# Lesson 10

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Lesson 10. Nuclear Reactions. Nomenclature. Consider the reaction 4 He + 14 N  17 O + 1 H Can write this as Projectile P + Target T Residual Nucleus R and Emitted Particle x Or T(P,x)R 14 N( 4 He,p) 17 O. Conservation Laws. Conservation of neutrons, protons and nucleons
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Lesson 10Nuclear ReactionsNomenclature
• 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)17OConservation Laws
• Conservation of neutrons, protons and nucleons
• 59Co(p,n)?Protons 27 + 1 =0 + xNeutrons 32 +0=1 + yProduct is 59NiConservation Laws (cont.)
• Conservation of energy
• Consider 12C(4He,2H)14NQ=(masses of reactants)-(masses of products)Q=M(12C)+M(4He)-M(2H)-M14N)Q=+ exothermicQ=- endothermicConservation Laws(cont.)
• Conservation of momentum
• mv=(m+M)VTR=Ti*m/(m+M)
• Suppose we want to observe a reaction where Q=-.
• -Q=T-TR=T*M/(M+m)T=-Q*(M+m)/MCenter of Mass Systempi=pTptot=0velocity of cm =Vcmvelocity of incident particle = v-Vcmvelocity of target nucleus =Vcmm(v-Vcm)=MVm(v-Vcm)-MV=0Vcm=mv/(m+M)T’=(1/2)m(v-Vcm)2+(1/2)MV2T’=Ti*m/(m+M)Center of Mass SystemCenter of Mass SystemcatkinKinematicsReaction Types and MechanismsReaction Types and MechanismsNuclear Reaction Cross Sectionsfraction of beam particles that react=fraction of A covered by nucleia(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 sectionsCharged Particles vs NeutronsI=particles/sIn reactors, particles traveling in all directionsNumber of reactions/s=Number of target atomsx  x (particles/cm2/s)What if the product is radioactive?Neutron Cross Sections-General ConsiderationsSemi-classicalQMThe transmission coefficient
• Sharp cutoff model (higher energy neutrons)
• Low energy neutrons
• 1/vCharged Particle Cross Sections-General Considerationsp=(2mT)1/2 = (2)1/2(-B)1/2 = (2)1/2(1-B/)1/2reduced mass =A1A2/(A1+A2)Semi-classicalQMBarriers for charged particle induced reactionsVtot(R)=VC(R)+Vnucl(R)+Vcent(R)Rutherford ScatteringRutherford ScatteringConsider I0 particles/unit area incident on a plane normal to the beam.Flux of particles passing through a ring of width dbbetween b and b+db isdI = (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 modelDirect 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
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