1. Nuclear Physics, JU, Second Semester, 2010-2011
Nuclear Models
Nuclear force is not yet fully understood.
No absolutely satisfying model, but models.
Specific experimental data  specific model.
Model  success in a certain range.
Some are:
Individual particle model. (Energy. states, static properties, …).
Liquid drop model. (Strong force, B.E., Fission, …).
Collective model.
-particle model.
Optical model.
Fermi Gas model.
Statistical model.
others …..
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

2. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Electron configuration….
1s2 2s2 2p6 3s2 3p6 4s2 3d10 4p6 ….
Atomic Electron magic numbers: 2, 10, 18, 36, 54, …
Common center of “external” attraction.
Well understood Coulomb force.
One kind of particles.
Clear meaning for electron orbits. …
Nuclear magic numbers: 2, 8, 20, 28, 50, 82,126, …
(for Z or N).
Chemistry!
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

3. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Evidence:
End of radioactive series:
thorium series 208Pb uranium series 206Pb actinium series 207Pb neptunium series 209Bi
At Z and N mn’s there are relatively large numbers of isotopes and isotones.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

4. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

5. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

6. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Natural abundances.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

7. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Neutron capture cross section.
NEUTRON CAPTURE
CROSS SECTION
NEUTRON NUMBER
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

8. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Binding energy of the last neutron
(Separation Energy).
(The measured values are plotted relative to the calculations without ).
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

9. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Excited states.
Pb (even-A) isotopes.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

10. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
All are even-even.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

11. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Nucleons are in definite states of energy and angular momentum.
Nucleon orbit ?? Continuous scattering expected ..!!
No vacancy for scattering at low energy levels.
Nuclear potential?
Infinite square well:
Harmonic oscillator:
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

12. Shell model ? ?
2(2l + 1)
accounts correctly for the number of nucleons in each level.
But what about magic numbers? ?   
Infinite spherical well
(R=8F)
Harmonic oscillator
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

13. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
More realistic! (Can it solve the problem?)
Finite square well potential:
Rounded well potential:
Correction for asymmetry and Coulomb repulsion.
Adjusted by the separation energies.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

14. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

15. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Coulomb repulsion? Vc(r) = ??
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

16. Shell model Nuclear reactions? Transition probability?
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

17. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Separation of variables:
For a given spherically symmetric potential V(r), the bound-state energy levels can be calculated from radial wave equation for a particular orbital angular momentum l.
Notice the important centrifugal potential.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

18. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

19. Nuclear Physics, JU, Second Semester, 2010-20111f 2p 1g 2d 3s
2(2l +1) 2 6 10 14 18
Total 8 20 34 40 58 68 70 ml ms
2, 8, ok.
What about other magic numbers?
Situation does not improve with other potentials.
Something very fundamental about the single-particle interaction picture is missing in the description…..!!!!!
Spin-orbit coupling.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

20. Shell model
So far, 2(2l + 1) accounts correctly for the number of nucleons in each level, since we already considered both orbital angular momentum, and spin, but still not for closed shells.
Separate.
Spherical Harmonics, Eigenfunctions of L2 and Lz.
But this representation does not solve the problem.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

21. Shell model Spin-Orbit Coupling
M. G. Mayer and independently Haxel, Jensen, and Suess.
Spin-Orbit term added to the Hamiltonian:
Orientation
No longer
Spherically symmetric
Central, attractive
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

22. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model L S LL
antiparallel UL
parallel J
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

23. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
2j+1
2(2x3 + 1) = 14
l = 3
1f7/2 j
First time
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

24. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
HW 7
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

25. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Notes:
1. The shell model is most useful when applied to closed-shell or near closed-shell nuclei.
2. Simple versions of the shell model do not take into account pairing forces, the effects of which are to make two like-nucleons combine to give zero orbital angular momentum. The pairing force increases with l.
3. Away from closed-shell nuclei collective models taking into account the rotation and vibration of the nucleus are more appropriate.
4. Shell model does not treat distortion effects (deformed nuclei) due to the attraction between one or more outer nucleons and the closed-shell core.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

26. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Ground state: (near closed shells)
1. Angular momentum of odd-A nuclei is determined by the angular momentum of the last nucleon that is odd.
2. Even-even nuclei have zero ground-state spin, because the net angular momentum associated with even N and even Z is zero, and even parity.
3. In odd-odd nuclei the last neutron couples to the last proton with their intrinsic spins in parallel orientation.
Provided that the ordering is known….!!
A < 150
190 < A < 220
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

27. Shell model Harmonic oscillator Near drip line No spin-orbit coupling
Near valley of  stability
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

28. Nuclear Physics, JU, Second Semester, 2010-2011
(Saed Dababneh).

29. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

30. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
17 p, 21 n.
p in 1d3/2 l  s   = +
n in 1f7/2 l  s   = -
Rule 3  sp  sn   lp  ln 
½ + ½ + 3 – 2 = 2
 total  = -
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

31. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Excited states:
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

32. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Extreme independent particle model!!! Does the core really remain inert?
1d3/2
1p3/2 ? ?
1p1/2?
l  pairing 
2s1/2
1d5/2
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

33. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model 20
Core
Extreme independent particle model  only 23rd neutron.
More complete shell model  all three “valence” nucleons.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

34. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Discuss the energy levels of nuclei with odd number of nucleons in the 1f7/2 shell.
HW 8
and 43Sc, 43Ti.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

35. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Dipole Magnetic Moment
HW 9 Show that
and examine Eqs. 5.9 in Krane. In addition, work out problem 5.8 in Krane  Conclusion?
Proton: gs(free) = ? gl = ?
Neutron: gs(free) = ? gl = ?
What about + and -?
Schmidt lines.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

36. Shell model Electric Quadrupole Moment Refined QM 
In the xy-plane: Q  - r2.
Electric Quadrupole Moment
Refined QM 
Extremes
Single particle: n = 1  - ive Q
Single hole: n = 2j  +ive Q
Number of protons in a subshell
Examine Table 5.1 and Fig.5.10 in Krane
<r2> for a uniformly charged sphere
(0.03 – 0.3 b)
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

37. Nuclear Physics, JU, Second Semester, 2010-2011
Why not zero?
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

38. Nuclear Physics, JU, Second Semester, 2010-2011
Shell model
Nuclide
Q (b)
2H (D)
17O
59Co
+0.40
63Cu
-0.209
133Cs
-0.003
161Dy
+2.4
176Lu
+8.0
209Bi
-0.37
+ vs. –
Holes vs. particles.
Validity
A < 150
190 < A < 220
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).