1. Neutron Excess Asymmetry Remember HWc 1.
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

2. Abundance Systematics
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

3. Abundance Systematics
NEUTRON CAPTURE
CROSS SECTION
Formation process 
Abundance
NEUTRON NUMBER
ABUNDANCE
r s
r s
MASS NUMBER
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

4. Nuclear and Radiation Physics, BAU, Second Semester, 2009-2010 (Saed Dababneh).

5. The Semi-empirical Mass Formula
von Weizsäcker in 1935.
Liquid drop. Shell structure.
Main assumptions:
Incompressible matter of the nucleus  R  A⅓.
Nuclear force saturates.
Binding energy is the sum of terms:
Volume term. 4. Asymmetry term.
Surface term. 5. Pairing term.
Coulomb term. 6. Closed shell term.
…..
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

6. The Semi-empirical Mass Formula
Volume Term Bv = + av A
Bv  volume  R3  A  Bv / A is a constant
i.e. number of neighbors of each nucleon is independent of the overall size of the nucleus.
constant
The other terms are “corrections” to this term.
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

7. The Semi-empirical Mass Formula
Surface Term Bs = - as A⅔
Binding energy of inner nucleons is higher than that at the surface.
Light nuclei contain larger number (per total) at the surface.
At the surface there are:
Nucleons.
Remember t/R  A-1/3
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

8. The Semi-empirical Mass Formula
Coulomb Term BC = - aC Z(Z-1) / A⅓
Charge density   Z / R3.
W  2 R5. Why ???
W  Z2 / R.
Actually:
W  Z(Z-1) / R.
BC / A =
- aC Z(Z-1) / A4/3
Remember HW 8 … ?!
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

9. The Semi-empirical Mass Formula
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

10. The Semi-empirical Mass Formula
Quiz 1
From our information so far we can write:
For A = 125, what value of Z makes M(A,Z) a minimum?
Is this reasonable…???
So …..!!!!
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

11. The Semi-empirical Mass Formula
Asymmetry Term Ba = - aa (A-2Z)2 / A
Light nuclei: N = Z = A/2 (preferable).
Deviation from this “symmetry”  less BE and stability.
Neutron excess (N-Z) is necessary for heavier nuclei.
Ba / A = - aa (N-Z)2 / A2.
Back to this when we talk about
the shell model.
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

12. The Semi-empirical Mass Formula
Pairing Term Bp = 
Extra Binding between pairs of identical nucleons in the same state (Pauli !)  Stability (e.g. -particle, N=2, Z=2).
even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei.
Remember HWc 1\ ….?!
Bp expected to decrease with A; effect of unpaired nucleon decrease with total number of nucleons. But empirical evidence show that:
  A-¾ .
Effect on:
Fission.
Magnetic moment.
Effect of high angular momentum.
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

13. The Semi-empirical Mass Formula
Closed Shell Term Bshell = 
Extra binding energy for magic numbers of N and Z.
Shell model.
1 – 2 MeV more binding.
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

14. The Semi-empirical Mass Formula
Fitting to experimental data.
More than one set of constants av, as …..
In what constants does r0 appear?
Accuracy to ~ 1% of experimental values (BE).
Atomic masses 1 part in 104.
Uncertainties at magic numbers.
Additional term for deformation.
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

15. The Semi-empirical Mass Formula
Variations…….
Additional physics….
Fitting……(Global vs. local)…..
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

16. Work it out …
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

17. Mass Parabolas and Stability
HW 16
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

18. Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

19. Mass Parabolas and Stability
Double  decay!
Both Sides!
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

20. Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

21. Mass Parabolas and Stability
Vertical spacing between both parabolas ?
Determine constants from atomic masses.
Odd-Odd
Even-Even
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

22. Mass Parabolas and Stability
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

23. Nuclear Spin
Neutrons and protons have s = ½ (ms = ± ½) so they are fermions and obey the Pauli-Exclusion Principle.
The Pauli-Exclusion Principle applies to neutrons and protons separately (distinguishable from each other) (Isospin).
Nucleus seen as single entity with intrinsic angular momentum .
Associated with each nuclear spin is a nuclear magnetic moment which produces magnetic interactions with its environment.
The suggestion that the angular momenta of nucleons tend to form pairs is supported by the fact that all nuclei with even Z and even N have nuclear spin =0.
Iron isotopes (even-Z), for even-N (even-A) nuclei =0.
Odd-A  contribution of odd neutron  half-integer spin.
Cobalt (odd-Z), for even-N  contribution of odd proton  half-integer spin.
Odd-N  two unpaired nucleons  large integer spin.
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

24. Nuclear Spin - Z A Spin Natural Abundance Half-life Decay 26 54 0.059
0.059
stable
... 55
3/2
2.7y EC 56
0.9172 57
1/2
0.021 58
0.0028 60
1.5My -
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).

25. Nuclear Spin Z A Spin Natural Abundance Half-life Decay 27 56 4 ...+ 57
7/2
271d EC 59
1.00
stable 60 5
5.272y -
Nuclear and Radiation Physics, BAU, Second Semester, (Saed Dababneh).