Nuclear Fission

Energy is released when a neutron causes the fission of a fissionable isotope such as235U.

n + 235U → 144Ba + 90Kr + n + n

The energy released in this reaction is ~ 200 MeV split approximately. This is 45 million times greater energy per atom of fuel than would be released in a chemical reaction.

Kinetic Energy from fission fragments 165 ± 5 MeV
Prompt γ-ray energy  7 ± 1 MeV
Kinetic energy of fission neutrons 5 ± 0.5 MeV
β-particles from fission products   7 ± 1 MeV
α-particles from fission products 6 ± 1 MeV
Neutrinos from fission products 10 ± 1 MeV


The release of fission neutrons is crucial as it allows the possibility of a chain reaction. Neutrons are uncharged so can approach a nucleus at low energies without being repulsed by the coulomb force. The cross-section of interaction is greater at low energies.

A reproduction constant k is defined as 

k =      number of neutrons in one generation       
      number of neutrons in the previous generation

k > 1 leads to a supercritical reaction which is used in weopens
k < 1 leads to a subcritical reaction and the reactions dies out
k = 1 is known as critical and leads to a stable reaction


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 σs

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 σI

A+1X* → AX* + n

followed by AX* → AX + γ

Radiative capture σc

A+1X* → A+1X + γ

Emission of light charged particle σp

A+1X* → A(X-1)* + p

Fission σf

236U* → 147La +87Br + 2n

 

Total cross section σt= σs+ σI+ σc+ σp+ σf

Absorption cross section σa= σc+ σp+ σf

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 neutron kinetic energy is reduced

k.e. σs(b) σf(b) σI(b) σc(b)
2 MeV 4 0.6 2.9 0.2
0.3 MeV 9 0.009 0.5 0.2
1 keV 11 0.06 0 4
40 ev (thermal) 8 4.1 0 3.7


A chain reaction is difficult because as σf increases so does σc

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

k.e. σs(b) σf(b) σI(b) σc(b)
2 MeV 3.5 0.3 2.3 0
0.3 MeV 7 1.3 0.7 0
1 keV 10 8 0 3
40 ev (thermal) 10 580 0 100