Nuclear and Particle Physics

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Nuclear and Particle Physics
3 lectures Nuclear Physics Particle Physics
1 Particle Physics 2
2
Nuclear Physics Topics

• Composition of Nucleus
• features of nuclei
• Nuclear Models
• nuclear energy
• Fission
• Fusion
• Summary

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About Units

• Energy - electron-volt
• 1 electron-volt kinetic energy of an electron
  when moving through potential difference of 1
  Volt
• 1 eV 1.6 10-19 Joules
• 1 kWhr 3.6 106 Joules 2.25 1025 eV
• 1 MeV 106 eV, 1 GeV 109 eV, 1 TeV 1012 eV
• mass - eV/c2
• 1 eV/c2 1.78 10-36 kg
• electron mass 0.511 MeV/c2
• proton mass 938 MeV/c2 0.938 GeV/ c2
• neutron mass 939.6 MeV/c2
• momentum - eV/c
• 1 eV/c 5.3 10-28 kg m/s
• momentum of baseball at 80 mi/hr ? 5.29 kgm/s ?
  9.9 1027 eV/c
• Distance
• 1 femtometer (Fermi) 10-15 m

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Radioactivity

• Discovery of Radioactivity
• Antoine Becquerel (1896) serendipitous discovery
  of radioactivity penetrating radiation emitted
  by substances containing uranium
• A. Becquerel, Maria Curie, Pierre Curie(1896
  1898)
• also other heavy elements (thorium, radium) show
  radioactivity
• three kinds of radiation, with different
  penetrating power (i.e. amount
  of material necessary to attenuate beam)
• Alpha (a) rays (least penetrating stopped by
  paper)
• Beta (b) rays (need 2mm lead to absorb)
• Gamma (g) rays (need several cm of lead to be
  attenuated)
• three kinds of rays have different electrical
  charge a , b -, g 0
• Identification of radiation
• Ernest Rutherford (1899)
• Beta (b) rays have same q/m ratio as electrons
• Alpha (a) rays have same q/m ratio as He
• Alpha (a) rays captured in container show He-like
  emission spectrum

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Geiger, Marsden, Rutherford expt.

• (Geiger, Marsden, 1906 - 1911) (interpreted by
  Rutherford, 1911)
• get ? particles from radioactive source
• make beam of particles using collimators
  (lead plates with holes in them, holes
  aligned in straight line)
• bombard foils of gold, silver, copper with beam
  
• measure scattering angles of particles with
  scintillating screen (ZnS)

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Geiger Marsden experiment result

• most particles only slightly deflected (i.e. by
  small angles), but some by large angles - even
  backward
• measured angular distribution of scattered
  particles did not agree with expectations from
  Thomson model (only small angles expected),
• but did agree with that expected from scattering
  on small, dense positively charged nucleus with
  diameter lt 10-14 m, surrounded by electrons
  at ?10-10 m

Ernest Rutherford 1871-1937
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Proton

• Canal rays
• 1898 Wilhelm Wien
• opposite of cathode rays
• Positive charge in
• nucleus (1900 1920)
• Atoms are neutral
• positive charge needed to cancel electrons
  negative charge
• Rutherford atom positive charge in nucleus
• periodic table ? realized that the positive
  charge of any nucleus could be accounted for by
  an integer number of hydrogen nuclei -- protons

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Neutron

• Walther Bothe 1930
• bombard light elements (e.g. 49Be) with alpha
  particles ? neutral radiation emitted
• Irène and Frederic Joliot-Curie (1931)
• pass radiation released from Be target through
  paraffin wax ? protons with energies up to 5.7
  MeV released
• if neutral radiation photons, their energy
  would have to be 50 MeV -- puzzle
• puzzle solved by James Chadwick (1932)
• assume that radiation is not quantum radiation,
  but a neutral particle with mass approximately
  equal to that of the proton
• identified with the neutron suggested by
  Rutherford in 1920
• observed reaction was ? (24He) 49Be
  ? 613C
• 613C ? 612C n

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Beta decay -- neutrino

• Beta decay puzzle
• decay changes a neutron into a proton
• apparent non-conservation of energy
• apparent non-conservation of angular momentum
• Wolfgang Pauli predicted a light, neutral,
  feebly interacting particle (called it neutron,
  later called neutrino by Fermi)
• Although accepted since it fit so well, not
  actually observed initiating interactions until
  1956-1958 (Cowan and Reines)

