Nuclear Reactor Theory

1. Nuclear Reactor Theory William D’haeseleer BNEN NRT William D’haeseleer BNEN – NRT – 2010-2011

2. Nuclear Reactor Theory • Review of Nuclear Physics • Interaction of Neutrons with Matter • Nuclear Fission • Neutron Chain-Reaction Systems • The Diffusion of Neutrons • Neutron Moderation without Absorption William D’haeseleer BNEN – NRT – 2010-2011

3. Nuclear Reactor Theory • Review of Nuclear Physics • Interaction of Neutrons with Matter • Nuclear Fission • Neutron Chain-Reaction Systems • The Diffusion of Neutrons • Neutron Moderation without Absorption William D’haeseleer BNEN – NRT – 2010-2011

4. Review of Nuclear Physics Chapter 1 = Brief summary of some important concepts William D’haeseleer BNEN – NRT – 2010-2011

5. Review of Nuclear Physics1. The Constituents of Nuclei - A nucleus consists of: Z protons N neutrons Z + N ≡ A nucleons Z ≡ atom number N ≡ neutron number A ≡ mass number - Our notation: - Nuclei with the same atom number, but ≠ neutron number are called ISOTOPES William D’haeseleer BNEN – NRT – 2010-2011

6. Review of Nuclear Physics1. The Constituents of Nuclei - - free neutron is unstable - <life time> of neutron in nuclear reactor ~ 10-3 s → the fact that a neutron is unstable, is irrelevant for our applications! anti neutrino William D’haeseleer BNEN – NRT – 2010-2011

7. Review of Nuclear Physics2. Particle wavelenghts - Particles have a dual character: particle character &wave character Energy Momentum - For neutrons, because William D’haeseleer BNEN – NRT – 2010-2011

8. Review of Nuclear Physics3. Nuclear Radii - Nucleus ~ liquid drop model  ± average density  volume ~ number of nucleons  - volume V of a spherical nucleus - in terms of the “classical electron radius” William D’haeseleer BNEN – NRT – 2010-2011

9. Review of Nuclear Physics4. Nuclear Mass Mostly expressed in terms of the a m u = atomic mass unit William D’haeseleer BNEN – NRT – 2010-2011

10. Review of Nuclear Physics5. Binding Energy - Difference in mass between Σ (constituents of nucleus)andNucleus ≡ mass defect Δ - Mass defect in energy units: Binding Energy B = c² Δ = the energy is necessary to “dismantle” the nucleus completely nuclear mass with addition of mass electron atom masses William D’haeseleer BNEN – NRT – 2010-2011

11. Review of Nuclear Physics5. Binding Energy In fact: volume term surface term Coulomb striving for pairing term repulsion William D’haeseleer BNEN – NRT – 2010-2011

12. Review of Nuclear Physics5. Binding Energy William D’haeseleer BNEN – NRT – 2010-2011

13. Review of Nuclear Physics5. Binding Energy Fission part Fusion part Similar to Lamarsh NRT, Figure 1.1 William D’haeseleer BNEN – NRT – 2010-2011

14. Review of Nuclear Physics5. Binding Energy fission reaction ! Special stable nuclei: those with magic numbers Z or N = 2, 6, 8, 14, 20, 28, 50, 82, 126 cfr shell model Magic nuclei absorb few or no neutrons, e.g., William D’haeseleer BNEN – NRT – 2010-2011

15. Review of Nuclear Physics6. Excited states in nuclei - all of the above concerned the ground state - Nuclei can also become “excited” → so-called excited states → energy levels See Fig 1.2 William D’haeseleer BNEN – NRT – 2010-2011

16. Review of Nuclear Physics6. Excited states in nuclei Increasing density of levels with energy Increasing density of levels with mass number … except For the magic nuclei ~behave more like light nuclei C-12 light U-235 heavy Al-28 intermediary William D’haeseleer BNEN – NRT – 2010-2011

17. Review of Nuclear Physics6. Excited states in nuclei - with atoms: it is unusual to have more than one e- in higher energy levels simultaneously (usually, it is one by one) - with nuclei: simultaneous excitations of a number of nucleons is the rule!  a nucleus can be excited in a level > “ionization” or “binding” energy of a single nucleon The binding energy of the least-bound nucleon in a nucleus is the so-called virtual energy William D’haeseleer BNEN – NRT – 2010-2011

18. Review of Nuclear Physics6. Excited states in nuclei For E > Evirt : “virtual energy levels” E < Evirt : “bound energy levels” For E > Evirt : nuclei ‘can’ decay through nucleon emission!! (not necessarily: energy is distributed over several neutrons; the ejection is dependent upon favorable in-nucleus collisions) William D’haeseleer BNEN – NRT – 2010-2011

19. Review of Nuclear Physics7. Radio-activity Spontaneous desintegration of unstable nuclei = “radio-active decay” λ = probability/s that a nucleus decays λdt = probability that a nucleus decays within dt N λ dt = probab. that one of the N nuclei will decay within dt = average number of nuclei that will decay within dt Hence: William D’haeseleer BNEN – NRT – 2010-2011

20. Review of Nuclear Physics7. Radio-activity Decay rate λ = disintegration constant ; e-λt = probability that a nucleus does not decay within (0, t) Hence = probability that a nucleus decays within t and t + dt William D’haeseleer BNEN – NRT – 2010-2011

21. Review of Nuclear Physics7. Radio-activity p(t) is a proper probabililty density  eventually, the nucleus will decay Average life time of a nucleus William D’haeseleer BNEN – NRT – 2010-2011

22. Review of Nuclear Physics7. Radio-activity - radio-active decay and production in radio-active chain A→B→C, production rate R(t) = activity of mother nucleus A → solution William D’haeseleer BNEN – NRT – 2010-2011

23. Review of Nuclear Physics8. Decay of excited states - In case of decay of excited states, customary to work with the level width - ‘Average life time’ of an excited level:  large width: short life time  small width: more stable William D’haeseleer BNEN – NRT – 2010-2011

24. Review of Nuclear Physics8. Decay of excited states - Decay of excited states occurs in several different ways → radiation width → neutron width → etc … William D’haeseleer BNEN – NRT – 2010-2011

25. Review of Nuclear Physics9. Nuclear Reactions - Usually of the form - Conservation laws (most important ones) * conservation of number of nucleous * conservation of charge * conservation of momentum and angular momentum * conservation of energy William D’haeseleer BNEN – NRT – 2010-2011

26. Review of Nuclear Physics9. Nuclear Reactions “Q value” of a reaction = change of kinetic energy of the reacting particles For reaction (*) above: Q > o exothermal; Q < o endothermal conservation of energy William D’haeseleer BNEN – NRT – 2010-2011