Neutron Capture Cross-section
- 1/v Region
- Resonance Ragion
- Fast Neutrons Region
Since the mode of decay of the compound nucleus does not depend on the way the compound nucleus was formed, the nucleus sometimes emits a gamma ray (radiative capture) or sometimes emits a neutron (scattering). In order to understand the way, how a nucleus will stabilize itself, we have to understand the behaviour of compound nucleus.
The compound nucleus emits a neutron only after one neutron obtains an energy in collision with other nucleon greater than its binding energy in the nucleus. It have some delay, because the excitation energy of the compound nucleus is divided among several nucleons. It is obvious the average time that elapses before a neutron can be emitted is much longer for nuclei with large number of nucleons than when only a few nucleons are involved. It is a consequence of sharing the excitation energy among a large number of nucleons.
This is the reason the radiative capture is comparatively unimportant in light nuclei but becomes increasingly important in the heavier nuclei.
The lifetime of a compound nucleus is inversely proportional to its total width. Narrow resonances therefore correspond to capture while the wider resonances are due to scattering.Example:
Source: R. Lamarsh, Introduction to Nuclear Reactor Theory, 2nd ed., Addison-Wesley, Reading, MA (1983).
The first resonance in 238U at 6.67 eV, which corresponds to the first virtual level in 239U, has a total width of only 0.027 eV, and the mean life of this state is 2.4×10-14s. By contrast, the resonance observed at 443 keV in 16O, which corresponds to the first virtual state in 17O, has a total width of 41 keV, giving a mean lifetime of 1.5×10-21s. Thus it is highly likely that the compound state in 239U decays at least to some extent by gamma ray emission, while compound state in 17O must decay primarily by nucleon emission. The 443-keV resonance in 16O is clearly a scattering resonance, whereas the 6.67-eV resonance in 238U is in part a capture resonance.
Table of cross-sections.Radiative Capture Cross-section – region of resonances of 238U nuclei.
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data LibraryEnergy 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. Radiative capture and elastic scattering cross-sections in 16O and 238U.
The Doppler broadening of resonances is very important phanomenon, which improves reactor stability. The prompt temperature coefficient of most thermal reactors is negative, owing to an nuclear Doppler effect. Although the absorbtion cross-section depends significantly on incident neutron energy, the shape of the cross-section curve depends also on target temperature.
Nuclei are located in atoms which are themselves in continual motion owing to their thermal energy. As a result of these thermal motions neutrons impinging on a target appears to the nuclei in the target to have a continuous spread in energy. This, in turn, has an effect on the observed shape of resonance. The resonance becomes shorter and wider than when the nuclei are at rest.
Although the shape of a resonance changes with temperature, the total area under the resonance remains essentially constant. But this does not imply constant neutron absorbtion. Despite the constant area under resonance, a resonance integral, which determines the absorbtion, increases with increasing target temperature. This, of course, decreases coefficient k (negative reactivity is inserted).
Fast Neutrons Region
Cross-sections of key isotopes
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data LibraryXenon – 135. Neutron absorption and scattering. Comparison of cross-sections.
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data LibraryHydrogen. Neutron absorption and scattering. Comparison of cross-sections.
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data LibraryGadolinium 155 and 157. Comparison of radiative capture cross-sections.
Source: JANIS (Java-based Nuclear Data Information Software); The JEFF-3.1.1 Nuclear Data Library