Resonance escape probability is highly determined by the heterogeneous geometry of a reactor, because fast neutrons resulting from fission can leave the fuel and slow to thermal energies in a moderator, skipping over resonance energies before reentering the fuel.
The former collisions favor the retention and removal of resonant neutrons from the danger zone, while the latter lead to their loss.
The probability of avoiding resonance capture (coefficient φ) is related to the density of nuclei NS and the moderating power of the medium ξΣS by the relationship below, The JeFF value is called the effective resonance integral.
It characterizes the absorption of neutrons by a single nucleus in the resonance region and is measured in barnes.
The more 238U nuclei in the mixture, the less likely absorption by a single nucleus of the moderating neutrons will take place.
As an example, we can calculate the effective resonance integral in a homogeneous natural uranium-graphite mixture with the ratio N3/N8=215.
The scattering cross section of graphite σCS=4.7 barns; In a homogeneous environment, all 238U nuclei are in the same conditions with respect to the resonant neutron flux.
In a heterogeneous environment uranium is separated from the moderator, which significantly affects the resonant neutron absorption.
The inner 238U nuclei are shielded by the surface nuclei and participate less in the resonant neutron absorption, and the shielding increases with the increase of the fuel element diameter d. Therefore, the effective 238U resonance integral in a heterogeneous reactor depends on the fuel element diameter d: The constant a characterizes the absorption of resonance neutrons by surface and the constant b - by inner 238U nuclei.
Coefficient φ is dependent on the following; Which reflects the competition of two processes in the resonance region: absorption of neutrons and their deceleration.
Let us calculate the probability of avoiding resonance capture in homogeneous and heterogeneous environments natural uranium-graphite.
Taking into account that ξC=0.159, σCa=4.7 barn, we calculate the following probability; Calculating the coefficients φ in homogeneous and heterogeneous mixtures, we get; The transition from homogeneous to heterogeneous medium slightly reduces the thermal neutron absorption in uranium.
However, this loss is considerably overlapped by the decrease of the resonance neutron absorption, and the propagation properties of the medium improve.