1. Collective model Vibrational States Average shape Instantaneous shape
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

2. Collective model . = 1 dipole = 2 quadrupole = 3 octupole = 0 monopole
Symmetry
Instantaneous
coordinate
Spherical
harmonics
r0A1/3
Amplitude
= 1
dipole
= 2
quadrupole
= 3
octupole
= 0
monopole .
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

3. Collective model
= 0
monopole
R(t) = Ravr +00 Y00
= 1
dipole
Both monopole and dipole excitations require high energy.
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

4. Collective model
= 2
quadrupole
Quantization of quadrupole vibration is called a quadrupole phonon.
A phonon carries two units of angular momentum.
This mode is dominant. For most even-even nuclei, a low lying state with Jπ=2+ exists.
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

5. Collective model l = 4  = +4, +3, +2, +1, 0, -1, -2, -3, -4
Triplet
0+, 2+, 4+ -2 -1 1 2 -4 -3 +1 +2 +3 +4
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

6. Collective model
Two-phonon triplet at twice the energy of the single phonon state.
HW 24
Krane 5.10
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

7. Nuclear Reactions 14N(,p)17O X(a,b)Y First in 1919 by Rutherford:
4He + 14N  17O + 1H
14N(,p)17O
Incident particle may: change direction, lose energy, completely be absorbed by the target……
Target may: transmute, recoil……
b =   Capture reaction.
If B.E. permits  fission (comparable masses).
Different exit channels a + X  Y1 + b1
 Y2 + b2
 Y3 + b3 …….
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

8. Nuclear Reactions
Recoil nucleus Y could be unstable   or  emission.
One should think about:
Reaction dynamics and conservation laws i.e. conditions necessary for the reaction to be energetically possible.
Reaction mechanism and theories which explain the reaction.
Reaction cross section i.e. rate or probability.
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

9. Nuclear Reactions Conservation Laws
Charge, Baryon number, total energy, linear momentum, angular momentum, parity, (isospin??) ……. b pb  a pa X 
+ve Q-value  exoergic reaction.
-ve Q-value  endoergic reaction. pY Y
+ve Q-value  reaction possible if Ta  0.
-ve Q-value  reaction not possible if Ta  0. (Is Ta > |Q| sufficient?).
Conservation of momentum ……
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

10. Nuclear Reactions HW 25 double valued !? solve for Q
Conservation of momentum.
We usually do not detect Y.
Show that:
The threshold energy (for Ta): (the condition occurs for  = 0º).
+ve Q-value  reaction possible if Ta  0.
Coulomb barriers…….!!!
-ve Q-value  reaction possible if Ta > TTh.
HW 25
double valued !?
solve for Q
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

11. Nuclear Reactions HW 25 (continued)
The double valued situation occurs between TTh and the upper limit Ta\.
Double-valued in a forward cone.
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

12. Nuclear Reactions
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

13. Nuclear Reactions
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

14. Nuclear Reactions
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

15. Nuclear Reactions
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

16. Nuclear Reactions If the reaction reaches excited states of Y
58Ni(,p)61Cu
even less ….
less proton energy
Highest proton energy
See Figures 11.4 in Krane
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).

17. Nuclear Reactions HW 26 Neutron scattering
Inelastic  Q = -Eex (=-E*).
Elastic  Q = 0.
HW 26
Discuss the elastic and inelastic scattering of neutrons using the relations you derived in HW 25.
Nuclear and Radiation Physics, BAU, 1st Semester, (Saed Dababneh).