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

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

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 4 Reaction Cross Section(s) (Introduction) dd ,, IaIa Detector for particle “b” “X“ target Nuclei / cm 2 “a” particles / s “b” particles / s cm 2 Typical nucleus (R=6 fm): geometrical  R 2  1 b. Typical  : 10 6 b.

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

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 6 Coulomb Scattering b d r min vovo v min Elastic or inelastic. Elastic  Rutherford scattering. At any distance: V = 0 T a = ½mv o 2 l = mv o b No dependence on 

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

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 8 Coulomb Scattering n  target nuclei / cm 3 x  target thickness (thin). nx  target nuclei / cm 2 b    db  d  b HW 27 Show that and hence Rutherford cross section

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

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

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

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

Nuclear and Radiation Physics, BAU, 1 st Semester, (Saed Dababneh). 14 Compound Nucleus Reactions Consider p + 63 Cu at E p = 20 MeV. Calculate E p + [m( 63 Cu) + m(p) – m( 64 Zn)]c 2. Divide by 64  available energy per nucleon << 8 MeV. Evaporation 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 in Krane.

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

Nuclear and Radiation Physics, BAU, 1 st Semester, (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 ( s) CN ( s). [Consider a 20 MeV deuteron on A=50 target nucleus].  Angular distribution.

Nuclear and Radiation Physics, BAU, 1 st Semester, (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 HW 29 Show that for a (d,p) reaction taking place on the surface of a 90 Zr 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). l 0123  0º14.4º29º44º J  ( 90 Zr gs ) = 0 + J ( 91 Zr) = l ± ½,  = (-1) l Optical model, DWBA, Shell model, Spectroscopic Factor.