1 / 39

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

afram
Download Presentation

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

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 • http://nuclear.bau.edu.jo/Statistical Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  2. 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, First Semester, 2008-2009 (Saed Dababneh).

  3. Review Test Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  4. Projects • Radiation Protection and Shielding (Due December 6th). • Nuclear fuel cycles with emphasis on front ends (Due November 29th). • Work as a team. Divide and organize the job among you. • Try to explore local applicability. • Presentation: Will be scheduled later. • Other small projects will be announced in class. Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  5. 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, First Semester, 2008-2009 (Saed Dababneh).

  6. 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…….!!! • Neutrons vs. charged particles. • -ve Q-value  reaction possible if Ta> TTh. double valued !? solve for Q Q < 0 Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  7. 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 Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  8. Nuclear Reaction Energetics (revisited) HW 1(continued) • Discuss thoroughly the 7Li(p,n) reaction. • During the discussion emphasize on the case when the incident proton beam is 30 keV above the threshold. • Use your computing skills. • Discuss the elasticand inelastic scatteringof neutronsusing these relations. Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  9. Nuclear Reaction Energetics (revisited) Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  10. Nuclear Reaction Energetics (revisited) What about neutron induced reactions? Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  11. Nuclear Reaction Energetics (revisited) What about neutron induced reactions? Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  12. Nuclear Reaction Energetics (revisited) Nuclear Reactors, BAU, First Semester, 2008-2009 (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 Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  14. Nuclear Reaction Energetics (revisited) Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  15. 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, First Semester, 2008-2009 (Saed Dababneh).

  16. 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, First Semester, 2008-2009 (Saed Dababneh).

  17. 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, First Semester, 2008-2009 (Saed Dababneh).

  18. Reaction Cross Section (Simple terms) A (Area of what??!!) |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, First Semester, 2008-2009 (Saed Dababneh).

  19. 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 (per unit area of target). Study examples in Lamarsh Total cross section Total number of nuclei in the target Effective cross-sectional area of the nucleus. Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  20. 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, First Semester, 2008-2009 (Saed Dababneh).

  21. 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, First Semester, 2008-2009 (Saed Dababneh).

  22. 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, First Semester, 2008-2009 (Saed Dababneh).

  23. 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. Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  24. Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  25. n-TOF CERN Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  26. Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  27. 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, First Semester, 2008-2009 (Saed Dababneh).

  28. 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, First Semester, 2008-2009 (Saed Dababneh).

  29. Neutron Induced Reactions (revisited) Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  30. Statistical Factor (revisited) HW 3  Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  31. 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, First Semester, 2008-2009 (Saed Dababneh).

  32. 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, First Semester, 2008-2009 (Saed Dababneh).

  33. Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  34. Resonance Reactions (revisited) Damped Oscillator Oscillator strength Damping factor eigenfrequency Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  35. 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, First Semester, 2008-2009 (Saed Dababneh).

  36. 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, First Semester, 2008-2009 (Saed Dababneh).

  37. 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, First Semester, 2008-2009 (Saed Dababneh).

  38. Neutron Resonance Reactions (revisited) Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

  39. Neutron Activation Analysis (revisited) (Z,A) + n (Z, A+1) -  (-delayed -ray) (Z+1, A+1) Project 1 NAA and U Nuclear Reactors, BAU, First Semester, 2008-2009 (Saed Dababneh).

More Related