Key Characteristics of Elastic Scattering

Key Characteristics of Elastic Scattering

  • 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 is occurred with an head-on collision.
  • 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.
  • Scattering of slow neutrons by molecules is greater than by free nuclei.
  • Therefore one nucleus microscopic cross-sections do not describe the process correctly, while the macroscopic cross-section (Σs) has a precise meaning.
Scattering of slow neutrons by molecules is greater than by free nuclei.
Scattering of slow neutrons by molecules is greater than by free nuclei.
Scattering of slow neutrons by molecules is greater than by free nuclei.
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.

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.

Elastic scattering cross-sections for light elements
Elastic scattering cross-sections for light elements are more or less independent of neutron energy up to 1 MeV. Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library
Elastic scattering cross-sections for heavy elements
For intermediate and heavy elements, the elastic cross-section is constant at low energy with some specifics at higher energy.

 
References:
Nuclear and Reactor Physics:
  1. J. R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
  2. J. R. Lamarsh, A. J. Baratta, Introduction to Nuclear Engineering, 3d ed., Prentice-Hall, 2001, ISBN: 0-201-82498-1.
  3. W. M. Stacey, Nuclear Reactor Physics, John Wiley & Sons, 2001, ISBN: 0- 471-39127-1.
  4. Glasstone, Sesonske. Nuclear Reactor Engineering: Reactor Systems Engineering, Springer; 4th edition, 1994, ISBN: 978-0412985317
  5. W.S.C. Williams. Nuclear and Particle Physics. Clarendon Press; 1 edition, 1991, ISBN: 978-0198520467
  6. G.R.Keepin. Physics of Nuclear Kinetics. Addison-Wesley Pub. Co; 1st edition, 1965
  7. Robert Reed Burn, Introduction to Nuclear Reactor Operation, 1988.
  8. U.S. Department of Energy, Nuclear Physics and Reactor Theory. DOE Fundamentals Handbook, Volume 1 and 2. January 1993.

Advanced Reactor Physics:

  1. K. O. Ott, W. A. Bezella, Introductory Nuclear Reactor Statics, American Nuclear Society, Revised edition (1989), 1989, ISBN: 0-894-48033-2.
  2. K. O. Ott, R. J. Neuhold, Introductory Nuclear Reactor Dynamics, American Nuclear Society, 1985, ISBN: 0-894-48029-4.
  3. D. L. Hetrick, Dynamics of Nuclear Reactors, American Nuclear Society, 1993, ISBN: 0-894-48453-2. 
  4. E. E. Lewis, W. F. Miller, Computational Methods of Neutron Transport, American Nuclear Society, 1993, ISBN: 0-894-48452-4.

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Elastic Scattering

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