Fit Function: h_hin_adas

Fit Function \[\sigma_{ion}^{n>1}(E) = 10^{-16}A_1A_9^4 \Bigg[\frac{\tilde{E}^{A_2}e^{-A_3\tilde{E}}}{1 + A_4\tilde{E}^{A_5}} + \frac{A_6e^{\frac{-A_7}{\tilde{E}}} \ln(1+A_8\tilde{E})}{\tilde{E}} \Bigg], \tilde{E} = A_9^2E, A_9 = n\]
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 float
A3 fit coefficient keV-1 u float
A4 fit coefficient undef float
A5 fit coefficient float
A6 fit coefficient float
A7 fit coefficient keV u-1 float
A8 fit coefficient keV-1 u float
A9 main quantum number float
Return values
namedescriptionunitstype(s)
sigma cross section cm2 float, np.ndarray
Code 
def h_hin_adas(E, A1, A2, A3, A4, A5, A6, A7, A8, A9):
    """
    This function calculates proton impact ionization cross sections (in cm2) of 
    H n>1.
    param E: requested proton-impact energy in keV
    type E: float, np.ndarray
    param Ai: fit coefficient 
    type Ai: float
    """
    e = E * A9**2
    sigma = A9**4*1e-16*A1*(e**A2*np.exp(-A3*e)/(1+A4*e**A5) +
                            A6*np.exp(-A7/e)*np.log(1+A8*e)/e)
    return sigma