Fit Function: h_hin_javen_he_scaled

Fit Function \[\sigma_{ion}^{1,2,3}(E) =\Bigg( \frac{A_9}{3}\Bigg)^410^{-16}A_1 \Bigg[\frac{e^{-\frac{A_2}{E_n}}\ln(1+A_3E_n)}{E_n} + \frac{A_4e^{-A_5E_n}}{E_n^{A_6} + A_7E_n^{A_8}}\Bigg]; E_n = \Bigg( \frac{3}{n}\Bigg)^2E\]
Comments Python code requires NumPy imported as `np`.

Python

Arguments
namedescriptionunitstype(s)
E impact energy keV u-1 float, np.ndarray
A1 fit coefficient keV cm2 u-1 float
A2 fit coefficient keV u-1 float
A3 fit coefficient keV-1 u float
A4 fit coefficient undef float
A5 fit coefficient keV-1 u float
A6 fit coefficient float
A7 fit coefficient undef float
A8 fit coefficient float
A9 main quantum number float
Return values
namedescriptionunitstype(s)
sigma cross section cm2 float, np.ndarray
Code 
def h_hin_javen_he_scaled(E, A1, A2, A3, A4, A5, A6, A7, A8, A9):
    """
    This function calculates He+2 impact ionzation cross sections (in cm2) of 
    H n > 3.
    param E: requested impact energy in keV/u
    type E: float, np.ndarray
    param Ai: fit coefficient 
    type Ai: float
    """
    E = (A9/3)**2*E
    sigma = (A9/3)**4*1e-16 * A1 * (np.exp(-A2/E) * np.log(1 + A3*E) / E + 
                    A4*np.exp(-A5*E)/ (E**A6 + A7*E**A8))
    return sigma