Interpolation Problems



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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15 December 2012 T-2 Nuclear Information Service ryxm@lanl.gov