1. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 1 NEWS Lecture1: Chapter 0 is already on my Website

2. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 2 Chapter 1 Neutron Reactions March 2008

3. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 3 1.Review 2.Neutron Reactions 3.Nuclear Fission 4.Thermal Neutrons 5.Nuclear Chain Reaction 6.Neutron Diffusion 7.Critical Equation

4. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 4 2.8 Neutron Flux and Reaction Rate large number of neutronsgas   For large number of neutrons, it is physically convenient to consider them as a gas  description of movements and random motion based on molecular theory of gases.  Assymptions:  neutrons as a gas  move with a speed (all neutrons have the same speed)  mean free path  Time interval between two successive collisions for a given neutron is: Hence: number of collisions per second by neutron  For n neutrons per cm 3  total number of collisions/cm3 sec = number of collisions per neutron/sec X number of neutrons/cm 3 this similar to that found for neutron beam traveling in a given direction

5. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 5 2.8 Neutron Flux and Reaction Rate  Definition : neutron flux =  Hence, this formula is valid for an assembly of neutrons traveling in different and arbitrary directions which is the current case. Then, the reaction rate/cm 3 is: Reaction rate for a medium of volume V : Reality: neutrons in a reactor do not all have the same speed, hence it is necessary to generalize the definition of the neutron flux? How this can be done? SEE FIGURE 4.5

6. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 6 2.8 Neutron Flux and Reaction Rate  Alternative definition: in term of energies: number of neutrons with energies between  Then the flux is:  Another useful definition of the flux: 2.8 Neutron Flux and Reaction Rate

7. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 7 2.9 Energy dependence of Neutron Cross Sections Neutron cross sections  So far, Neutron cross sections depends on: nature of target nucleus + energy of interacting neutrons.  Let us focus now on the interacting neutrons…  It is convenient to classify neutrons that are involved in nuclear reactions according to the general behaviour of the various cross sections and devide the neutron energies into several regions to take into account these general trends.

8. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 8 2.9 Energy dependence of Neutron Cross Sections  There are 4 principal regions: 1.High-energy region neutron: energies between 10 Mev to 0.1 Mev  fast neutrons 2.Intermediate-energy region: energies between 0.1 Mev and 1000ev  intermediate neutrons. 3.Epithermal region: neutrons energies between 1000ev to 1 ev  epithermal neutrons. 4.Thermal region: neutrons energies between 1 ev and less  thermal neutrons or slow neutrons. What are the most probable reaction cross sections for each region??

9. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 9 2.9 Energy dependence of Neutron Cross Sections

10. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 10 2.9 Energy dependence of Neutron Cross Sections

11. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 11 2.9 Energy dependence of Neutron Cross Sections  The maxima are resonances in the capture cross section superimposed to background which is scattering cross section.  scattering cross section for energies between individual resonances is of order of barn, while capture cross section is of order of milibarn See Figure 4.7, page 98  Total background cross section between resonances is: double comparing to that of fast neutron! Continuation of Epithermal region…..

12. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 12 2.9 Energy dependence of Neutron Cross Sections  Energy dependence of in resonance region is given by Breit-Wigner formula: called single-level formula, since it describes resonances well separated and not overlapping probability for the corresponding reaction to take place measure the probability for the corresponding reaction to take place.

13. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 13 2.9 Energy dependence of Neutron Cross Sections is decay constant  Since the two processes are the only modes of decay of the compound nucleus in this energy region that need to be considered, then: This means: probability for (n,n) reaction is :

14. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 14 2.9 Energy dependence of Neutron Cross Sections

15. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 15 2.9 Energy dependence of Neutron Cross Sections

16. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 16 2.9 Energy dependence of Neutron Cross Sections  For light nuclei resonances are very broad and widely separated from each other so that is satisfied Thermal Neutrons:

17. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 17 2.9 Energy dependence of Neutron Cross Sections  Schematic representation of the variation of neutron cross section with energy for typical nucleus is given in Figure 4.7, page 98.  Thermal neutron absorption cross section sections for some representative nuclides are listed in Table 4.1.

18. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 18 2.10 Fission Cross Section  Some of the very heavy nuclei undergo fission as a result of neutron absorption.  Natural fissionable nuclides are: U 235 (fissionable by thermal and fast neutrons), U 238 (fast neutrons more than 1 Mev) and Th 232 (fast neutrons more than 1 Mev).

19. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 19 2.10 Fission Cross Section U 233 is produced artificially by neutron capture of Th 232 Pu 239 is produced artificially by neutron capture of U 238 U 233 and Pu 239 are fissionable by thermal and fast neutrons as well. See Figures 4.11 to 4.13, page 104

20. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 20 2.10 Fission Cross Section Nonfissionable materials fissionable materialsdifferent  BECAREFUL : Nonfissionable materials: absorption = capture fissionable materials: absorption different from capture, hence: Capture refers to radiative capture only. See Table 4.2: Thermal neutron cross section for some reactor fuel materials Example 4.8

21. A. Dokhane, PHYS487, KSU, 2008 Chapter1- Neutron Reactions 21 Homework Problems: 1, 3, 4, 6, 8, 11 of Chapter 4 in Text Book, Page 107 To be submitted next week.