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Neutron Attenuation (revisited)

Neutron Attenuation (revisited). X. I 0. I. Recall  t = N  t. mfp for scattering l s = 1/ S s mfp for absorption l a = 1/ S a total mfp l t = 1/ S t. Probability per unit path length. Probability. Neutron Flux and Reaction Rate. Recall F t =  t I N = I  t

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Neutron Attenuation (revisited)

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  1. Neutron Attenuation (revisited) X I0 I Recall t= N t • mfp for scattering ls = 1/Ss • mfp for absorption la= 1/Sa • total mfp lt = 1/St Probability per unit path length. Probability Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  2. Neutron Flux and Reaction Rate Recall Ft= t I N = I t Simultaneous beams, different intensities, same energy. Ft= t (IA + IB + IC + …) =t (nA + nB + nC + …)v In a reactor, if neutrons are moving in all directions n =nA + nB + nC + … Ft= t nv neutron flux  =nv Reaction Rate Rt Ft= t  =  /t (=nvNt) Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  3. Neutron Flux and Reaction Rate Different energies Density of neutrons with energy between E and E+dE n(E)dE Reaction rate for those “monoenergetic” neutrons dRt= t(E) n(E)dE v(E) Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  4. Neutron Flux and Reaction Rate • In general, neutron flux depends on: • Neutron energy, E. • Neutron angular direction, W. • Neutron spatial position, r. • Time, t. Various kinds of neutron fluxes (depending on the degree of detail needed). Time-dependent and time-independent angular neutron flux. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  5. Neutron Flux and Reaction Rate • 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 0.0253 eV. • Look for Thermal Cross Sections. • Actually, look for evaluated nuclear data. Reference What if not? Factor 2200 m/s flux Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  6. Neutron Moderation 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: After ns-wave collisions: where the average change in lethargy is HW 6 Collision Parameter Reference Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  7. Neutron Moderation HW 6 (continued) • Reproduce the plot. • Discuss the effect of the thermal motion of the moderator atoms. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  8. 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: • 1H 2H 4He graphite 238U ? • What is special about 1H? • Why we considered elastic scattering? • When does inelastic scattering become important? Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  9. Nuclear Fission Surface effect Coulomb effect ~200 MeV  Fission Fusion  Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  10. Nuclear Fission • B.E. per nucleon for 238U (BEU) and 119Pd (BEPd) ? • 2x119xBEPd – 238xBEU = ?? K.E. of the fragments  1011J/g • Burning coal  105J/g • Why not spontaneous? • Two 119Pd fragments just touching •  The Coulomb “barrier” is: • Crude …! What if 79Zn and 159Sm? Large neutron excess, released neutrons, sharp potential edge, spherical U…! Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  11. Nuclear Fission • 238U (t½ = 4.5x109 y) for -decay. • 238U (t½ 1016 y) for fission. • Heavier nuclei?? • Energy absorption from a neutron (for example) could form an intermediate state  probably above barrier  induced fission. • Height of barrier above g.s. is called activation energy. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  12. Nuclear Fission Liquid Drop Shell Activation Energy (MeV) Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  13. Nuclear Fission = Volume Term (the same) Surface Term Bs = - as A⅔ Coulomb Term BC = - aC Z(Z-1) / A⅓  fission  Crude: QM and original shape could be different from spherical. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  14. Nuclear Fission Consistent with activation energy curve for A = 300. Extrapolation to 47  10-20 s. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  15. Nuclear Fission 235U + n  93Rb + 141Cs + 2n Not unique. Low-energy fission processes. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  16. Nuclear Fission Z1 + Z2 = 92 Z1  37, Z2  55 A1 95, A2  140 Large neutron excess Most stable: Z=45 Z=58  Prompt neutrons within 10-16 s. Number depends on nature of fragments and on incident particle energy. The average number is characteristic of the process. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  17. Nuclear Fission The average number of neutrons is different, but the distribution is Gaussian. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  18. Higher than Sn? Delayed neutrons ~ 1 delayed neutron per 100 fissions, but essential for control of the reactor. Follow -decay and find the most long-lived isotope (waste) in this case. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  19. Nuclear Fission Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  20. Nuclear Fission 1/v Fast neutrons should be moderated. 235U thermal cross sections fission  584 b. scattering  9 b. radiative capture  97 b. Fission Barriers Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  21. Nuclear Fission Fissile • Q for 235U + n 236U is 6.54478 MeV. • Table 13.1 in Krane: Activation energy EAfor 236U 6.2 MeV (Liquid drop + shell)  235U can be fissioned with zero-energy neutrons. • Q for 238U + n 239U is 4.??? MeV. • EA for 239U  6.6 MeV  MeV neutrons are needed. • Pairing term:  = ??? (Fig. 13.11 in Krane). • What about 232Pa and 231Pa? (odd Z). • Odd-N nuclei have in general much larger thermal neutron cross sections than even-N nuclei (Table 13.1 in Krane). Fissionable Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  22. Nuclear Fission Why not use it? f,Th584 2.7x10-6 700 0.019 b Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  23. Nuclear Fission • 235U + n  93Rb + 141Cs + 2n • Q = ???? • What if other fragments? • Different number of neutrons. • Take 200 MeV as a representative value. 66 MeV 98 MeV Light fragments Heavy fragments miscalibrated Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  24. Nuclear Fission • Mean neutron energy  2 MeV. •  2.4 neutrons per fission (average)   5 MeV average kinetic energy carried by prompt neutrons per fission. • Show that the average momentum carried by a neutron is only  1.5 % that carried by a fragment. • Thus neglecting neutron momenta, show that the ratio between kinetic energies of the two fragments is the inverse of the ratio of their masses. Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  25. Nuclear Fission Enge Distribution of fission energy Krane sums them up as  decays. Lost … ! Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

  26. Nuclear Fission Segrè Lost … ! Nuclear Reactors, BAU, 1st Semester, 2007-2008 (Saed Dababneh).

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