Neutron Capture Cross Sections

The probability that a fission reaction will occur is related to the neutron capture cross section σ. There are two principle modes of interaction -

1. Elastic Scattering σ_s

n + ^AX → ^AX + n

The neutron scatters off the nucleus leaving the with the same number of protons and neutrons.

2. Compound nucleus formation

n + ^AX → ^A+1X*

The * denotes that the nucleus is in an excited state.

A neutron must be "captured" by the nucleus to initiate the fission. The cross section of the interaction varies with the energy of the incident neutron.

After the capture several things can then happen.

Inelastic scattering σ_I

^A+1X* → ^AX* + n

followed by ^AX* → ^AX + γ

Radiative capture σ_c

^A+1X* → ^A+1X + γ

Emission of light charged particle σ_p

^A+1X* → ^A(X-1)* + p

Fission σ_f

²³⁶U* → ¹⁴⁷La + ⁸⁷Br + 2n δ

Total cross section σ_t = σ_s + σ_I + σ_c + σ_p + σ_f

Absorption cross section σ_a = σ_c + σ_p + σ_f
i.e. the neutron is removed from the flux

Each cross section will vary with the kinetic energy of the neutron

For example the natural Uranium Cross Sections differ as the neuton kinetic energy is reduced

A chain reaction is difficult because as σ_f increases so does σ_c

But for ²³⁵U a chain reaction is more easily achieved as the k.e. → 0.3 MeV because σ_f > σ_c