Additional clues to nuclear structure

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Additional clues to nuclear structure

• Nuclear spins provide information about the
  strong interaction of protons and neutrons in
  nuclei
• Even-A nuclei have integer spins, odd-A
  half-integer
• Strong pairing nuclei with even Z and N have
  zero spin ? spin-1/2 ns and ps must anti-align
  in pairs (?? ?? ???)
• Patterns of nuclear stability and instability
  provide evidence about interactions of nucleons
• Start with a few observations and a tantalizing
  hint

• Started with size and shape information because
  it inspires first semiquantitative model of the
  nucleus
• Other input scattering with other probes and
  other interactions (?N and ?N) and higher energy
• Same pattern unexpected hard scatters reveal
  inner structure - quarks
• Anomalous magnetic moments of proton and neutron
  (both spin-1/2) also suggest substructure
• No bearing on the nuclear physics defer till
  later

2
Nuclear Instability and Radioactive Decay

• ?-radiation strongly ionizing (absorbed by a few
  cm of air) positively charged (deflection in E/B
  fields) spectroscopy and e/m ? He ions.

• Natural radioactivity discovered by Becquerel
  (1896). Came to be recognized as nuclear
  disinte- gration. Many unstable nuclides
  identified (Curies, et al.). Three types of
  radiation described.

• ?-radiation longer range (penetrates Pb foil)
  negatively charged e/m ? electrons.

Continuous Spectrum
Monoenergetic

• ?-radiation still longer range (penetrates cms
  of Pb) no electric charge EM radiation like
  X-rays, but more energetic.

3

• Plot of N vs. Z for all stable and unstable
  nuclei shows what it takes to build a nucleus and
  hold it together in spite of EM repulsion of the
  protons.

Observations

• A ? 20 line of stability is close to N Z
• A gt 20 stable nuclei show increasing need for
  more neutrons (for A gt 40, N ? 1.7Z)
• No stable nuclei above Z 82 (Pb). Z 83 (Bi)
  was believed to have a stable isotope (A209)
  until 2003 lifetime gt 1019 y

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• Qualitative explanation
• Larger nuclei have greater charge density
• Destabilizing effect of being surrounded by
  protons needs to be compensated by the presence
  of extra neutrons

• Look more closely at the stability data.
  Preference for configurations with paired nuclei
  is clear

• Strong Pairing hypothesis, also suggested by
  nuclear spins

• Understanding of nuclear sizes (incompressibility)
  , the neutron hunger of large nuclei, evidence
  for strong pairing must be incorporated into
  nuclear models
• Firsta few properties of the nuclear force

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Properties of the Strong Nuclear Force

• Info from scattering, other experiments (?N, nN,
  deuterons, etc.)
• Different from other forces, esp. EM
• Strong, but short range (?10-14 m)
• No effect on atomic physics. B/A does not depend
  on size ? p/n interact only with nearest
  neighbors
• Suggests (Yukawa) carrier is a particle with
  nonzero mass, not like photon
• Attractive on nuclear scale, repulsive core.
• Nuclei dont collapse, maintain constant density
• Qualitative potential helps with intuitive
  understanding, but limited quantitative
  application
• Charge independence
• n and p exhibit identical nuclear interactions
  after the effects of electric charge are
  eliminated

• Reveals basic symmetry of strong interaction
  isospin and sets the stage for deeper
  symmetries and the quark model

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• Next task
• Use qualitative and quantitative observations
  about properties of nuclei and the nuclear force
  to construct phenomenological models of nuclear
  structure.
• Most basic features
• Nuclei are spherical
• Nuclear radii satisfy R?A1/3 ? constant density

Read Das and Ferbel Chap. 3. Homework 3 to be
posted Friday.
Liquid Drop Model

• Nucleus behaves like a non-rotating
  incompressible liquid drop, with nuclei instead
  of molecules
• Individual quantum properties of nucleons are
  irrelevant
• Short-range attraction holds nucleons together,
  extremely-short-range repulsive force prevents
  collapse
• Stable central core of nucleons for which the
  nuclear force is saturated (?A)
• Surface layer of nucleons not as tightly bound
  for which the nuclear force is not saturated
  (?A2/3)
• Together these result in a net attraction toward
  the center ? surface tension

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Payoff Semi-Empirical Mass Formula

• Simple liquid drop picture does not yet have
  electromagnetic effect of the proton charges.
• Details depend on specific charge distribution,
  but in general

• With the nuclear-force effects and this Coulomb
  repulsion, we can make a first stab at a formula
  for the nuclear binding energy

Semi-empirical ? determine the coefficients by
fitting B.E. data
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(A good start, but still not good enough
incorporate some quantum properties.)
Fermi-Gas Model

• Treat nucleus as a gas of free ps and ns
  confined in a spherically symmetric potential
  well.
• Width nuclear diameter
• Depth whatever gives the observed B.E.

• ps and ns are spin-1/2 and must obey
  Fermi-Dirac statistics and the Pauli exclusion
  principle.
• ? Two identical nucleons (? and ?) per state

Ignore for now potentials for n and p must be
different because of charge.
In the ground state, levels fill from the bottom
to the Fermi level. To exchange a proton for a
neutron takes energy.
9
Start at NZ
Total energy increment for N Z to some N gt Z
with A constant approaches
Remember! Simplified treatment of energy levels
? no difference between increasing Z and
increasing N. Reality symmetry broken by proton
charge.