Key Characteristics of Elastic Scattering
- Elastic scattering is the most important process for slowing down neutrons.
- The total kinetic energy of the system is conserved in elastic scattering.
- In this process, energy lost by the neutron is transferred to the recoiling nucleus.
- Maximum energy transfer occurs with a head-on collision.
- The kinetic energy of the recoiled nucleus depends on the recoiled angle φ of the nucleus.
- Elastic scattering cross-sections for light elements are more or less independent of neutron energy up to 1 MeV.
- For intermediate and heavy elements, the elastic cross-section is constant at low energy with some specifics at higher energy.
- A good approximation is, σs = const, for all elements that are of importance.
- At low energy, σs can be described by the one-level Breit-Wigner formula.
- Nearly all elements have scattering cross-sections in the range of 2 to 20 barns.
- The important exception is for water and heavy water.
- If the kinetic energy of an incident neutron is large compared with the chemical binding energy of the atoms in a molecule, the chemical bound can be ignored.
- If the kinetic energy of an incident neutron is of the order or less than the chemical binding energy, the cross-section of the molecule is not equal to the sum of cross-sections of its individual nuclei.
- The scattering of slow neutrons by molecules is greater than by free nuclei.
- Therefore one nucleus microscopic cross-section does not describe the process correctly, while the macroscopic cross-section (Σs) has a precise meaning.
If the kinetic energy of an incident neutron is of the order or less than the chemical binding energy, the cross-section of the molecule is not equal to the sum of cross-sections of its individual nuclei.
Elastic Scattering Cross-section
To be an effective moderator, the probability of elastic reaction between neutron and the nucleus must be high. In terms of cross-sections, the elastic scattering cross-section of a moderator’s nucleus must be high.
