1. Nuclear Binding Energy
Is the nucleon bounded equally to every
other nucleon?
C ≡ this presumed binding energy.
Btot = C(A-1)  A  ½
Bave = ½ C(A-1) Linear ??!!! Directly proportional ??!!! Clearly wrong … !  wrong assumption
 finite range of strong force,
and force saturation.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

2. Nuclear Binding Energy
Pairing Energy.
Extra Binding between pairs of “identical” nucleons in the same state (Pauli … !)
Sn (A, Z, even N) – Sn (A-1, Z, N-1)
This is the neutron pairing energy.
even-even more stable than even-odd or odd-even and these are more tightly bound than odd-odd nuclei.
Odd N
Even N
Total
Odd Z
Even Z
HW 1\
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

3. Nuclear Physics, JU, Second Semester, 2010-2011
Neutron Excess
Remember HW 1.
Asymmetry
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

4. Nuclear Binding Energy
For constant Z
Sn (even N) > Sn (odd N)
For constant N
Sp (even Z) > Sp (odd Z)
Remember (Krane 3.14) in HW 6.
208Pb (doubly magic)  can then easily remove the “extra” neutron in 209Pb.
Nuclear magic numbers: 2, 8, 20, 28, 50, 82,126, …(for Z or N).
Lead isotopes Z = 82
208Pb
Neutron Separation Energy Sn (MeV)
Neutron Number N
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

5. Abundance Systematics
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

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

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

8. 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 Physics, JU, Second Semester,
(Saed Dababneh).

9. 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 Physics, JU, Second Semester,
(Saed Dababneh).

10. 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.
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

11. 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 5 … ?!
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

12. The Semi-empirical Mass Formula
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

13. The Semi-empirical Mass Formula
Surface effect
Coulomb effect
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

14. 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 Physics, JU, Second Semester,
(Saed Dababneh).

15. 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 Physics, JU, Second Semester,
(Saed Dababneh).

16. 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 HW 1\ ….?!
Bp expected to decrease with A; effect of unpaired nucleon decrease with total number of nucleons. But empirical evidence show that:
  A-¾ .
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).

17. 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 Physics, JU, Second Semester,
(Saed Dababneh).

18. 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 Physics, JU, Second Semester,
(Saed Dababneh).

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

20. Nuclear Physics, JU, Second Semester, 2010-2011
Work it out …
Nuclear Physics, JU, Second Semester,
(Saed Dababneh).