What is Compound Nucleus and what is Resonance?

There is no difference between the compound nucleus and the nuclear resonance.

The compound nucleus is the intermediate state formed in a compound nucleus reaction. It is normally one of the excited states of the nucleus formed by the combination of the incident particle and target nucleus. If a target nucleus X is bombarded with particles a, it is sometimes observed that the ensuing nuclear reaction takes place with appreciable probability only if the energy of the particle a is in the neighborhood of certain definite energy values. These energy values are referred to as resonance energies. The compound nuclei of these certain energies are reffered to as nuclear resonances. Resonances are usually found only at relatively low energies of the projectile. The widths of the resonances increase in general with increasing energies. At higher energies the widths may reach the order of the distances between resonances and then no resonances can be observed. The narrowest and resonances are usually the compound states of heavy nuclei (such as fissionable nuclei) and thermal neutrons (usually in (n,γ) capture reactions). The observation of resonances is by no means restricted to neutron nuclear reactions.

Resonances and Neutron Cross-section

For the compound nucleus peaks in the cross-section are typical. Each peak is manifesting a particular compound state of nucleus. These peaks and the associated compound nuclei are usually called resonances. The behaviour of the cross-section between two resonances is usually strongly affected by the effect of nearby resonances.

Resonances (particular compound states) are mostly created in neutron nuclear reactions, but  it is by no means restricted to neutron nuclear reactions. The formation of resonances is caused by the quantum nature of nuclear forces. Each nuclear reaction is a transition between different quantum discrete states or energy levels. The discrete nature of energy transitions plays a key role. If the energy of the projectile (the sum of the Q value and the kinetic energy of the projectile) and the energy of target nucleus is equal to a compound nucleus at one of the excitation states, a resonance can be created and peak occurs in the cross section. For light nucleus, the allowable state density in this energy region is much lower and the “distance” between states is higher. For heavy nuclei, such as 238U, we can observe large resonance region in the neutron absorption cross-section.

It is obvious the compound states (resonances) are observed at low excitation energies. This is due to the fact, the energy gap between the states is large. At high excitation energy, the gap between two compound states is very small and the widths of resonances may reach the order of the distances between resonances. Therefore at high energies no resonances can be observed and the cross section in this energy region is continuous and smooth.

Compound Nucleus
The position of the energy levels during the formation of a compound nucleus.
Energy levels of compound state. For neutron absorption reaction on 238U the first resonance E1 corresponds to the excitation energy of 6.67eV. E0 is a base state of 239U.
Region of Resonances
Region of resonances of 238U nuclei.

Source: JANIS (Java-based Nuclear Data Information Software); The ENDF/B-VII.1 Nuclear Data Library

Uranium 235. Comparison of total fission cross-section and cross-section for radiative capture.
Uranium 235. Comparison of total fission cross-section and cross-section for radiative capture.

Source: JANIS (Java-based Nuclear Data Information Software); The ENDF/B-VII.1 Nuclear Data Library

Gadolinium 155 and 157. Comparison of radiative capture cross-sections. Both nuclei have region of resonances.
Gadolinium 155 and 157. Comparison of radiative capture cross-sections. Both nuclei have region of resonances.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

Boron 10. Comparison of total cross-section and cross-section for (n,alpha) reactions.Isotope 10B do not have any region of resonances.
Boron 10. Comparison of total cross-section and cross-section for (n,alpha) reactions.Isotope 10B do not have any region of resonances.

Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library

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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