Nuclear Reactors, BAU, 1 st Semester, 2007-2008 (Saed Dababneh). 1 Neutron Attenuation (revisited) X eraction X eraction no t t e X P e X P 1 ) ( ) ( int int Recall t = N t Probability per unit path length. X I 0 I Probabil ity mfp for scattering s = 1/s mfp for absorption a = 1/a total mfp t = 1/t X t e I X I 0 ) (
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 - PowerPoint PPT Presentation
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Different energiesDifferent energiesDensity of neutrons with energy between E and E+dEn(E)dEReaction rate for those “monoenergetic” neutronsdRt = t(E) n(E)dE v(E)
Nuclear Fission• B.E. per nucleon for 238U (BEU) and 119Pd (BEPd) ?• 2x119xBEPd – 238xBEU = ?? K.E. of the fragments 1011 J/g• Burning coal 105 J/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…!
• 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.
Most stable:Z=45 Z=58Prompt neutronsPrompt neutrons within 10-16 s.Number depends on nature of fragments and on incident particle energy.The average number is characteristic of the process.
• Q for 235U + n 236U is 6.54478 MeV.• Table 13.1 in Krane: Activation energy EA for 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).
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.