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1 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. Accelerator Physics, JU, First Semester, (Saed Dababneh).

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2 Reaction Cross Section(s) 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.. HW 14 Accelerator Physics, JU, First Semester, (Saed Dababneh).

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3 Reaction Cross Section(s) (Introduction) 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. Accelerator Physics, JU, First Semester, (Saed Dababneh).

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4 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. Accelerator Physics, JU, First Semester, (Saed Dababneh). Spectroscopic Factor.

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5 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. Q CN E a CM Accelerator Physics, JU, First Semester, (Saed Dababneh).

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6 Compound Nucleus Reactions Consider p + 63 Cu at E p CM = 20 MeV. Calculate E p CM + [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. Accelerator Physics, JU, First Semester, (Saed Dababneh).

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7 Random collisions nearly isotropic angular distribution. Direct reaction component strong angular dependence. See also Fig in Krane. Direct Reactions Accelerator Physics, JU, First Semester, (Saed Dababneh).

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