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Puzzle with Beta Spectrum

• Three-types of radioactivity a, b, g
• Both a, g discrete spectrum because
• Ea, g Ei Ef
• But b spectrum continuous
• Energy conservation violated??
• Bohr At the present stage of atomic theory,
  however, we may say that we have no argument,
  either empirical or theoretical, for upholding
  the energy principle in the case of ß-ray
  disintegrations

• F. A. Scott, Phys. Rev. 48, 391 (1935)

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Desperate Idea of Pauli
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Positron

• Positron (anti-electron)
• Predicted by Dirac (1928) -- needed for
  relativistic quantum mechanics
• existence of antiparticles doubled the number of
  known particles!!!
• Positron track going
• upward through lead
• plate
• P.A.M. Dirac
• Nobel Prize (1933)
• member of FSU faculty (1972-1984)
• one of the greatest physicists of the 20th century

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Structure of nucleus

• size (Rutherford 1910, Hofstadter 1950s)
• R r0 A1/3, r0 1.2 x 10-15 m 1.2 fm
• i.e. 0.15 nucleons / fm3
• generally spherical shape, almost uniform
  density
• made up of protons and neutrons
• protons and neutron -- nucleons are
  fermions (spin ½), have magnetic moment
• nucleons confined to small region (potential
  well)
• ? occupy discrete energy levels
• two distinct (but similar) sets of energy
  levels, one for protons, one for neutrons
• proton energy levels slightly higher than those
  of neutrons (electrostatic repulsion)
• spin ½ ? Pauli principle ? only two
  identical nucleons per eng. level

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Nuclear Sizes - examples
Find the ratio of the radii for the following
nuclei 1H, 12C, 56Fe, 208Pb, 238U
1 2.89 3.83 5.92 6.20
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A, N, Z

• for natural nuclei
• Z range 1 (hydrogen) to 92 (Uranium)
• A range from 1 ((hydrogen) to 238 (Uranium)
• N neutron number A-Z
• N Z neutron excess increases with Z
• nomenclature
• ZAXN or AXN or AX or X-A

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Atomic mass unit

• atomic number Z
• Number of protons in nucleus
• Mass Number A
• Number of protons and neutrons in nucleus
• Atomic mass unit is defined in terms of the mass
  of 126C, with A 12, Z 6
• 1 amu (mass of 126C atom)/12
• 1 amu 1.66 x 10-27kg
• 1 amu 931.494 MeV/c2

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Properties of Nucleons

• Proton
• Charge 1 elementary charge e 1.602 x 10-19 C
• Mass 1.673 x 10-27 kg 938.27 MeV/c2
  1.007825 u 1836 me
• spin ½, magnetic moment 2.79 eh/2mp
• Neutron
• Charge 0
• Mass 1.675 x 10-27 kg 939.6 MeV/c2
  1.008665 u 1839 me
• spin ½, magnetic moment -1.9 eh/2mn

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Nuclear masses, isotopes

• Nuclear masses measured, e.g. by mass
  spectrography
• masses expressed in atomic mass units (amu),
• energy units MeV/c2
• all nuclei of certain element contain same
  number of protons, but may contain different
  number of neutrons
• examples
• deuterium, heavy hydrogen 2D or 2H heavy
  water D2O (0.015 of natural water)
• U- 235 (0.7 of natural U), U-238 (99.3 of
  natural U),

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Nuclear energy levels example

• Problem Estimate the lowest possible energy of a
  neutron contained in a typical nucleus of radius
  1.3310-15 m.

