The six-factor formula is used in nuclear engineering to determine the multiplication of a nuclear chain reaction in a non-infinite medium. The formula is
k
=
η
f
p
ε
P
F
N
L
P
T
N
L
The symbols are defined as:
ν
,
ν
f
and
ν
t
are the average number of neutrons produced per fission in the medium (2.43 for Uranium-235).
σ
f
F
and
σ
a
F
are the microscopic fission and absorption cross sections for fuel, respectively.
Σ
a
F
and
Σ
a
are the macroscopic absorption cross sections in fuel and in total, respectively.
N
i
is the number density of atoms of a specific nuclide.
I
r
,
A
,
i
is the resonance integral for absorption of a specific nuclide.
I
r
,
A
,
i
=
∫
E
t
h
E
0
d
E
′
Σ
p
m
o
d
Σ
t
(
E
′
)
σ
a
i
(
E
′
)
E
′
.
ξ
¯
is the average lethargy gain per scattering event.
Lethargy is defined as decrease in neutron energy.
u
f
(fast utilization) is the probability that a fast neutron is absorbed in fuel.
P
F
A
F
is the probability that a fast neutron absorption in fuel causes fission.
P
T
A
F
is the probability that a thermal neutron absorption in fuel causes fission.
B
g
2
is the geometric buckling.
L
t
h
2
is the diffusion length of thermal neutrons.
L
t
h
2
=
D
Σ
a
,
t
h
.
τ
t
h
is the age to thermal.
τ
=
∫
E
t
h
E
′
d
E
″
1
E
″
D
(
E
″
)
ξ
¯
[
D
(
E
″
)
B
g
2
+
Σ
t
(
E
′
)
]
.
τ
t
h
is the evaluation of
τ
where
E
′
is the energy of the neutron at birth.
The multiplication factor, k, is defined as (see Nuclear chain reaction):
k
=
number of neutrons in one generation
number of neutrons in preceding generation
If k is greater than 1, the chain reaction is supercritical, and the neutron population will grow exponentially.
If k is less than 1, the chain reaction is subcritical, and the neutron population will exponentially decay.
If k = 1, the chain reaction is critical and the neutron population will remain constant.
