Elastic and Inelastic Scattering

Elastic vs. Inelastic Scattering of Neutrons

Generally, a neutron scattering reaction occurs when a target nucleus emits a single neutron after a neutron-nucleus interaction. In an elastic scattering reaction between a neutron and a target nucleus, there is no energy transferred into nuclear excitation.

Besides, in an inelastic scattering reaction between a neutron and a target nucleus some energy of the incident neutron is absorbed to the recoiling nucleus and the nucleus remains in the excited state. Thus while momentum is conserved in an inelastic collision, kinetic energy of the “system” is not conserved.

Key Characteristics of Elastic Scattering

See also: Neutron Elastic Scattering

  • Elastic scattering is the most important process for slowing down neutrons.
  • 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.

Key Characteristics of Inelastic Scattering

See also: Neutron Inelastic Scattering

  • During an inelastic scattering the neutron is absorbed and then re-emitted.
  • While momentum is conserved in an inelastic collision, kinetic energy of the “system” is not conserved.
  • Some energy of the incident neutron is absorbed to the recoiling nucleus and the nucleus remains in the excited state.
  • The nucleus gives up excitation energy by emitting one or more gamma rays.
  • General notation: A(n, n’)A* or A(n, 2n’)B; Example: 14O(n, n’)14O*.
  • Inelastic scattering is a threshold reaction and occurs above a threshold energy.
  • Inelastic scattering cross section is relatively small for light nuclei.
  • For hydrogen nucleus, inelastic scattering does not occur, because it does not have excited states.
  • Inelastic scattering plays an important role in slowing down neutrons especially at high energies and by heavy nuclei (e.g. 238U).
  • Inelastic scattering may be significant for heterogeneous reactors with highly enriched fuel (e.g. in fast neutron reactors).
 
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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