Fit Function: h_ein_johnson

Fit Function \[\begin{align*} \sigma_{ion}^{n>3}(E) = 1.76 \times 10^{-16}\frac{IA_1^2}{E} \bigg(1 - e^{-\frac{A_2E}{I}} \bigg) \Bigg[A_3 \ln \bigg( \frac{E}{I} \bigg) \\ + \bigg(A_4 - A_3\ln\big(2A_1^2\big)\bigg) \bigg(1 - \frac{I}{E} \bigg)^2 \Bigg] \end{align*}\]
Comments Python code requires NumPy imported as `np`.

Python

Arguments
namedescriptionunitstype(s)
E impact energy eV float, np.ndarray
A1 main quantum number float
A2 fit coefficient float
A3 fit coefficient cm2 float
A4 fit coefficient cm2 float
I ionization energy eV float
Return values
namedescriptionunitstype(s)
sigma cross section cm2 float, np.ndarray
Code 
def h_ein_johnson(E, A1, A2, A3, A4, I):
    """
    This function calculates electron impact ionization cross sections (in cm2) of 
    H n > 3.
    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 = 1.76e-16*A1**2/(E/I)*(1-np.exp(-A2*E/I)) * 
           (A3*np.log(E/I)+(A4-A3*np.log(2*A1**2)) * (1-1/(E/I))**2)
    return sigma