Fit Function: li_hex_wutte

Fit Function \[\begin{align} & \sigma_p^{exc}(E_p) = \sigma_e^{exc}(E_e) = \frac{5.984 \times 10^{-16}}{E} \Bigg[\frac{E- I}{E} \Bigg]^{A_6} \Bigg[ \sum_{j=1}^{4}\frac{A_j}{(E/I)^{j-1}} + A_5\ln\bigg( \frac{E}{I} \bigg) \Bigg] \\ & \quad E_p(keV/amu) = 0.918E_e(eV)\Bigg[1 - \frac{dE(eV)}{1.15E_e(eV)} + \sqrt{\bigg(1- \frac{dE(eV)}{E_e(eV)}\bigg)} \Bigg] \\ \end{align}\]
Comments Python code requires NumPy imported as `np` and SciPy as 'sp'. Scaled from electron impact CCC calculations.

Python

Arguments
namedescriptionunitstype(s)
E impact energy keV u-1 float, np.ndarray
A1 fit coefficient cm2 eV float
A2 fit coefficient cm2 eV float
A3 fit coefficient cm2 eV float
A4 fit coefficient cm2 eV float
A5 fit coefficient cm2 eV float
A6 fit coefficient float
I threshold energy eV float
Return values
namedescriptionunitstype(s)
sigma cross section cm2 float, np.ndarray
Code 
def li_hex_wutte(E, A1, A2, A3, A4, A5, A6, I):
    """
    This function calculates proton impact excitation cross sections (in cm2) of 
    Li.
    param E: requested electron-impact energy in eV
    type E: float, np.ndarray
    param Ai: fit coefficient 
    type Ai: float
    param I: threshold energy in eV
    type I: float
    """
    energy = np.logspace(np.log10(I), 5, num=500)
    sigma_e = 5.984e-16/E * ((energy-I)/energy)**A6 * (A1/((energy/I)**0) + A2/((energy/I)**1) +  A3/((energy/I)**2) + A4/((energy/I)**3) + A5*np.log(energy/I))
    ref_E = 0.918*energy*(1-I/(1.15*energy) + np.sqrt(1-I/energy))
    sigma_p = sp.interpolate.interp1d(ref_E, sigma_e, kind='linear', fill_value='extrapolate')
    return sigma_p(E)