Nuclear Reactions Nomenclature and Conservation Laws Explained

1. Lesson 10 Nuclear Reactions

2. Nomenclature • Consider the reaction 4He + 14N  17O + 1H • Can write this as Projectile P + Target T Residual Nucleus R and Emitted Particle x • Or T(P,x)R 14N(4He,p)17O

3. Conservation Laws • Conservation of neutrons, protons and nucleons 59Co(p,n)? Protons 27 + 1 =0 + x Neutrons 32 +0=1 + y Product is 59Ni

4. Conservation Laws (cont.) • Conservation of energy Consider 12C(4He,2H)14N Q=(masses of reactants)-(masses of products) Q=M(12C)+M(4He)-M(2H)-M14N) Q=+ exothermic Q=- endothermic

5. Conservation Laws(cont.) • Conservation of momentum mv=(m+M)V TR=Ti*m/(m+M) • Suppose we want to observe a reaction where Q=-. -Q=T-TR=T*M/(M+m) T=-Q*(M+m)/M

6. Center of Mass System pi=pT ptot=0 velocity of cm =Vcm velocity of incident particle = v-Vcm velocity of target nucleus =Vcm m(v-Vcm)=MV m(v-Vcm)-MV=0 Vcm=mv/(m+M) T’=(1/2)m(v-Vcm)2+(1/2)MV2 T’=Ti*m/(m+M)

7. Center of Mass System

8. Center of Mass System catkin

9. Kinematics

10. Reaction Types and Mechanisms

11. Reaction Types and Mechanisms

12. Nuclear Reaction Cross Sections fraction of beam particles that react= fraction of A covered by nuclei a(area covered by nuclei)=n(atoms/cm3)*x(cm)* ((effective area of one nucleus, cm2)) fraction=a/A=nx -d=nx trans=initiale-nx initial-trans= initial(1-e-nx)

13. Factoids about  • Units of  are area (cm2). • Unit of area=10-24 cm2= 1 barn • Many reactions may occur, thus we divide  into partial cross sections for a given process, with no implication with respect to area. • Total cross section is sum of partial cross sections.

14. Differential cross sections

15. Charged Particles vs Neutrons I=particles/s In reactors, particles traveling in all directions Number of reactions/s=Number of target atoms x  x (particles/cm2/s)

16. What if the product is radioactive?

18. Neutron Cross Sections-General Considerations

20. Semi-classicalQM

21. The transmission coefficient • Sharp cutoff model (higher energy neutrons) • Low energy neutrons

22. 1/v

23. Charged Particle Cross Sections-General Considerations p=(2mT)1/2 = (2)1/2(-B)1/2 = (2)1/2(1-B/)1/2 reduced mass =A1A2/(A1+A2)

24. Semi-classicalQM

26. Barriers for charged particle induced reactions Vtot(R)=VC(R)+Vnucl(R)+Vcent(R)

28. Rutherford Scattering

29. Rutherford Scattering

32. Consider I0 particles/unit area incident on a plane normal to the beam. Flux of particles passing through a ring of width db between b and b+db is dI = (Flux/unit area)(area of ring) dI = I0 (2b db)

35. Elastic (Q=0) and inelastic(Q<0) scattering • To represent elastic and inelastic scattering, need to represent the nuclear potential as having a real part and an imaginary part. This is called the optical model

42. Direct Reactions • Direct reactions are reactions in which one of the participants in the initial two body interaction leaves the nucleus without interacting with another particle. • Classes of direct reactions include stripping and pickup reactions. • Examples include (d,p), (p,d), etc.

43. (d,p) reactions

44. (d,p) reactions