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Nuclear Physics at BAU nuclear.bau.jo/ This course nuclear.bau.jo/Reactors

501503747 Nuclear Reactors. Nuclear Physics at BAU http://nuclear.bau.edu.jo/ This course http://nuclear.bau.edu.jo/Reactors Prerequisites Nuclear and Radiation Physics 742 http://nuclear.bau.edu.jo/nuclear-radiation Advanced Statistical Mechanics 761. General subjects to be covered.

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Nuclear Physics at BAU nuclear.bau.jo/ This course nuclear.bau.jo/Reactors

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

  2. General subjects to be covered • 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. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  3. Grading Review Test 05% Mid-term Exam 20% Projects, quizzes and HWs 25% Final Exam 50% • 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 Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  4. Review Test Nuclear Reactors, BAU, 1st 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 5th. • Presentation: Will be scheduled later. • Other small projects will be announced in class. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  6. Nuclear Reaction Energetics (revisited) • Conservation Laws • Charge, Baryon number, total energy, linear momentum, angular momentum, parity, (isospin??)……. b pb  gs a pa X  +ve Q-value  exoergic reaction. -ve Q-value  endoergic reaction. pY Y Stationary X ?? +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 Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  7. Nuclear Reaction Energetics (revisited) HW 1 • 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. double valued !? solve for Q Q < 0 Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  8. Nuclear Reaction Energetics (revisited) HW 1(continued) • The double valued situation occurs between TTh and the upper limit Ta\. • Double-valued in a forward cone. Q < 0 Discuss the elasticand inelastic scatteringof neutronsusing these relations. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

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

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

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

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

  13. Nuclear Reaction Energetics (revisited) • 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 What about neutron induced reactions? Nuclear Reactors, BAU, 1st 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: • Inelastic scattering (n,n\). Q = -E* Inelastic gammas. Threshold? • Elastic scattering (n,n). Q = ?? (Potential and CN). Neutron moderation? • Radiative capture (n,). Q = ?? Capture gammas. • (n,), (n,p). Q = ?? Absorption Reactions. • (n,2n), (n,3n) Q = ?? Energetic neutrons on heavy water can easily eject the loosely bound neutron. • Fission. (n,f). • HW 2 Examples of such exo- and endo-thermic reactions with Q calculations. Non-elastic Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  15. Neutron Scattering (revisited) • 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. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

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

  17. Reaction Cross Section (Simple terms) A (Area of the beam!!) |v| X Position of a neutron 1 s before arriving at target Target with N atoms.cm-3 or NAX atoms. Monoenergetic neutrons of speed v (cm.s-1) and density n (cm-3) Volume = vA containing nvA neutrons that hit the “whole” target in 1 s. Beam Intensity InvA/A = nv (cm-2s-1) Number of neutrons interacting with target per second  I, A, X and N = t I N A X Nuclear Reactors, BAU, 1st 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 • tI neutrons interact with any single nucleus. Thus, • measures the probability for a neutron to hit a nucleus. Study examples in Lamarsh Total cross section Total number of nuclei in the target Effective cross-sectional area of the nucleus. Nuclear Reactors, BAU, 1st 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 cm3 per second (Collision Density) Ft= t I N = I t t= N t Study examples in Lamarsh Total cross section Volume of the target Macroscopic total cross section. Probability per unit path length. Attenuation not moderation ! Mean free path Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

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

  21. Reaction Cross Section (revisited) Look for b Detector for particle “b” d Ia “b” particles / s , cm2 “X“ target Nuclei / cm2 “a” particles / s Typical nucleus (R=6 fm): geometrical R2  1 b. Typical : <b to >106 b. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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