Thus energy will be released in the fission of a heavy nucleus into two medium mass nuclei and in the fusion of two light nuclei into a single medium mass nucleus.

M(A,Z)
M(A_{1},Z_{1}) +
M(A_{2},Z_{2}) |

The

Q = B(A_{1},Z_{1}) +
B(A_{2},Z_{2}) - B(A,Z) |

The mass of constituents cancels out since the total number is the same before and after.

The binding energies can be estimated from the liquid drop model (neglecting pairing and asymmetry terms). As the total number of nucleons

In order to simplify the calculation we assume that in splitting up the nucleus the protons and neutrons divide in the same ratio. That is we assume< BR>

A_{1}/A = Z_{1}/Z = y_{1}
say and A_{2}/A = Z_{2}/Z = y_{2} with y_{1} + y_{2} = 1 |

The energy released can then be expressed in terms of the

Q = E_{s}(1 -
(y_{1})^{2/3} - (y_{2})^{2/3}) +
E_{c}(1 - (y_{1})^{5/3} -
(y_{2})^{5/3}) |

The maximum

Q = 0.37E_{c} - 0.26E_{s} |

Thus on the basis of this simple model fission into two equal nuclei - so called

x = E_{c}/(2E_{s}) =
(Z^{2}/A)/(2a_{s}/a_{c}) ~
(Z^{2}/A)/50 > 0.35 |

Indicating that all nuclei with

The process of fission is suppressed by the presence of a potential barrier. The figure below shows schematically the shape of the barrier as a function of the deformation or fragment separation for different values of the atomic mass number,

At large separations the barrier shape is determined by the coulomb potential between the charges of the two nuclei.

At small distortions there is competition between the

The

for quadrupole distortion of the nuclear shape. The figure shows the energy of deformation in units of the surface energy

X = exp(-) where =
2(h/2)^{-1}(2m)^{1/2} (V(r) - E)^{1/2}dr |

Note the dependence of on mass and that in this case the mass is very large. This means that the transmission factor is very small and so explains why the lifetimes are so long.

Fragment kinetic energy |
165 MeV |

Prompt neutrons |
5 MeV |

Prompt gamma rays |
7 MeV |

Radioactive decay fragments |
25 MeV |

The radioactive decay occurs because the fragment nuclei produced have a

The

It is clear that for low energies some modification of the simple picture is required and this is thought to be due to the effect of individual particle states. At low excitation there is hardly enough energy to drive the two fragments of the nucleus apart and the process of division will only proceed if as much binding energy as possible is transformed into the motion separating them out. Thus the individual nucleons settle into the lowest energy configurations. There is a strong tendency to produce a heavy fragment of

It is no longer a simple case of barrier penetration but one involving a complicated map of the potential with valleys allowing an easier transition to fission. One such surface for

n + ^{235}U ^{236}U* ^{139}Xe + ^{95}Sr
+ 2n |

and a schematic picture of such a process is shown below.

The induction of fission by neutron absorption and the susequent emission of neutrons in the process of fission leads to the possibility of a

The particular reaction involved is indicated in brackets in each case.

^{235}**U**will fission (**n,f**) at all energies of the absorbed neutron. It is a**FISSILE**material.

^{238}**U**has a threshold for fission (**n,f**) at a neutron energy of**1MeV**. The difference between these two isotopes of uranium is explained by the presence of the**pairing term**in the**Semi-empirical mass formula**.

- There is very strong reasonant capture of neutrons
(
**n,**) for energies in the range**10-100 eV**- particularly in the case of^{238}**U**where the cross-section reaches very high values.

- The fission neutron energy spectrum (see figure below) peaks
at around
**1 MeV**and at this energy the inelastic cross-section (**n,n'**) in^{238}**U**exceeds the fission cross-section. This effectively prevents fission from occuring in^{238}**U**.

The fact that the fission cross-section is small at the energy of the fission neutrons and that neutrons are generally absorbed in other processes means that a lump of natural uranium cannot sustain a fission chain reaction.

We can make this more quantitative by examining what happens to the fission neutrons in a lump of natural uranium. Starting with

To enable the use of fission for power generation there are basically two ways round this limitation.

- By enriching the
^{235}**U**content then sufficient fission of this isotope will occur. For example a**50-50**mix of the two isotopes will sustain a chain reaction with most of the fission events occuring in^{235}**U**at neutron energies in the range**0.3 - 2.0 keV**. A reactor working in this way is called a**FAST REACTOR**.

- By mixing natural uranium with a material which slows down the
neutrons without absorption, sufficient of them will get to low energies where the
fission cross-section for
^{235}**U**is extremely large. Such a slowing down medium is called a**moderator**. In this case most of the fissions are induced by neutrons with thermal energy (**0.025 eV**) - hence the name**THERMAL REACTOR**. We will conclude this section with a brief description of the principle features of each type of fission reactor.

Generally the

Periodically within the lattice there are

The

The first example shown below is of a

This is a very common type and makes use of the excellent properties of water both as a coolant and a moderator. A slight disadvantage of ordinary water is that it does absorb neutrons. This is through the conversion of hydrogen into deuterium. This means that for water moderated reactors the fuel has to be enriched with fissile material (eg

A limitation of using water to convey the heat from the core is that the highest temperature of liquid water is its so called

_{th} =
1 - T_{2}/T_{1} |

where in this ideal case the heat is received isothermally by the working fluid at

An obvious step from the

As mentioned above the

The very high power density means that liquid metals have to be used as coolants.

^{238}U(n,)^{239}U (^{-}) ^{239}Np(^{-}) ^{239}Pu. |

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© 1999 - FH Combley, 2005 - CN Booth, 2009 - NJC Spooner