1. NE 301 - Introduction to Nuclear Science Spring 2012 Classroom Session 5: Isotopes and Decay Diagrams Nuclear Reactions Energy of nuclear reactions Neutron Cross Sections Activation Calculations Radioactive Decay and Growth

2. Reminder Load TurningPoint Reset slides Load List 2

3. Page 98-Shultis  -,  + produce three products: Cannot say energy of  Neutrinos by Fermi (1933) We only can say maximum energy of 

4. Binary Nuclear Reactions Binary = 2 reactants (many times 2 products too) Most important type of nuclear reaction Most elements produced by binary rxns. in stars Nomenclature: 4 Light nuclide usually projectile Heavy nuclide usually target Heavy Product Light Product

5. 5 For Binary Reactions: x +X  Y + y x is a projectile with KE (E x ). X is a target stationary nucleus E X =0 simplification

6. 6 A 5.5 MeV  particle is incident on Li causing 7 Li( ,n) 10 B. What is the KE of neutron scattered 30 o ?

7. 7 1. 0 MeV 2. 0.31 MeV 3. 1.31 MeV 4. 2.31 MeV 5. 3.31 MeV 6. 5.5 MeV

8. 7 Li(alpha,n) 10 B 8 FIRST BALANCE THE EQUATION!!! Endothermic Rxn Neutron Energy = 1.31MeV What would be the neutron energy if incident alpha particle is 1MeV instead? Can’t happen…

9. Solution exists only if Potential “  ” Factors Q<0 Heavy projectiles ( m Y -m x <0 ) Large scattering angles Cos  <0 Big enough E x can guarantee Physical meaning: Threshold Energy Argument of root >0

10. 10 Kinematic Threshold (only if Q<0) Arises from conservation of: Energy Linear momentum (Details are in the textbook) In most nuclear reactions (m i ’s>Q), the kinematic threshold simplifies to: ONLY FOR Q<0 i.e. endothermic rxns.

11. What is the kinematic threshold for: 7 Li( ,n) 10 B ? 11 1. 0.4 MeV 2. 1.4 MeV 3. 2.4 MeV 4. 3.4 MeV 5. 4.4 MeV

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13. What is the kinematic threshold for: 13 C(d,t) 12 C 13 1. -1.5 MeV 2. 0 MeV 3. 1.5 MeV 4. 3 MeV 5. 9.6 MeV Remember: Kinematic Threshold only for Endothermic Reactions

14. Balance. Then: (13.003355+2.014102-12-3.016049)*931.494 Q=1.31154 MeV 14 Remember: Kinematic Threshold only for Endothermic Reactions Exothermic = Kinematic Threshold is 0 MeV

15. 15 Coulomb Barrier Threshold (fig. 3.9) ONLY when the incident nuclide is charged All nuclides are positive Projectile needs energy to overcome electrostatic repulsion Engineering Equation. MeV units already worked out (don’t worry) NOT for incident NEUTRONS nor  ’s Binding Energy Coulombic Threshold

16. What is the coulomb barrier threshold for: 7 Li( ,n) 10 B ? 16 1. 1 MeV 2. 2 MeV 3. 3 MeV 4. 4 MeV 5. 5 MeV

17. Clicker Answer 17

18. What is the coulomb barrier threshold for: 14 N(n,  ) 11 B ? 18 1. 0 MeV 2. 1 MeV 3. 2 MeV 4. 3 MeV 5. 0.98 x Q MeV

19. 19 Overall Threshold Energy Neutral Incident particle=No Coulomb Barrier. Q>0 = No Kinetic Threshold Charged particles and Q<0 = both thresholds apply, and: Do NOT add – Use BIGGEST of the two

20. What would be the minimum KE of Products? – think about it! 20 Min. Kinetic Energy of the products is: Energy produced in the reaction Minimum required energy of the incident particle

21. What is the threshold for the 7 Li( ,n) 10 B nuclear reaction? 21 1. 0 MeV 2. 2.06 MeV 3. 4.4 MeV 4. 6.46 MeV Remember: Threshold is minimum energy the incident particle has to have

22. What is the threshold of 14 C(p,n) 14 N ? And Minimum KE of the Products ? 22 1. 3.1 MeV and 3.74 MeV 2. 2.1 MeV and 2.74 MeV 3. 3.1 MeV and 2.74 MeV 4. 2.1 MeV and 3.74 MeV 5. 0 MeV and 6 MeV

23. 14 C(p,n) 14 N 23

24. 24 Neutron Scattering First Type:  Scattering reactions  Elastic scattering (Q=0)  Inelastic scattering (Q<0)

25. 25 N Scattering Kinematics Solving for the scattering angle: Simplifies to: It is still a binary rxn. So eq. still applies, but

26. What is the energy of a 5MeV neutron after it is elastically scattered 30 o by a 10 B atom? 26 1. 1.9 MeV 2. 2.9 MeV 3. 3.9 MeV 4. 4.9 MeV 5. 5.9 MeV Hint: for elastic collisions only “+” matters

27. Notice it is an elastic collision: Q=0 27

28. Accelerator in Columbia (8.4 MeV d) 28 How many of these could happen?