Energy Grids

As discussed in the RECONR section, the zero-temperature PENDF tape uses a unionized energy grid that represents the cross sections to within certain accuracy criteria using linear-linear interpolation. As shown on the preceeding page, the shapes of the cross sections can change radically after Doppler broadening, and we should expect that the optimum unionized energy grid will have to change also.

As an example of this, the following graph shows the 20 eV resonance in the (n,γ) cross section of Pu-240 for the two temperatures 0K and 300000K. Note that the broadened curve doesn't need as many energy points near the center of the resonance as the zero-temperature curve, but it needs more points out on the steep sides of the wings of the resonance near 15 eV and 25 eV.

Postscript Figure

BROADR generates the new grid using a method very similar to the one used for resonance reconstruction by RECONR. Starting at one particular energy point, BROADR skips forward over some of the energy points in the input grid to find the top of a "panel" to be relinearized. The top of the panel is determined by trying several criteria, such as a maximum lethargy step, or a maximum number of points skipped. But most important, in NJOY97, BROADR tries to keep energy values that end with several zeros. This means that the original "node" values from RECONR will be kept in the new grid. These include standard values like .02530000, 1.000000+2, 2.000000+2, 5.000000+2, and 1.000000+3. But they also include the center energies of the resonances and the two half-height values used to seed resonance reconstruction. This approach keeps all the convenient simple points, preserves all the important structure, and allows BROADR the most possible freedom for generating an ideal new energy grid within these constraints.

Once the upper and lower limits of the panel have been determined, the code then checks whether it should be divided in half by comparing the computed Doppler-broadened cross section at the midpoint to the linearly interpolated value. It uses the same stack logic, fractional accuracy checks ,and resonance integral checks as RECONR. Of course, all of the broadened reactions are checked at each midpoint, which preserves the union nature of the energy grid.


23 January 2013 T-2 Nuclear Information Service