E p2/2m (cp)2/2mc2
?x ?p h/2? ? ?x ?(cp) hc/2? ?(cp) hc/(2?
?x) hc/(2? r) ?(cp) 6.63x10-34 Js 3x108
m/s / (2? 1.33x10-15 m) ?(cp) 2.38x10-11 J
148.6 MeV
E p2/2m (cp)2/2mc2 (148.6 MeV)2/(2940 MeV)
11.7 MeV
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Nuclear Masses, binding energy

• Mass of Nucleus ? Z(mp) N(mn)
• mass defect ?m difference between mass of
  nucleus and mass of constituents
• energy defect binding energy EB EB ?m c2
• binding energy amount of energy that must be
  invested to break up nucleus into its
  constituents
• binding energy per nucleon EB /A

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Nuclear Binding Energy

• The difference between the energy (or mass) of
  the nucleus and the energy (or mass) of its
  constituent neutrons and protons.
• the energy needed to break the nucleus apart.
• Average binding energy per nucleon total
  binding energy divided by the number of nucleons
  (A).
• Example Fe-56

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Problem set 4

• Compute binding energy per nucleon for
• 42He 4.00153 amu
• 168O 15.991 amu
• 5626Fe 55.922 amu
• 23592U 234.995 amu
• Is there a trend?
• If there is, what might be its significance?
• note
• 1 amu 931.5 MeV/c2
• m(proton) 1.00782 amu
• m(neutron) 1.00867 amu

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Binding energy per nucleon

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Nuclear Radioactivity

• Alpha Decay
• AZ ? A-4(Z-2) 4He
• Number of protons is conserved.
• Number of neutrons is conserved.
• Gamma Decay
• AZ ? AZ ?
• An excited nucleus loses energy by emitting a
  photon.

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Beta Decay

• Beta Decay
• AZ ? A(Z1) e- an anti-neutrino
• A neutron has converted into a proton, electron
  and an anti-neutrino.
• Positron Decay
• AZ ? A(Z-1) e a neutrino
• A proton has converted into a neutron, positron
  and a neutrino.
• Electron Capture
• AZ e- ? A(Z-1) a neutrino
• A proton and an electron have converted into a
  neutron and a neutrino.

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Radioactivity

• Electron capture
• g decay

• Several decay processes
• a decay
• b- decay
• b decay

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Law of radioactive decay

• Activity A number of
  decays per unit time
• decay constant ? probability of decay per unit
  time
• Rate of decay ? number N of nuclei
• Solution of diff. equation (N0 nb. of nuclei at
  t0)
• Mean life ? 1/ ?

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Nuclear decay rates
At t 1/?, N is 1/e (0.368) of the original
amount
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Nuclear (strong) force

• atomic nuclei small -- about 1 to 8fm
• at small distance, electrostatic repulsive
  forces are of macroscopic size (10 100 N)
• there must be short-range attractive force
  between nucleons -- the strong force
• strong force essentially charge-independent
• mirror nuclei have almost identical binding
  energies
• mirror nuclei nuclei for which n ? p or p ? n
  (e.g. 3He and 3H, 7Be and 7Li, 35Cl and 35Ar)
  slight differences due to electrostatic
  repulsion
• strong force must have very short range ltlt
  atomic size, otherwise isotopes would not have
  same chemical properties

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Strong force -- 2

• range fades away at distance 3fm
• force between 2 nucleons at 2fm distance 2000N
• nucleons on one side of U nucleus hardly
  affected by nucleons on other side
• experimental evidence for nuclear force from
  scattering experiments
• low energy p or ? scattering scattered
  particles unaffected by nuclear force
• high energy p or ? scattering particles can
  overcome electrostatic repulsion and can
  penetrate deep enough to enter range of nuclear
  force

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N-Z and binding energy vs A

• small nuclei (Alt10)
• All nucleons are within range of strong force
  exerted by all other nucleons
• add another nucleon ? enhance overall cohesive
  force ? EB rises sharply with increase in A
• medium size nuclei (10 lt A lt 60)
• nucleons on one side are at edge of nucl. force
  range from nucleons on other side ? each addl
  nucleon gives diminishing return in terms of
  binding energy ? slow rise of EB /A
• heavy nuclei (Agt60)
• adding more nucleons does not increase overall
  cohesion due to nuclear attraction
• Repulsive electrostatic forces (infinite range!)
  begin to have stronger effect
• N-Z must be bigger for heavy nuclei (neutrons
  provide attraction without electrostatic
  repulsion
• heaviest stable nucleus 209Bi all
  nuclei heavier than 209Bi are unstable
  (radioactive)

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EB/A vs A
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Nuclear Models liquid drop model

• liquid drop model (Bohr, Bethe, Weizsäcker)
• nucleus drop of incompressible nuclear fluid.
  
