Definition of cross sections 1 - Moodle

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Low-energy variation of cross sections 1We consider a resonance located at an energy e x,1 above the thermal energy domain (> 1eV) and study its contribution at thermal energies. We will rewrite the SLBW formulas andtake their limits as e x,1 approaches zero.If R/̷λ
Low-energy variation of cross sections 21. These equations are valid at energies E ≤ 300 keV for a heavy nuclide and atenergies E ≤ 1 MeV for an intermediate nuclide (A ≃ 40).2. We will next consider an isotope without negative resonance and without resonancesin the thermal energy domain. In this case, the energy-variation of the cross sectionsat thermal energies is dictated by the energy variation of ̷λ and Γ n,1 . Theabsorption-type widths, such as Γ γ,1 or Γ f,1 , are constant in energy.3. The neutron width Γ n,1 , on the other hand, varies as √ E for a s wave interaction, asE 3/2 for a p wave interaction and as E 5/2 for a d wave interaction. The squaredreduced wavelength ̷λ 2 varies as 1/E.4. We therefore observe that s wave absorption-type reactions feature a characteristic1/v–dependence. At low energies, the probability of these interactions is directlyproportional to the time the neutron spends within the reach of the nuclear force.5. Assuming s wave interaction, we see that σ e (e exc ) is almost constant at low energyand that the absorption-type reactions with no threshold energy vary as 1/ √ E.ENE6101: Week 4 Cross sections – 37/37
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 and 10: Definition of cross sections 7In a
Page 11 and 12: Formation of a compound nucleus 2Ty
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: Plutonium-239 total cross section 1

Definition of cross sections 1 - Moodle

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