INDIANA UNIVERSITY, DEPARTMENT OF PHYSICS, P451 LABORATORY
Neutron activation and flux determination
A. Activation: basics
Thermal neutrons react with the nuclei (A,Z) in the sample predominantly by an (n,
γ
)
reaction. The result is a new isotope (A+1,Z) of the same element. Typically, the isotope
is formed in an excited state, but very quickly decays by gamma emission to the ground
state. Typically, the new isotope is radioactive and decays with a half life
T
½
. The so
called decay constant is given by
2
1
2
ln
T
≡
λ
.
(1)
If
N
is the number of active nuclei, the decay rate is given by
N
dt
dN
λ
−
=
.
(2)
The neutron flux
Φ
is defined by the number of neutrons that traverse a unit area per unit
time in any direction. The probability that a reaction takes place is measured by the
activation cross section
σ
. The units for cross section are cm
2
. Often 1b (barn) =10
24
cm
2
is used. Now, consider a foil of area
a
(cm
2
) and thickness
d
(nuclei per cm
2
)
exposed to flux
Φ
(s1cm2) during a time
t
(s). The number of active nuclei that are
generated is then given by
t
t
d
e
N
e
e
a
N
λ
λ
σ
λ
−
−
−
+
−
−
⋅
Φ
=
0
)
1
(
)
1
(
(3)
Here,
N
0
is the number of active nuclei that are already present at the beginning of the
irradiation. If the foil is inactive at the start (
N
0
=0) and thin (
σ
d«1) and the irradiation time
is short, the exponentials can be expanded and eq.3 reduces to
t
d
a
N
⋅
⋅
⋅
⋅
Φ
=
σ
(4)
Note, that
a
ּ
d
represents the total number
n
of (A,Z) nuclei in the foil, and can be
obtained from the mass
M
(in g) of the foil by
M
A
n
d
a
⋅
⋅
=
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 Fall '09
 Neutron, Neutron flux

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