Fit Function: na_hex

Fit Function \[\sigma_{p}^{hex, Na}(E) = 10^{-16} A_1 \Bigg[ \frac{e^{-\frac{A_2}{E}} \big(A_{12} + \ln(A_{11} + A_3E)\big)}{E} + A_4\frac{e^{-A_5E}}{(A_{13}E)^{A_6}} + A_7\frac{e^{-\frac{A_8}{E}}}{1 + (A_9E)^{A_{10}}} \Bigg]\]
Comments Python code requires NumPy imported as `np`.

Python

Arguments
namedescriptionunitstype(s)
E impact energy keV u-1 float, np.ndarray
A1 fit coefficient cm2 keV u-1 float
A2 fit coefficient keV u-1 float
A3 fit coefficient keV-1 u float
A4 fit coefficient keV-1 u float
A5 fit coefficient keV-1 u float
A6 fit coefficient float
A7 fit coefficient keV-1 u float
A8 fit coefficient keV u-1 float
A9 fit coefficient keV-1 u float
A10 fit coefficient float
A11 fit coefficient float
A12 fit coefficient float
A13 fit coefficient keV-1 u float
Return values
namedescriptionunitstype(s)
sigma cross section cm2 float, np.ndarray
Code 
def na_hex(E, A1, A2, A3, A4, A5, A6, A7, A8, A9, A10, A11, A12, A13):
    """
    This function calculates proton impact excitation cross sections (in cm2) of 
    Na 3s to 5s.
    param E: requested electron-impact energy in keV/u
    type E: float, np.ndarray
    param Ai: fit coefficient 
    type Ai: float
    """
    sigma =  A1*1e-16*((np.exp(-A2/E) * (A12 + np.log(A11 + A3*E)))/E + 
                       A4*np.exp(-A5*E)/(A13*E)**A6 + A7*np.exp(-A8/E)/(1 + (A9*E)**A10))
    return sigma