Fit Function: na_ein

Fit Function \[\sigma_{e}^{ion, Na}(E) = \frac{10^{-13}A_7}{I_{nl}E}\Bigg[A_5 \ln\bigg( \frac{E}{I_{nl}} \bigg) + A_6 e^{-\frac{E}{I_{nl}}}+ \sum_{j=1}^{4}A_j\bigg(1-\frac{I_{nl}}{E}\bigg)^{j-1} \Bigg]\]
Comments Python code requires NumPy imported as `np`.

Python

Arguments
namedescriptionunitstype(s)
E impact energy eV float, np.ndarray
A1 fit coefficient float
A2 fit coefficient float
A3 fit coefficient float
A4 fit coefficient float
A5 fit coefficient float
A6 fit coefficient float
A7 fit coefficient eV2 cm2 float
I ionization energy eV float
Return values
namedescriptionunitstype(s)
sigma cross section cm2 float, np.ndarray
Code 
def na_ein(E, A1, A2, A3, A4, A5, A6, A7, I):
    """
    This function calculates electron impact ionization cross sections (in cm2) of 
    Na 3s to 5s.
    param E: requested electron-impact energy in eV
    type E: float, np.ndarray
    param Ai: fit coefficient 
    type Ai: float
    param I: ionization energy in eV
    type I: float
    """
    sigma =  A7*1e-13/(E*I) * (A5*np.log(E/I) + A6 * np.exp(-E/I) + A1*(1 - I/E)**0 + 
                               A2*(1 - I/E)**1 + A3*(1 - I/E)**2 + A4*(1 - I/E)**3)
    return sigma