Geoscience Reference
In-Depth Information
Fortunately, it is not necessary to carry out the analysis in an absolute manner
because another isotope of uranium,
235
U, can be made to undergo fission by the
absorption of slow neutrons. (Such an
induced fission
is the heart of the generation
of power in nuclear reactors and atomic bombs.) The induced fission of
235
Uis
achieved by putting the sample in a reactor and bombarding it with slow neutrons
for a specified time (hours). This provides us with a standard against which to
calibrate the number of tracks per unit area (track density).
The analysis that follows assumes that neither of the other two isotopes of
uranium that occur naturally (
234
U and
235
U) contributes significantly to the spon-
taneous fissions; we can make this assumption because their fission branching
ratios and isotope abundances are very low relative to those of
238
U. The analysis
also assumes that there has been no previous interaction with neutrons, which
would have contributed neutron-induced fission tracks from
235
U. This is almost
always a safe assumption unless the uranium has been associated with any of the
natural thermal nuclear reactors that occurred in uranium mineral deposits in the
early Precambrian (an example is the set of natural nuclear reactors at Oklo in
Gabon). At that time,
235
Uwas relatively more abundant than it is now since it
has a shorter half-life than
238
U.
The number of induced fissions of
235
U,
D
I
,isdefined as
D
I
=
[
235
U
]
now
σ
n
(6.58)
where
is the known neutron-capture cross section (the probability that capture
of a neutron by
235
U will occur) and
n
is the neutron dose in the reactor (the
number of neutrons crossing a square centimetre). Since the fission products of
235
Uhave almost exactly the same average kinetic energy as the fission products of
238
U, we can assume that, if uranium-235 is distributed throughout the sample in
the same even way as uranium-238, the same proportion of both fission products
will cross the sample's polished surface and be counted. This being the case, we
can combine Eqs. (6.57) and (6.58)toobtain
σ
238
U
235
U
e
λ
t
λ
S
λ
−
1
σ
D
S
D
I
=
N
S
N
I
=
(6.59)
n
now
where
N
S
and
N
I
are the numbers of spontaneous and induced fission tracks
counted in a given area. The time
t
can then be determined by rearranging
Eq. (6.59) and using the uranium isotopic ratio [
238
U
235
U]
now
=
/
137.88:
log
e
1
+
1
λ
N
S
N
I
λ
λ
S
σ
n
137
.
88
t
=
(6.60)
In practice, after the number of spontaneous fission tracks
N
S
has been counted,
the sample is placed in the reactor for a specified time and then etched again
(which enlarges the original spontaneous fission tracks as well as etching the
newly induced fission tracks) so that the number of induced
235
U fission tracks
N
I
can be counted.
One major advantage of using these ancient fission tracks as a geological
dating method is that their stability is temperature-dependent (Eq. (6.25)). At
