Neutron cross section
Isotopes which have a large scatter cross section and a low mass are good neutron moderators (see chart below).
Nuclides which have a large absorption cross section are neutron poisons if they are neither fissile nor undergo decay.
[2] This is the reason why some reactors use heavy water (in which most of the hydrogen is deuterium) instead of ordinary light water as moderator: fewer neutrons are lost by capture inside the medium, hence enabling the use of natural uranium instead of enriched uranium.
The likelihood of interaction between an incident neutron and a target nuclide, independent of the type of reaction, is expressed with the help of the total cross section σT.
However, it may be useful to know if the incoming particle bounces off the target (and therefore continue travelling after the interaction) or disappears after the reaction.
Because neutrons interact with the nuclear potential, the scattering cross-section varies for different isotopes of the element in question.
For a given target and reaction, the cross section is strongly dependent on the neutron speed.
Such physical constraints explain why most operational nuclear reactors use a neutron moderator to reduce the energy of the neutron and thus increase the probability of fission which is essential to produce energy and sustain the chain reaction.
as While the assumptions of this model are naive, it explains at least qualitatively the typical measured energy dependence of the neutron absorption cross section.
For neutrons of wavelength much larger than typical radius of atomic nuclei (1–10 fm, E = 10–1000 keV)
The Doppler broadening of neutron resonances is a very important phenomenon and improves nuclear reactor stability.
The prompt temperature coefficient of most thermal reactors is negative, owing to the nuclear Doppler effect.
Nuclei are located in atoms which are themselves in continual motion owing to their thermal energy (temperature).
= n v: Assuming that there is not one but N targets per unit volume, the reaction rate R per unit volume is: Knowing that the typical nuclear radius r is of the order of 10−12 cm, the expected nuclear cross section is of the order of π r2 or roughly 10−24 cm2 (thus justifying the definition of the barn).
The so-called nuclear cross section is consequently a purely conceptual quantity representing how big the nucleus should be to be consistent with this simple mechanical model.
In the case of a beam with multiple particle speeds, the reaction rate R is integrated over the whole range of energy: Where σ(E) is the continuous cross section, Φ(E) the differential flux and N the target atom density.
In order to obtain a formulation equivalent to the mono energetic case, an average cross section is defined: Where Φ =
Using the equation derived above, the reaction rate R can be derived using only the neutron flux Φ and the macroscopic cross section Σ: The mean free path λ of a random particle is the average length between two interactions.
To account for the interactions, L is divided by the total number of reactions R to obtain the average length between each collision λ: From § Microscopic versus macroscopic cross section: It follows: where λ is the mean free path and Σ is the macroscopic cross section.
Pure 4He fusion leads to 8Be, which decays back to 2 4He; therefore the 4He must fuse with isotopes either more or less massive than itself to result in an energy producing reaction.
