The six-factor formula is used in
nuclear engineering
Nuclear engineering is the branch of engineering concerned with the application of breaking down atomic nuclei ( fission) or of combining atomic nuclei ( fusion), or with the application of other sub-atomic processes based on the principles of n ...
to determine the multiplication of a
nuclear chain reaction
In nuclear physics, a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series of these reactions. The specific nu ...
in a non-infinite medium.
The symbols are defined as:
*
,
and
are the average number of neutrons produced per fission in the medium (2.43 for
uranium-235
Uranium-235 (235U or U-235) is an isotope of uranium making up about 0.72% of natural uranium. Unlike the predominant isotope uranium-238, it is fissile, i.e., it can sustain a nuclear chain reaction. It is the only fissile isotope that exi ...
).
*
and
are the microscopic fission and absorption cross sections for fuel, respectively.
*
and
are the macroscopic absorption cross sections in fuel and in total, respectively.
*
is the number density of atoms of a specific
nuclide
A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state.
The word ''nuclide'' was co ...
.
*
is the resonance integral for absorption of a specific
nuclide
A nuclide (or nucleide, from atomic nucleus, nucleus, also known as nuclear species) is a class of atoms characterized by their number of protons, ''Z'', their number of neutrons, ''N'', and their nuclear energy state.
The word ''nuclide'' was co ...
.
**
.
*
is the average lethargy gain per scattering event.
**Lethargy is defined as decrease in neutron energy.
*
(fast utilization) is the probability that a fast neutron is absorbed in fuel.
*
is the probability that a fast neutron absorption in fuel causes fission.
*
is the probability that a thermal neutron absorption in fuel causes fission.
*
is the
geometric buckling.
*
is the diffusion length of thermal neutrons.
**
.
*
is the age to thermal.
**
.
**
is the evaluation of
where
is the energy of the neutron at birth.
Multiplication
The multiplication factor, , is defined as (see
nuclear chain reaction
In nuclear physics, a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series of these reactions. The specific nu ...
):
:
* If is greater than 1, the chain reaction is ''supercritical,'' and the neutron population will grow exponentially.
* If is less than 1, the chain reaction is ''subcritical,'' and the neutron population will exponentially decay.
* If , the chain reaction is ''critical'' and the neutron population will remain constant.
See also
*
Critical mass
In nuclear engineering, a critical mass is the smallest amount of fissile material needed for a sustained nuclear chain reaction. The critical mass of a fissionable material depends upon its nuclear properties (specifically, its nuclear fi ...
*
Nuclear chain reaction
In nuclear physics, a nuclear chain reaction occurs when one single nuclear reaction causes an average of one or more subsequent nuclear reactions, thus leading to the possibility of a self-propagating series of these reactions. The specific nu ...
*
Nuclear reactor
A nuclear reactor is a device used to initiate and control a fission nuclear chain reaction or nuclear fusion reactions. Nuclear reactors are used at nuclear power plants for electricity generation and in nuclear marine propulsion. Heat fr ...
*
Four factor formula
The four-factor formula, also known as Fermi's four factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in an infinite medium.
The symbols are defined as:
*\nu, \nu_f and \nu_t are the averag ...
References
{{reflist
Nuclear technology
Radioactivity