4511_Lec4_30Jan08

1
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.

2

• An unstable nucleus decays because there is an
  arrangement of its component parts that is
  energetically favored over the original.
• We learn a great deal about the strong
  interaction from the patterns of stability.

• Small nuclei (A ? 40) are stable with N ? Z, but
  larger nuclei demand more neutrons (N ? 1.7Z).

• Protons have attractive nuclear forces and
  repulsive Coulomb forces neutrons have just the
  nuclear force and act as extra glue.
• Why dont small nuclei demand more neutrons too?

3

• 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.
• First, peek at some properties of the nuclear
  force.

4
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 (lt10-14 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 const. 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.

5

• 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

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.

6
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
7
(A good start, but still not good enough.)
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.
8
Start at NZ
Total energy increment for N Z ? to some N gt Z
with A constant approaches
Simplified treatment of energy levels ? no
difference between increasing Z and increasing N.
Reality symmetry broken by proton charge.
9

• Potential well has energy spacing that is
  inversely proportional to size

• Combining this with the previous result, we get a
  new term for the B.E. reflecting the price of
  p/n asymmetry.

One more effect to incorporate strong pairing.