Direct Nuclear Reactions

Nuclear reactions that occur in a time comparable to the time of transit of an incident particle across the nucleus (~10-22 s) are called direct nuclear reactions. Interaction time is critical for defining the reaction mechanism. The very short interaction time allows for an interaction of a single nucleon only (in extreme cases).

To understand the nature of nuclear reactions, the classification according to the time scale of these reactions has to be introduced. Interaction time is critical for defining the reaction mechanism.

There are two extreme scenarios for nuclear reactions (not only neutron nuclear reactions):

  • A projectile and a target nucleus are within the range of nuclear forces for a very short time allowing for an interaction of a single nucleon only. These types of reactions are called direct nuclear reactions.
  • A projectile and a target nucleus are within the range of nuclear forces, allowing for a large number of interactions between nucleons. These types of reactions are called the compound nucleus reactions.

Direct Nuclear Reactions

Nuclear reactions that occur in a time comparable to the time of transit of an incident particle across the nucleus (~10-22 s) are called direct nuclear reactions. Interaction time is critical for defining the reaction mechanism. The very short interaction time allows for an interaction of a single nucleon only (in extreme cases). There is always some non-direct (multiple internuclear interactions) component in all reactions, but the direct reactions have this component limited. The reaction has to occur at high energy to limit the time available for multiple internuclear interactions.

Direct reactions have another very important property. Products of a direct reaction are not distributed isotropically in angle, but they are forward-focused. This reflects that the projectiles make only one, or very few, collisions with nucleons in the target nucleus, and its forward momentum is not transferred to an entire compound state.

The cross-sections for direct reactions vary smoothly and slowly with energy in contrast to the compound nucleus reactions. These cross-sections are comparable to the geometrical cross-sections of target nuclei. Types of direct reactions:

  • Elastic scattering in which a passing particle and targes stay in their ground states.  
  • Inelastic scattering in which a passing particle changes its energy state.  For example, the (p, p’) reaction.
  • Transfer reactions in which one or more nucleons are transferred to the other nucleus. These reactions are further classified as:
    • Stripping reaction in which one or more nucleons are transferred to a target nucleus from passing particles. For example, the neutron stripping in the (d, p) reaction.
    • Pick-up reaction in which one or more nucleons are transferred from a target nucleus to a passing particle. For example, the neutron pick-up in the (p, d) reaction.
  • Break-up reaction in which a breakup of a projectile into two or more fragments occurs.
  • Knock-out reaction in which a single nucleon or a light cluster is removed from the projectile by a collision with the target.

Direct nuclear reaction

Example: This threshold reaction of a fast neutron with an isotope 10B is one of the ways how radioactive tritium in the primary circuit of all PWRs is generated.

Direct Reactions vs. Compound Nucleus Reactions

Direct Reactions

  • The direct reactions are fast and involve a single-nucleon interaction.
  • The interaction time must be very short (~10-22 s).
  • The direct reactions require incident particle energy larger than ∼ 5 MeV/Ap. (Ap is the atomic mass number of a projectile)
  • Incident particles interact on the surface of a target nucleus rather than in the volume of a target nucleus.
  • Products of the direct reactions are not distributed isotropically in angle, but they are forward-focused.
  • Direct reactions are of importance in measurements of nuclear structure.

Compound Nucleus Reactions

  • The compound nucleus reactions involve many nucleon-nucleon interactions.
  • A large number of collisions between the nucleons leads to a thermal equilibrium inside the compound nucleus.
  • The time scale of compound nucleus reactions is 10-18 s – 10-16 s.
  • The compound nucleus reactions are usually created if the projectile has low energy.
  • Incident particles interact in the volume of a target nucleus.
  • Products of the compound nucleus reactions are distributed near isotropically in angle (the nucleus loses memory of how it was created – Bohr’s hypothesis of independence).
  • The decay mode of the compound nucleus does not depend on how the compound nucleus is formed.
  • Resonances in the cross-section are typical for the compound nucleus reaction.

 

 
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

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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See above:

Neutron Nuclear Reactions

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