1. Nuclear Binding Energy
Btot(A,Z) = [ ZmH + Nmn - m(A,Z) ] c Bm
Bave(A,Z) = Btot(A,Z) / A HW 9 Krane 3.9
Atomic masses from: HW 10 Krane 3.12
Separation Energy
Neutron separation energy: (BE of last neutron)
Sn = [ m(A-1,Z) + mn – m(A,Z) ] c2
= Btot(A,Z) - Btot(A-1,Z)  HW 11 Show that
HW 12 Similarly, find Sp and S.
HW 13 Krane 3.13 HW 14 Krane 3.14
Magic
numbers
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

2. Nuclear Binding Energy
Magic
numbers
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

3. Nuclear Binding Energy
In general
X  Y + a
Sa(X) = (ma + mY –mX) c2
= BX –BY –Ba
The energy needed to remove a nucleon from a nucleus ~ 8 MeV  average binding energy per nucleon (Exceptions???).
Mass spectroscopy  B.
Nuclear reactions  S.
Nuclear reactions  Q-value
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

4. Nuclear Binding Energy
Surface effect
Coulomb effect
~200 MeV
 Fission
HWc 4
Think of a computer program to reproduce this graph.
Fusion 
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

5. Nuclear Binding Energy
HW 15
A typical research reactor has power on the order of 10 MW.
Estimate the number of 235U fission events that occur in the reactor per second.
b) Estimate the fuel-burning rate in g/s.
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

6. 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 and Radiation Physics, BAU, First Semester, (Saed Dababneh).

7. Nuclear Binding Energy
Lead isotopes Z = 82
For constant Z
Sn (even N) > Sn (odd N)
For constant N
Sp (even Z) > Sp (odd Z)
Remember HW 14 (Krane 3.14).
208Pb (doubly magic)  can then easily remove the “extra” neutron in 209Pb.
208Pb
Neutron Separation Energy Sn (MeV)
Neutron Number N
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

8. Nuclear Binding Energy
Extra Binding between pairs of “identical” nucleons in the same state (Pauli … !)  Stability (e.g. -particle, N=2, Z=2).
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.
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

9. Abundance Systematics
Odd N
Even N
Total
Odd Z
Even Z
HWc 1\
Compare:
even Z to odd Z.
even N to odd N.
even A to odd A.
even-even to even-odd to odd-even to odd-odd.
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

10. Neutron Excess Asymmetry Remember HWc 1. Odd A Even A Z = N
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

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

12. Abundance Systematics
Nuclear and Radiation Physics, BAU, First Semester, (Saed Dababneh).

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

14. Nuclear and Radiation Physics, BAU, First Semester, 2007-2008 (Saed Dababneh).

15. 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, First Semester, (Saed Dababneh).

16. 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, First Semester, (Saed Dababneh).

17. 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, First Semester, (Saed Dababneh).

18. 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, First Semester, (Saed Dababneh).

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

20. 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, First Semester, (Saed Dababneh).