Fit Function: PHACX

Fit Function \[\begin{align*} \sigma = \frac{f1}{1.0 + f2 } \text{ where } f1 = pcf(3) \; pcf(7) \ln\Bigg(\frac{pcf(4) \sqrt{pcf(7)}}{10^{-3} \times pe}\Bigg); \\ f2 = \left(\frac{ 10^{-6} \times pcf(5)(pe)^{2}}{pcf(7)}\right) + pcf(6) \left( \frac{10^{-3} \times pe}{ \sqrt{pcf(7)}}\right )^{4.5} \\ \end{align*}\]
Comments pcf(7) = q, the charge state of the projectile ion. This must be input into the fit coefficient array, as it is not included in the fit coefficients.

Fortran

Arguments
namedescriptionunitstype(s)
pe projectile energy eV amu-1 real, dimension(:)
pcf coefficient data array real, dimension(7)
kncf number of coefficients in the data array integer
pfit cross section cm2 real, dimension(:)
kermsg error message character
Return values
namedescriptionunitstype(s)
pfit cross section cm2 real, dimension(:)
Code 
c
c###################################################################
c
      subroutine alphacx(pe, pcf, kncf, pfit, kermsg)
c
c     this is a subroutine to calculate cross section for
c     projectile energy (ev/amu).
c
c     the approximate range of valiity of the fit is given by the
c     parameters pcf(1) and pcf(2) which are the scaled energies
c     pe/dsqrt(q) (ev/u), where q is the charge state of the ion.
c
c     pe = projectile energy (ev/amu)
c
c     kermsg = blank if no errors
c
c     pfit = cross section in cm[2]
c
c     pcf(1) = lower limit of the range of validity of the scaled
c              projectile energy in ev/(u*sqrt(q)).
c     pcf(2) = upper limit of the range of validity of the scaled
c              projectile energy in ev/(u*sqrt(q)).
c     pcf(3-6) = a, b, c, d fitting parameters
c     pcf(7) = q, the charge state of the projectile ion. this must be
c              input into the coefficient array. this is not included
c              in the data entries.
c
c     written by j. j. smith , iaea atomic and molecular data unit
c     corrected for invalid definition of energy pek (30/01/90)
c
c------------------------------------------------------------------------
c
      double precision pe, pcf, pfit
      double precision pek, q, q2, a, b, c, d, f1, f2, elow, ehigh
      dimension pcf(7)
      character*(*) kermsg
      a = pcf(3)
      b = pcf(4)
      c = pcf(5)
      d = pcf(6)
      q = pcf(7)
      q2 = dsqrt(q)
c
c---  determine the projectile energy - pek in kev/amu
c
      pek = pe*1.0d-03
c
c---  check that the energy is within the valid energy ranges
c
      elow = pcf(1)*1.0d-03
      ehigh = pcf(2)*1.0d-03
c
      kermsg = ' '
c
      if(q .lt. 5 .or. q .gt. 26) then
        kermsg =
     &   'the charge state (q) must be in the range 5 <= q <= 26'
        return
      endif
c
      f1 = a * q * dlog ( b * q2 / pek )
      f2 = ( c * pek * pek / q )  +  d * ( ( pek / q2 ) ** 4.5d0 )
      pfit = f1 / ( 1.0d0 + f2 )
c
      return
c
      end

Python

Arguments
namedescriptionunitstype(s)
pe projectile energy eV amu-1 float, np.ndarray
pcf coefficient data array float, np.ndarray
kncf number of coefficients in the data array int
pfit cross section cm2 float, np.ndarray
kermsg error message str
Return values
namedescriptionunitstype(s)
pfit cross section cm2 float, np.ndarray
Code