• fluid made of nucleons, nucleons interact
  strongly (by nuclear force) with each other,
  just like molecules in a drop of liquid.
• introduced to explain binding energy and mass
  of nuclei
• predicts generally spherical shape of nuclei
• good qualitative description of fission of
  large nuclei
• provides good empirical description of
  binding energy vs A

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Bethe Weizsäcker formula for binding energy

• Bethe - Weizsäcker formula
• an empirically refined form of the liquid drop
  model for the binding energy of a nucleus of mass
  number A with Z protons and N neutrons
• binding energy has five terms describing
  different aspects of the binding of all the
  nucleons
• volume energy
• surface energy
• Coulomb energy (electrostatic repulsion of the
  protons,)
• an asymmetry term (N vs Z)
• an exchange (pairing) term (even-even vs
  odd-even vs odd-odd number of nucleons)

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liquid drop terms in B-W formula
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Independent Particle Models

• assume nucleons move inside nucleus without
  interacting with each other
• Fermi- gas model
• Protons and neutrons move freely within nuclear
  volume, considered a rectangular box
• Protons and neutrons are distinguishable and so
  move in separate potential wells
• Shell Model
• formulated (independently) by Hans Jensen
  and Maria Goeppert-Mayer
• Each nucleon (proton or neutron) moves in the
  average potential of remaining nucleons, assumed
  to be spherically symmetric.
• Also takes account of the interaction between a
  nucleons spin and its angular momentum
  (spin-orbit coupling)
• derive magic numbers (of protons and/or
  neutrons) for which nuclei are particularly
  stable 2, 8, 20, 28, 50, 82, 126, ..

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Fermi-Gas Model of Nucleus

• Ground State
• In each potential well, the lowest energy states
  are occupied.
• Because of the Coulomb repulsion the proton well
  is shallower than that of the neutron.
• But the nuclear energy is minimized when the
  maximum energy level is about the same for
  protons and neutrons

• Therefore, as Z increases we would expect nuclei
  to contain progressively more neutrons than
  protons.
• U has A 238, Z 92

Potential well
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Collective model

• collective model is eclectic, combining
  aspects of other models
• consider nucleus as composed of stable core
  of closed shells, plus additional nucleons
  outside of core
• additional nucleons move in potential well due
  to interaction with the core
• interaction of external nucleons with the core ?
  agitate core set up rotational and vibrational
  motions in core, similar to those that occur in
  droplets
• gives best quantitative description of nuclei

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Nuclear energy

• very heavy nuclei
• energy released if break up into two medium
  sized nuclei
• fission
• light nuclei
• energy released if two light nuclei combine --
  fuse into a heavier nucleus fusion

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Nuclear Energy - Fission
about 200 MeV energy
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Fission
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Nuclear Fusion
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Suns Power Output

• Unit of Power
• 1 Watt 1 Joule/second
• 100 Watt light bulb 100 Joules/second
• Suns power output
• 3.826 x 1026 Watts
• exercise calculate suns power output using
  Stefan-Boltzmann law (assume sun is a black body)

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The Proton-Proton Cycle
1H 1H ? 2H e n e e- ? g g 2H
1H ? 3He g 3He 3He ? 4He 1H 1H
1 pp collision in 1022 ? fusion!
4H ? 4He
Deuterium creation
3He creation
4He creation
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Super Kamiokande Solar Neutrinos
Solar neutrino
Electron
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A Nearby Super-Giant
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Life of a 20 Solar Mass Super-Giant

• Hydrogen fusion
• 10 million years
• Helium fusion
• 1 million years
• Carbon fusion
• 300 years
• Oxygen fusion
• 9 months
• Silicon fusion
• 2 days

http//cassfos02.ucsd.edu/public/tutorial/SN.html
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Supernova 1987A
Before
After
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Stardust
Sir Fred Hoyle 1915-2001
7.65 MeV above 12C ground state
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Stardust II
7.19 MeV
7.12 MeV
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Summary

• nuclei made of protons and neutrons, held
  together by short-range strong nuclear force
• models describe most observed features, still
  being tweaked and modified to incorporate
  newest observations
• no full-fledged theory of nucleons yet
• development of nuclear theory based on QCD has
  begun
• nuclear fusion is the process of energy
  production of Sun and other stars
• we (solar system with all thats in it) are
  made of debris from dying stars