All zeroes of the jls are distinct no energy degeneracy in n and l'

1
Count the available states
Closed Shells
n 1 l 0 ? 2 l 1 ? 6 l 2 ? 10 l
3 ? 14 l 4 ? 18

• All zeroes of the jls are distinct ? no energy
  degeneracy in n and l.
• For given n and l, all mls are degenerate in
  energy (2l 1)
• For given n, l and ml, there are ? and ? spin
  states for n and p.
• Total degeneracy 2(2l 1) slots to fill for
  every n and l.

Good News predicts existence of nuclear magic
numbers.
Bad News Only some of the predicted magic
numbers match observed ones.
Other ns bring in other closed shells, but still
not the right set.
What do we try next? More/different/better
potentials to start.
2
Harmonic Oscillator
Has some degeneracy, reduced set of magic
s. Still not the right set!
3
Keep trying

• Tweak the wells Get rid of features like
  infinite barriers/sharp edges.
• Reasonable nuclear potentials, incl.
  Woods-Saxon, adjust energy levels, break some
  degeneracies ? new magic numbers.
• Still the wrong ones.
• Bottom line No central potential can produce all
  of the observed magic numbers and only the right
  ones.
• Need a more complicated strong interaction for
  the nucleon in a nucleus.

4
Spin-Orbit Interaction

• Atomic Physics

Spin of e ? magnetic dipole moment, interacts
with EM field (magnetic field component in e rest
frame).

• Nuclear Physics

Nucleon-nucleon strong interaction postulated to
have spin-orbit term. Nucleon deep in nucleus
feels no effect (symmetry), but one near surface
feels net interaction with all others.
Differs from atomic f(r) to be chosen Sign
chosen to match observed level splitting
Next step is to exercise our facility with
angular momentum and deduce the form of the
resulting level splitting.
5
Compute the energy shifts (perturbatively)
Total splitting
Key observation Splitting grows with l ? can
reorder the levels.
6
And it does

• Even-Even Nuclei JP 0
• Odd-A Spin-Parity Assignments
• p and n levels fill independently
• paired in every level ??
• Last unpaired nucleons j determines nuclear spin
  and its l determines nuclear parity (-1)l.

6 protons, all paired ? no effect
7 neutrons
j 1/2 l 1 ? odd parity

• The SPSM has been coaxed to do what we need
  provide a physics rationale for observed level
  ordering in the nucleus.
• Deduce consequences!

Other successes magnetic moments Omission
odd-odd nuclei
7
Nuclear Physics
?

• A pastiche of slightly related ideas and
  techniques
• Assessment of theoretical nuclear physics by
  W.S.C. Williams, an experimental nuclear
  physicist.
• Models do not represent a coherent, fundamental
  framework, because
• Underlying interaction (strong force) is not well
  understood.
• Many-body effects are very difficult to handle,
  central to collective models of nuclear
  matter, but
• Still, it works quite well on an empirical level.
• Choose your function intelligently and give it
  enough parameters and you can both fit the
  elephant and make its tail wiggle.
• Set aside any misgivings and use these models and
  empirical tools to address observed behaviors of
  nuclei, especially radioactive decay, but also
  the energy-producing processes of fission and
  fusion.

8
Radioactivity
(2006 PDB p. 274 for units/radiation safety)

• 1 Becquerel (Bq) Amount of material giving 1
  decay per second
• 1 Curie (Ci) Amount of material giving 37
  billion decays per second (e.g. 1 g of 226Ra)

• For radiation safety, its not the raw counts,
  but the effect
• Energy Deposition (integrated)
• 1 Gray (Gy) 100 rad ? 1 J/kg or 6.24 ? 1012
  MeV/kg
• Exposure/Photon Fluence ? ionization
• 1 Roentgen (R) 2.58 ? 10-4 C/kg
• Equivalent Dose ? tissue damage
• 1 Sievert (Sv) 100 rem,
• absorbed dose in Gy times a
• weighting factor)

9
Radioactive Decay
(DF 5.4 for math review)
All of this applies in the rest frame of the
decaying particle. Remember ?? in the lab.
10

• Decay chains of unstable nuclides can be complex,
  with multiple steps involving ?, ?, ?, and even a
  few other processes.
• Some states decay in more than one way

11
For very short-lived particles.
?
Lifetime ?
Full Width ?