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The limitation to "graph paper" interpolation schemes causes
some problems for reactions that are a sum of processes with
different characteristic shapes. The classic example of this
is the total cross section at low energies. At zero temperature,
the elastic cross section tends to be constant for many materials,
and it can be represented well using linear-linear interpolation.
But the radiative capture cross section usually goes like
1/v, and it is best described using log-log interpolation.
Clearly, the sum of these two reactions will be OK at the
grid points, but values intermediate between the grid points
cannot be calculated with either linear-linear or log-log
interpolation.
For this reason, summation cross sections, such as MT=1 (total
cross sectin), MT=4 (total inelastic), and sometimes MT=18 (total
fission), must not be considered fundamental. They must always
be reconstructed from the sum of their parts.
In the NJOY Nuclear Data Processing System, linearization takes
place in the RECONR module. A new energy grid is chosen
iteratively that will represent each fundamental cross section,
such as MT=2 and MT=102 as described above, to some desired
accuracy (e.g., 0.1%). The total cross section is then
regenerated on the new grid by adding up the parts.
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