Title: Additional clues to nuclear structure
1Additional 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
2Nuclear 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
4- 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
5Properties 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
6- 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
7Payoff 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
8(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.
9Start 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.