International Reactor Dosimetry File 2002 - IAEA Publications

Burnup is defined as the nuclear transmutation of a given isotope, and the
correction for the nuclear burnup of a stable target isotope is given by:
where:
B = [1 – exp(–sjt)] (II.4)
B
jt
s
t
j
is the burnup correction factor (i.e. the ratio of the measured reaction
rate to the true reaction rate);
is the neutron fluence for the irradiation;
is the spectral averaged cross-section;
is the irradiation time;
is the total neutron flux.
sj can be defined as the product of the activation cross-section and the
neutron flux spectrum integrated over the entire neutron energy spectrum, and
is also equal to the total activation rate in product atoms per target atoms per
second that can be calculated from reactor dosimetry activation measurements.
Prior to neutron spectral adjustment, measured activation data are converted
to these saturated activation rates. Equation (II.4) may be applied in order to
determine if a burnup correction may be required for a specific reaction.
However, if the burnup is significant, the measured reaction rate will be much
lower than the true reaction rate as implied in Eq. (II.4). Furthermore, the
possibility of burnup of the product atoms has to be considered, which may well
be at a higher rate than that of the target atoms. The more general form of the
burnup equation (which also takes into account the decay of the product atom)
is given by:
where:
B = l[exp(–s a jt) – exp(–s b jt)]/[(l + s b j – s a j)(1 – exp(–lt))] (II.5)
B is the ratio of the measured reaction rate to the true reaction rate;
s a and s b are the spectral averaged cross-sections for the target and product
atom, respectively;
l is the decay constant for the product isotope.
As noted above, this equation requires that the true reaction rates be
known, whereas only a measured reaction rate for the target reaction may be
known. This problem can be easily solved by applying an iterative procedure.
Given a measured and uncorrected reaction rate for the target isotope, the
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