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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 1 1/ v 235 U thermal cross sections fission 584 b. scattering 9 b. radiative capture 97 b. Fast neutrons should be moderated. Fission Barriers Neutron Cross Section (Different Features)

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 2 Neutron Induced Reactions X ( n,b ) Y n ( E n ) b ( Q + E n ) For thermal neutrons Q >> E n b ( Q ) constant Probability to penetrate the potential barrier P o ( E thermal ) = 1 P > o ( E thermal ) = 0 Non-resonant

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 3 Neutron Induced Reactions

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 4 HW 3 Statistical Factor (revisited) Generalization

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 5 Resonance Reactions (revisited) Entrance Channel a + X Exit Channel b + Y Compound Nucleus C* Excited State ExEx J a + X Y + bQ > 0 b + Y X + aQ < 0 Inverse Reaction QM Statistical Factor ( ) Identical particles Nature of force(s). Time-reversal invariance. HW 4 More Generalization

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 6 Projectile Target Q-value Projectile Q-value Target Direct Capture (all energies) Resonant Capture (selected energies with large X-section) E = E + Q - E ex Q + E R = E r Resonance Reactions (revisited)

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 7

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8 Resonance Reactions (revisited) Damped Oscillator eigenfrequency Damping factor Oscillator strength

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 9 Resonance Reactions (revisited) Breit-Wigner formula All quantities in CM system Only for isolated resonances. Reaction Elastic scattering HW 5 HW 5 When does R take its maximum value? Usually a >> b.

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 10 Resonance Reactions J a + J X + l = J (-1) l (J a ) (J X ) = (J) (-1) l = (J) Natural parity. Exit Channel b + Y Compound Nucleus C* Excited State ExEx J Entrance Channel a + X

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 11 Resonance Reactions (revisited) Cross section ECEC a Energy What is the Resonance Strength …? What is its significance? In what units is it measured? Charged particle radiative capture ( a, ) (What about neutrons?)

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 12 Neutron Resonance Reactions (revisited)

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 13 Neutron Activation Analysis ( Z,A ) + n ( Z, A+1 ) - ( Z+1, A+1 ) ( -delayed -ray) Project 1 NAA and U

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 14 Recall F t = n v t N = I t same energy Simultaneous beams, different intensities, same energy. F t = t (I A + I B + I C + …) = t (n A + n B + n C + …)v reactorall directions In a reactor, if neutrons are moving in all directions n = n A + n B + n C + … F t = t nv neutron flux = nv Reaction Rate R t F t = t = / t (=nvN t ) Neutron Flux and Reaction Rate Not talking about a beam anymore. same energy

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 15 Different energies Density of neutrons with energy between E and E+dE n(E)dE Reaction rate for those monoenergetic neutrons dR t = t (E) n(E)dE v(E) Neutron Flux and Reaction Rate

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 16 Neutron Flux and Reaction Rate In general, neutron flux depends on: Neutron energy, E. Neutron spatial position, r. Neutron angular direction, Time, t. Various kinds of neutron fluxes (depending on the degree of detail needed). Time-dependent and time-independent angular neutron flux.

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Thermal Reactorsabsorption Maxwellian In Thermal Reactors, the absorption rate in a medium of thermal (Maxwellian) neutrons Usually 1/v cross section, thus then The reference energy is chosen at eV. Look for Thermal Cross Sections. Actually, look for evaluated nuclear data. Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 17 Neutron Flux and Reaction Rate Reference 2200 m/s flux Independent of n(E). ENDF

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