X-Ray Spectra

• Bigger shifts as expected
• Again two lines A2/3

0.5
DE (eV)
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)
0
A2/3
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1.6 Isotope Shift in muonic atoms

• See dependence on Rnucl
• Because a0 1/m the effect is 0.4, i.e. much
  larger than for an electron
• Changing Rnucl by increasing A gives changes in
  isotope shifts of 2 keV

Data on Isotope Shift of K Xrays from muonic
atoms in which a muon with m207me takes the
place of the atomic 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)
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1.6 Isotope Shift Conclusions

• All types of isotopes shifts show A2/3 as
  expected for an R2nucl dependence
• This holds for all types of nuclei
• When fitting the slopes we find the same R0 in
  RnuclR0A1/3
• This tells us that the nuclear density is a
  universal constant