Definition of cross sections 1 - Moodle

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Formation of a compound nucleus 1Any nuclear reaction with formation of a compound nucleus are proceeding in twosuccessive steps:1. The incident neutron is absorbed by the target nucleus A ZX to form an excited state ofnucleus A+1ZX called the compound nucleus. During the formation process, theavailable kinetic energy of the incident neutron e exc and the binding energy of thisadditional neutron S n (A+1,Z) are distributed among all the nucleons of thecompound nucleus. The binding energy is computed in term of the mass default using(10)S n (A+1,Z) = [M(A,Z)+m n −M(A+1,Z)]c 2where M(A,Z) is the mass of isotope A Z X expressed in u, m n = 1.008665u is themass of the neutron and c 2 = 931.5MeV/u is the square of the light velocity in void.2. The compound nucleus decay with a half life between 10 −22 and 10 −14 second,without reminding how it was formed. The neutronic reactions are not the only onesthat can produce a compound nucleus; a photo-nuclear interaction (with an incident γray) can produce the same effect. This decay can occur following a number of decaychannels, as represented in table. Each decay channel involves the production ofsecondary rays and/or particles which can emerge in ground or excited state.ENE6101: Week 4 Cross sections – 10/37
Formation of a compound nucleus 2Type of reactionNumber of decay channels1○ elastic scattering 1 channel2○ inelastic scattering 1 channel if e exc ≥ −Q3○ radiative capture very high number of channels4○ fission ≃ 2 or 3 channels if e exc +S n ≥ e fThe compound nucleus model consists to write the interaction as a two-stage reaction,(11)AZ X +1 0 n → A+1Z X∗ →where the asterisk indicates that the compound nucleus is in an excited state. The first arrowdenotes the formation stage and the second, the decay stage. The energy-level diagram forthis reaction is shown in figure.⎧⎪⎨⎪⎩1○2○3○4○,ENE6101: Week 4 Cross sections – 11/37
Page 1 and 2: Cross sectionsAlain Hébertalain.he
Page 3 and 4: Definition of cross sections 11. Th
Page 5 and 6: Definition of cross sections 3The m
Page 7 and 8: Definition of cross sections 5The r
Page 9: Definition of cross sections 7In a
Page 13 and 14: Formation of a compound nucleus 4A
Page 15 and 16: Selection rules 1The parity π is a
Page 17 and 18: Resonances 21. Each excitation leve
Page 19 and 20: Resonances 4The first three values
Page 21 and 22: Porter and Thomas distribution 1P(x
Page 23 and 24: Wigner distribution 1S(x)0.80.70.60
Page 25 and 26: The SLBW formula 2The parameter σ
Page 27 and 28: The SLBW formula 4The first values
Page 29 and 30: The SLBW formula 6This is a very we
Page 31 and 32: The SLBW formula 8The SLBW equation
Page 33 and 34: Uranium-235 total cross section 1Mi
Page 35 and 36: Plutonium-239 total cross section 1
Page 37: Low-energy variation of cross secti

Definition of cross sections 1 - Moodle

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