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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 1 Neutron Attenuation Recall t = N t Probability per unit path length. X I0I0 I Probability mfp for scattering s = 1/ s mfp for absorption a = 1/ a …………. total mfp t = 1/ t

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elastic Show that, after elastic scattering the ratio between the final neutron energy E \ and its initial energy E is given by: For a head-on collision: s -wave After n s -wave collisions: lethargy where the average change in lethargy is HW 6 2Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). Neutron Moderation (revisited) Reference Average decrease in ln(E) after one collision. 1 H ?

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Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh). 3 Neutron Moderation HW 6 (continued) Reproduce the plot. Discuss the effect of the thermal motion of the moderator atoms. On 12 C. Most probable and average energies?

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Neutron Moderation HW 6 (continued) Neutron scattering by light nuclei then the average energy loss and the average fractional energy loss How many collisions are needed to thermalize a 2 MeV neutron if the moderator was: 1 H 2 H 4 Hegraphite 238 U? What is special about 1 H? Why we considered elastic scattering? When does inelastic scattering become important? 4Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh).

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Nuclear Fission ~200 MeV Fission Fusion Coulomb effectSurface effect 5Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh).

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Nuclear Fission B.E. per nucleon for 238 U (BE U ) and 119 Pd (BE Pd ) ? 2x119xBE Pd – 238xBE U = ?? K.E. of the fragments J/g Burning coal 10 5 J/g Why not spontaneous? Two 119 Pd fragments just touching The Coulomb barrier is: Crude …! What if 79 Zn and 159 Sm ? Large neutron excess, released neutrons, sharp potential edge, spherical U …! 6Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh).

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Nuclear Fission 238 U (t ½ = 4.5x10 9 y) for -decay. 238 U (t ½ y) for spontaneous fission. Heavier nuclei?? Energy absorption from a neutron (for example) could form an intermediate state probably above barrier induced fission. Height of barrier is called activation energy. 7Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh).

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Nuclear Fission Liquid Drop Shell Activation Energy (MeV) 8Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh).

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Nuclear Fission Surface Term B s = - a s A Coulomb Term B C = - a C Z(Z-1) / A = Volume Term (the same) fission Crude: QM and original shape could be different from spherical. 9Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh).

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Nuclear Fission Extrapolation to s. Consistent with activation energy curve for A = Nuclear Reactor Theory, JU, Second Semester, (Saed Dababneh).

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