Lesson 10 Nuclear Reactions

Projectile P + Target T Residual Nucleus R and Emitted Particle x 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

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

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

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

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)

Center of Mass System

Center of Mass System catkin

Kinematics

Reaction Types and Mechanisms

Reaction Types and Mechanisms

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)

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.

Differential cross sections

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)

What if the product is radioactive?

Neutron Cross Sections-General Considerations

Semi-classicalQM

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

1/v

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)

Semi-classicalQM

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

Rutherford Scattering

Rutherford Scattering

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)

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

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.

(d,p) reactions

(d,p) reactions