1 / 26

Nuclear Reaction Energetics

Nuclear Reaction Energetics. Conservation Laws Charge, Baryon number , total energy, linear momentum, angular momentum, parity, ( isospin ??) ……. b. p b. . gs. a. p a. X. . +ve Q -value  exoergic reaction. -ve Q -value  endoergic reaction. p Y. Y. Stationary X ??.

adele
Download Presentation

Nuclear Reaction Energetics

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. Nuclear Reaction Energetics • 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 …… Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  2. Nuclear Reaction Energetics HW b1 • 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 Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  3. Nuclear Reaction Energetics HW b1(continued) • The double valued situation occurs between TTh and the upper limit Ta\. • Double-valued in a forward cone. Q < 0 Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  4. Nuclear Reaction Energetics HW b1(continued) • Discuss the elasticand inelastic scatteringof neutronsusing these relations. • If the reaction reaches excited states of Y Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  5. Nuclear Reaction Energetics Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  6. Nuclear Reaction Energetics Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  7. Nuclear Reaction Energetics Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  8. Nuclear Reaction Energetics Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  9. Neutron Interactions • Chadwick’s discovery. • Neutrons interact with nuclei, not with atoms. (Exceptions). • Recall: • 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 b2Examples of such exo- and endo-thermic reactions with Q calculations. Non-elastic Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  10. Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  11. n-TOF CERN Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  12. Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  13. Reaction Cross Section • 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? Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  14. Neutron Induced Reactions 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 Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  15. Neutron Induced Reactions Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  16. Nuclear Fission 1/v Fast neutrons should be moderated. 235U thermal cross sections fission  584 b. scattering  9 b. radiative capture  97 b. Fission Barriers Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  17. Resonance Reactions 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 Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  18. Resonance Reactions 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) Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  19. Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  20. Resonance Reactions Damped Oscillator Oscillator strength Damping factor eigenfrequency Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  21. Resonance Reactions Breit-Wigner formula • All quantities in CM system • Only for isolated resonances. Reaction Elastic scattering Usually a>> b. HW b3When does R take its maximum value? Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  22. Neutron Resonance Reactions Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  23. Neutron Activation Analysis (Z,A) + n (Z, A+1) -  (-delayed -ray) (Z+1, A+1) Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  24. Neutron Moderation Show that, after elastic scattering the ratio between the final neutron energy E\ and its initial energy E is given by: For a head-on collision: After ns-wave collisions: where the average change in lethargy is HW b4 1H ? Collision Parameter Reference Average decrease in ln(E) after one collision. Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  25. Neutron Moderation • Reproduce the plot. • Discuss the effect of the thermal motion of the moderator atoms. On 12C. Most probable and average energies? Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

  26. Neutron Moderation • How many collisions are needed to thermalize a 2 MeV neutron if the moderator was: • 1H 2H 4He graphite 238U ? • What is special about 1H? • Why we considered elastic scattering? • When does inelastic scattering become important? Radiation Detection and Measurement, JU, 1st Semester, 2008-2009 Saed Dababneh

More Related