Charged particles with a LAW=5 and LIDP=1, because -1**0 = -1 and (-1)**0 = 1

[whaeck]

A problem was detected when running acer to produce an incident charged particle ace file: NaN values were appearing in the ACE file for a specific case where the incident charged particle and the target where the same type, with a spin s = 0. I'll add an example input file and corresponding example evaluation later.

For charged particle elastic scattering in the ENDF file, we can use MF6 LAW=5. Whenever we do this for identical particles (LIDP=1) such as proton on proton, deuteron on deuteron, triton on triton, etc., we need to calculate the coulomb scattering cross section using formula 6.10:

\sigma_{ci} = \frac{2\eta^2}{k^2 (1-\mu^2)} \left[ \frac{1+\mu^2}{1-\mu^2} + \frac{(-1)^{2s}}{2s+1} cos( \eta \ln( \frac{1 + \mu}{1 - \mu} ) ) \right]

In the case where mu = 0, this reduces to:

\sigma_{ci} ~ \left[ 1 + \frac{(-1)^{2s}}{2s+1} \right]

or when the spin s = 0 as well:

\sigma_{ci} ~ 1 + (-1)^0 ~ 2

In acer, this formula is implemented in acefc.f90, on line 6428:

               if (lidp.eq.1) sigc=((2*eta**2/wn**2)&
                 /(1-amuu**2))*((1+amuu**2)/(1-amuu**2)&
                 +(-1**i2s)*cos(eta*log((1+amuu)/(1-amuu)))&
                 /(2*spi+1))

For mu = 0, this becomes equivalent to:

\sigma_{ci} ~ \left[ 1 + \frac{-1^{2s}}{2s+1} \right]

or when the spin s = 0 as well:

\sigma_{ci} ~ 1 + -1^0 = 0

Later on (line 6439), this value would be used as the denominator in a division, thus leading to the NaN values in the resulting ACE file. Adding the missing parentheses in the coding solves the issue.

Half integer spins do not have the issue. For integer spins different from 0 (s=1,2, etc.) there still is the same issue, but it will not lead to NaN values (because of the 2s + 1 term in the denominator).

[whaeck]

The issue appears in GROUPR as well. The branch fix/cpt fixes this both in ACER and GROUPR.

These appear to be the only instances of a problem like this in the entire NJOY2016 source.

[whaeck]

The following input illustrates the issue using ENDF/B-VIII.0 alpha+alpha:
input.txt
a-002_He_004-ENDF8.0.endf.txt