Fit Function: HEXC5

Fit Function \[\begin{align*} \sigma (pe) &= \text{pcf}(2) \cdot \text{pcf}(3) \cdot (c_1 + c_2) \\ \text{where} \quad c_1 &= \begin{cases} \frac{\exp\left(-\frac{\text{pcf}(4)}{pe}\right) \cdot \ln\left(1 + \text{pcf}(5) \cdot pe\right)}{pe} & \text{if } \left|\frac{\text{pcf}(4)}{pe}\right| < 700 \\ 0 & \text{otherwise} \end{cases} \\ c_2 &= \begin{cases} \frac{\text{pcf}(6) \cdot \exp(-\text{pcf}(7) \cdot pe)}{pe^{\text{pcf}(8)}} & \text{if } \left|\text{pcf}(7) \cdot pe\right| < 700 \\ 0 & \text{otherwise} \end{cases} \end{align*}\]
Comments Python code requires NumPy imported as `np`.

Fortran

Arguments
namedescriptionunitstype(s)
pe requested energy keV u-1 real, dimension(:)
pcf coefficient data array real, dimension(9)
kncf number of coefficients in the data array integer
pxs cross section cm2 real, dimension(:)
kermsg error message character
Return values
namedescriptionunitstype(s)
pxs cross section cm2 real, dimension(:)
Code 
c
c
c###################################################################
c
      subroutine hexc5(pe, pcf, kncf, pxs, kermsg)
c
c     this is a subroutine to calculate cross sections (cm[2])
c     versus proton energy (ev).
c
c     pe = collision energy in kev/amu
c
c     pcf(1) = lower limit of the validity of the analytic fit.
c     pcf(2-8) = parameters for the analytic function.
c
c     kermsg = blank if no errors
c
c     pxs = cross section in 10e-16 cm[2]
c
c------------------------------------------------------------------------
c
      double precision pe, pcf, pxs
      double precision a1, a2, a3, a4, a5, a6, b1, n, m
      double precision arg1, arg2, zero, c1, c2, dexpr, e, one
c
      dimension pcf(9)
      character*(*) kermsg
      data dexpr/7.00d+02/
      data zero/0.00d+00/
      data one/1.00d+00/
c
      e = pe
      b1= pcf(2)
      a1= pcf(3)
      a2= pcf(4)
      a3= pcf(5)
      a4= pcf(6)
      a5= pcf(7)
      a6= pcf(8)
c
      arg1=-a2/e
      c1=zero
      if (dabs(arg1) .lt. dexpr) c1=dexp(arg1) * dlog(one+(a3*e))/e
      arg2=-a5*e
      c2=zero
      if (dabs(arg2) .lt. dexpr) c2=a4*dexp(arg2)/(e**a6)
      pxs = a1 * b1 * ( c1 + c2)
c
      return
      end

Python

Arguments
namedescriptionunitstype(s)
pe requested energy keV u-1 float, np.ndarray
pcf coefficient data array float, np.ndarray
Return values
namedescriptionunitstype(s)
pxs cross section cm2 float, np.ndarray
Code 
def hexc5(pe, pcf):
    """
    This function calculates the cross-section for proton collisions.

    pe: collision energy in keV/amu
    pcf: parameter data array
        pcf[0]: lower limit of the validity of the analytic fit
        pcf[1:8]: parameters for the analytic function
    """
    dexpr = 700.0
    arg1 = -pcf[3]/pe
    c1 = np.where(np.abs(arg1) < dexpr, np.exp(arg1) * np.log(1 + pcf[4] * pe)/pe, 0.0)

    arg2 = -pcf[6] * pe
    c2 = np.where(np.abs(arg2) < dexpr, pcf[5] * np.exp(arg2)/(pe**pcf[7]), 0.0)

    pxs = pcf[1] * pcf[2] * (c1 + c2)

    return pxs