1. Nuclear Reactors, BAU, First Semester, 2007-2008 (Saed Dababneh). 1 Nuclear Physics at BAU http://nuclear.bau.edu.jo/ This course http://nuclear.bau.edu.jo/ReactorsPrerequisites Nuclear and Radiation Physics 742 http://nuclear.bau.edu.jo/nuclear-radiation Advanced Statistical Mechanics 761 501503747 Nuclear Reactors

2. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 2 Review of relevant studied material in nuclear physics. Concepts in neutron physics. The relevant physics related to nuclear technology:  Fission chain reaction.  Neutron diffusion and moderation.  Heat removal from nuclear reactors.  Isotope separation.  … Components of nuclear reactors. Nuclear reactor fuels and fuel cycles. Nuclear reactor theory. Basic concepts of radiation protection and nuclear safety, shielding and waste disposal. Issues and prospects of nuclear power today and in the future. General subjects to be covered

3. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 3 Grading Review Test05% Mid-term Exam20% Projects, quizzes and HWs25% Final Exam50% Homeworks are due after one week unless otherwise announced. Remarks or questions marked in red without being announced as homeworks should be also seriously considered! Some tasks can (or should) be sent by email: saed@dababneh.com

4. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 4 Review Test Review relevant material in 742. Read Lamarsh Chs 1, 2 and 3. Will do the test afterwards.

5. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 5 Projects  Consider nuclear fuel cycles with emphasis on front ends. Work as a team. Divide and organize the job among you. Try to explore local applicability. Due date (for written version) : December 5 th. Presentation: Will be scheduled later.  Other small projects will be announced in class.

6. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 6 Nuclear Reaction Energetics (revisited) Conservation Laws Charge, Baryon number, total energy, linear momentum, angular momentum, parity, (isospin??) …….   a papa X pYpY pbpb Y b +ve Q-value  exoergic reaction. -ve Q-value  endoergic reaction. +ve Q-value  reaction possible if T a  0. -ve Q-value  reaction not possible if T a  0. (Is T a > |Q| sufficient?). Conservation of momentum ……

7. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 7 Conservation of momentum. We usually do not detect Y. Show that: The threshold energy (for T a ): (the condition occurs for  = 0º). +ve Q-value  reaction possible if T a  0. Coulomb barriers…….!!! -ve Q-value  reaction possible if T a > T Th. HW 1 Nuclear Reaction Energetics (revisited)

8. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 8 Nuclear Reaction Energetics (revisited) The double valued situation occurs between T Th and the upper limit T a \. Double-valued in a forward cone. HW 1 (continued) elastic inelastic scattering neutrons Discuss the elastic and inelastic scattering of neutrons using these relations.

9. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 9 Nuclear Reaction Energetics (revisited)

10. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 10 Nuclear Reaction Energetics (revisited) What about neutron induced reactions?

11. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 11 Nuclear Reaction Energetics (revisited) What about neutron induced reactions?

12. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 12 Nuclear Reaction Energetics (revisited) What about neutron induced reactions?

13. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 13 Nuclear Reaction Energetics (revisited) If the reaction reaches excited states of Y 58 Ni( ,p) 61 Cu Highest proton energy less proton energy even less …. See Figures 11.4 in Krane What about neutron induced reactions?

14. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 14 Neutron Interactions (revisited) Chadwick’s discovery. Neutrons interact with nuclei, not with atoms. (Exceptions). Recall from Nuclear Physics 742: o Inelastic scattering ( n,n \ ). Q = -E*  Inelastic gammas. Threshold? o Elastic scattering ( n,n ). Q = ?? (Potential and CN). Neutron moderation? o Radiative capture ( n,  ). Q = ??  Capture gammas. o ( n,  ), ( n,p ). Q = ?? Absorption Reactions. o ( n,2n ), ( n,3n ) Q = ?? Energetic neutrons on heavy water can easily eject the loosely bound neutron. o Fission. (n,f). HW 2 HW 2 Examples of such exo- and endo-thermic reactions with Q calculations.

15. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 15 Elastic or inelastic. Analogous to diffraction. Alternating maxima and minima. First maximum at Minimum not at zero (sharp edge of the nucleus??) Clear for neutrons. Protons? High energy, large angles. Why? Inelastic  Excited states, energy, X-section and spin-parity. Neutron Scattering (revisited)

16. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 16 Probability. Projectile a will more probably hit target X if area is larger. Classically:  =  (R a + R X ) 2. Classical  = ??? (in b) n + 1 H, n + 238 U, 238 U + 238 U Quantum mechanically:  =   2. Coulomb and centrifugal barriers  energy dependence of . What about neutrons? Nature of force: Strong: 15 N(p,  ) 12 C  ~ 0.5 b at E p = 2 MeV. Electromagnetic: 3 He( ,  ) 7 Be  ~ 10 -6 b at E  = 2 MeV. Weak: p(p,e + )D  ~ 10 -20 b at E p = 2 MeV. Experimental challenges to measure low X-sections.. Reaction Cross Section (revisited)

17. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 17 Reaction Cross Section (Simple terms) X A (Area of the beam!!) Monoenergetic neutrons of speed v (cm.s -1 ) and density n (cm -3 ) Target with N atoms.cm -3 or NAX atoms. Position of a neutron 1 s before arriving at target |v| Volume = vA containing nvA neutrons that hit the “whole” target in 1 s. Beam Intensity I  nvA/A = nv (cm -2 s -1 ) Number of neutrons interacting with target per second  I, A, X and N =  t I N A X

18. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 18 Reaction Cross Section (Simple terms) Number of neutrons interacting with target per second =  t I N A X Number of interactions with a single nucleus per second =  t I Interpretation and units of . nvA = IA neutrons strike the target per second, of these  t I neutrons interact with any single nucleus. Thus, measures the probability for a neutron to hit a nucleus. Total cross section Total number of nuclei in the target Effective cross-sectional area of the nucleus. Study examples in Lamarsh

19. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 19 Reaction Cross Section (Simple terms) Number of neutrons interacting with target per second =  t I N A X Number of interactions per cm 3 per second (Collision Density) F t =  t I N = I  t  t = N  t Total cross section Volume of the target Macroscopic total cross section. Probability per unit path length. Mean free path Study examples in Lamarsh

20. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 20 Reaction Cross Section (Simple terms) Homogeneous Mixture Molecule x m y n N x =mN, N y =nN given that events at x and y are independent. Study examples in Lamarsh

21. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 21 Reaction Cross Section (revisited) dd ,, IaIa Detector for particle “b” “X“ target Nuclei / cm 2 “a” particles / s “b” particles / s cm 2 Typical nucleus (R=6 fm): geometrical  R 2  1 b. Typical  : 10 6 b.

22. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 22 Reaction Cross Section (revisited) Many different quantities are called “cross section”. Krane Table 11.1 Angular distribution “Differential” cross section  ( ,  ) or  (  ) or “cross section” …!! Units … ! Doubly differential Energy state in “Y”  t for all “b” particles.

23. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 23

24. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 24n-TOFCERN

25. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 25

26. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 26 1/ v 235 U thermal cross sections  fission  584 b.  scattering  9 b.  radiative capture  97 b. Fast neutrons should be moderated. Fission Barriers Different Features (revisited)

27. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 27 Neutron Induced Reactions (revisited) X ( n,b ) Y n(En)n(En) b(Q+En)b(Q+En) For thermal neutrons Q >> E n  b ( Q )  constant Probability to penetrate the potential barrier P o ( E thermal ) = 1 P > o ( E thermal ) = 0 Non-resonant

28. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 28 Neutron Induced Reactions (revisited)

29. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 29 HW 3  Statistical Factor (revisited)

30. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 30 Resonance Reactions (revisited) Entrance Channel a + X Exit Channel b + Y Compound Nucleus C* Excited State ExEx JJ a + X  Y + bQ > 0 b + Y  X + aQ < 0 Inverse Reaction QM Statistical Factor (  ) Identical particles Nature of force(s). Time-reversal invariance. HW 4

31. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 31 Projectile Target Q-value Projectile Q-value Target Direct Capture (all energies) Resonant Capture (selected energies with large X-section) E  = E + Q - E ex Q + E R = E r Resonance Reactions (revisited)

32. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 32

33. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 33 Resonance Reactions (revisited) Damped Oscillator eigenfrequency Damping factor Oscillator strength

34. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 34 Resonance Reactions (revisited) Breit-Wigner formula All quantities in CM system Only for isolated resonances. Reaction Elastic scattering HW 5 HW 5 When does  R take its maximum value? Usually  a >>  b.

35. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 35 Resonance Reactions (revisited) J a + J X + l = J (-1) l  (J a )  (J X ) =  (J) (-1) l =  (J) Natural parity. Exit Channel b + Y Compound Nucleus C* Excited State ExEx JJ Entrance Channel a + X

36. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 36 Resonance Reactions (revisited) Cross section ECEC    a     Energy What is the “Resonance Strength” …? What is its significance? In what units is it measured? Charged particle radiative capture ( a,  ) (What about neutrons?)

37. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 37 Neutron Resonance Reactions (revisited)

38. Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 38 Neutron Activation Analysis (revisited) ( Z,A ) + n  ( Z, A+1 ) -- ( Z+1, A+1 )  (  -delayed  -ray) http://ie.lbl.gov/naa http://ie.lbl.gov/naa ! Project 1