
All ENDFformat evaluations define their cross sections over
at least part of the energy range using tabulations. In many
cases, part of some of these tabulations specify that a
nonlinear interpolation scheme is to be used to obtain
intermediate values. NJOY wants to get everything in linear form
for several reasons:
 the method used for Doppler broadening requires linearly
interpolated piecewise functions;
 the ACE files for use with MCNP require linearlinear
functions;
 linear functions are easy to average into multigroup
form;
 linear functions are easy to plot; and
 summation cross sections, such as the total cross section,
total inelastic, or total fission, cannot be properly
defined as the sum of their parts except when given as
linear.
The classic example of the last point is the thermal energy range,
where the zerodegree elastic cross section is usually constant
with energy (and uses linearlinear interpolation), but the
radiative capture cross section follows a 1/v law and
uses loglog interpolation. There is no simple "graphpaper"
interpolation scheme that can represent the sum of the elastic
and capture cross sections to the same accuracy as the original
parts. However, if both the elastic and the capture are
linearized to a given accuracy on the same "union grid," their
sum is also linearized to the same accuracy on this grid.
RECONR solves this problem as follows. It first skips the
total cross section and goes to the elastic cross section
(MF=3, MT=2). It starts with a list of "nodes" that may
include energy values given by the user, may include energies
derived from the resonance parameters, and certainly includes
the thermal value .0253 eV. It then adds in any energy points
given in the elastic section of File 3, and if necessary, it
adds in points on the 1, 2, 5, 10, ... grid for each energy
decade. Now it looks at each "panel" described by a pair of
these nodes and decides whether to divide the panel in half.
It will divide the panel if the energy step is too large to
represent the 1/v function to within the specified accuracy,
or if the interpolation scheme is nonlinear, it will divide
the panel if the difference between the specified interpolated
function and the linear interpolate is too large. It continues
subdividing and checking until the desired accuracy has been
achieved over the entire energy range.
The reason for checking the 1/v accuracy for elastic
scattering is that Doppler broadening tends to add a 1/v
component to the elastic cross section, and this grid will
help to handle that correctly in BROADR, even when the
radiative capture reaction is missing or extraordinarily
small.
Once the elastic cross section has been linearized, the code
moves on to the next reaction, perhaps (n,2n), and determines
whether any additional points have to be inserted in the union
grid to represent that reaction to within the desired tolerance.
RECONR continues in this way until all the reactions have been
checked. The result is therefore a union grid able to represent
all the cross sections with linear interpolation, and that implies
that it can also represent the sums of those cross sections with
the same accuracy.
The following input deck will carry out the linearization and
unionization process for H1 from ENDF/VVI (assuming that the
appropriate ENDF file has been mounted on unit 20):
