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Nuclear Reactions

Nuclear Reactions. Categorization of Nuclear Reactions According to: bombarding particle, bombarding energy, target, reaction product, reaction mechanism. Bombarding particle: Charged particle reactions. [ (p,n) (p, ) (,) heavy ion reactions ]. Neutron reactions. [ (n,) (n,p) ….. ].

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Nuclear Reactions

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  1. Nuclear Reactions • Categorization of Nuclear Reactions • According to: bombarding particle, bombarding energy, target, reaction product, reaction mechanism. • Bombarding particle: • Charged particle reactions. [ (p,n) (p,) (,) heavy ion reactions ]. • Neutron reactions. [ (n,) (n,p) ….. ]. • Photonuclear reactions. [ (,n) (,p) … ]. • Electron induced reactions…………. • Bombarding energy: • Thermal. • Epithermal. • Slow. • Fast. • Low energy charged particles. • High energy charged particles. ? Neutrons. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  2. Nuclear Reactions • Targets: • Light nuclei (A < 40). • Medium weight nuclei (40 < A < 150). • Heavy nuclei (A > 150). • Reaction products: • Scattering. Elastic 14N(p,p)14N Inelastic 14N(p,p/)14N* • Radiative capture. • Fission. • Spallation. • ….. • Reaction mechanism: • Direct reactions. • Compound nucleus reactions. • More in what follows …. • What is a transfer reaction….????? Pickup Resonant Stripping Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  3. Reaction Cross Section(s) (Introduction) • Probability. • Projectile a will more probably hit target X if area is larger. • Classically:  = (Ra + RX)2. • Classical  = ??? (in b)1H + 1H, 1H + 238U, 238U + 238U • Quantum mechanically:  =  2. • Coulomb and centrifugal barriers  energy dependence of . • Nature of force: • Strong: 15N(p,)12C  = 0.5 b at Ep = 2 MeV. • Electromagnetic: 3He(,)7Be  = 10-6 b at E = 2 MeV. • Weak: p(p,e+)D  = 10-20 b at Ep = 2 MeV. • Experimental challenges to measure low X-sections.. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  4. Reaction Cross Section(s) (Introduction) Detector for particle “b” d Ia “b” particles / s , cm2 “X“ target Nuclei / cm2 “a” particles / s Typical nucleus (R=6 fm): geometrical R2  1 b. Typical : <b to >106 b. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  5. Reaction Cross Section(s) (Introduction) Many different quantities are called “cross section”. Krane Table 11.1 Angular distribution Units … ! “Differential” cross section (,) or ( ) or “cross section” …!! Doubly differential t for all “b” particles. Energy state in “Y” Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  6. Coulomb Scattering • Elastic or inelastic. • Elastic  Rutherford scattering. • At any distance: V = 0 Ta = ½mvo2 l = mvob vmin vo rmin b d Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh). No dependence on 

  7. Coulomb Scattering Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  8. Coulomb Scattering b < b >  dbd n target nuclei / cm3 x target thickness (thin). nx  target nuclei / cm2 HW 27 Show that and hence b Rutherford cross section Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  9. Coulomb Scattering Study Fig. 11.10 (a,b,c,d) in Krane See also Fig. 11.11 in Krane. HW 28 Show that the fraction of incident alpha particles scattered at backward angles from a 2 m gold foil is 7.48x10-5. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  10. Coulomb Scattering • Elastic  Rutherford scattering. • Inelastic Coulomb excitation. See the corresponding alpha spectrum of Fig. 11.12 in Krane. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  11. Nuclear Scattering • Elastic or inelastic. • Analogous to diffraction. • Alternating maxima and minima. • First maximum at • Minimum not at zero (sharp edge of the nucleus??) • Clear for neutrons. • Protons? High energy, large angles. Why? • Inelastic  Excited states, energy, X-section and spin-parity. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  12. Compound Nucleus Reactions Direct • Time. • Energy. CN decays • Two-step reaction. • CN “forgets” how it was formed. • Decay of CN depends on statistical factors that are functions of Ex, J. • Low energy projectile, medium or heavy target. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  13. Compound Nucleus Reactions a + X  C* Y1 + b1  Y2 + b2  Y3 + b3 ….. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  14. Compound Nucleus Reactions • Considerp + 63Cu at Ep = 20 MeV. • Calculate Ep + [m(63Cu) + m(p) – m(64Zn)]c2. • Divide by 64  available energy per nucleon << 8 MeV. • Multiple collisions  “long” time  statistical distribution of energy  small chance for a nucleon to get enough energy Evaporation. • Higher incident energy  more particles “evaporate”. See also Fig. 11.21 in Krane. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  15. Compound Nucleus Reactions • Random collisions  nearly isotropic angular distribution. • Direct reaction component  strong angular dependence. See also Fig. 11.20 in Krane. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  16. Direct Reactions • Peripheral collision with surface nucleon. • 1 MeV incident nucleon   ??  more likely to interact with the nucleus  CN reaction. • 20 MeV incident nucleon   ??  peripheral collision  Direct reaction. • CN and Direct (D) processes can happen at the same incident particle energy. Distinguished by: • D (10-22 s) CN (10-18-10-16 s). [Consider a 20 MeV deuteron on A=50 target nucleus]. • Angular distribution. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

  17. Direct Reactions • (d,n) stripping (transfer) reactions can go through both processes. • (d,p) stripping (transfer) reactions prefer D rather than CN; protons do not easily evaporate (Coulomb). [(p,d) is a pickup reaction]. • What about (,n) transfer reactions? HW 29 Show that for a (d,p) reaction taking place on the surface of a 90Zr nucleus, and with 5 MeV deuterons, the angular momentum transfer can be approximated by l = 8sin(/2), where  is the angle the outgoing proton makes with the incident deuteron direction. (Derive a general formula first). J(90Zrgs) = 0+ J(91Zr) = l ± ½, = (-1)l Optical model, DWBA, Shell model, Spectroscopic Factor. Nuclear and Radiation Physics, BAU, 1st Semester, 2006-2007 (Saed Dababneh).

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