Fit Function: h_hex_janev_nm_he

Fit Function \[\begin{align} \sigma_{ex}^{n > 3 \rightarrow m > n} (E) &= \frac{8.8 \times 10^{-17} A_1^4}{e}\big[BDL + FGH \big], e = \frac{E}{50} \\ \end{align}\]
Comments Python code requires NumPy imported as `np`. The values of `B`, `D`, `L`, `F`, `G`, and `H` are specific to the code and should be referred to the source code for actual values and details.

Python

Arguments
namedescriptionunitstype(s)
E impact energy keV u-1 float, np.ndarray
A1 original main quantum number float
A2 subsequent main quantum number float
Return values
namedescriptionunitstype(s)
sigma cross section cm2 float, np.ndarray
Code 
def h_hex_janev_nm_he(E, A1, A2):
    """
    This function calculates He+2 impact excitation cross sections (in cm2) of 
    of H n>3 to m>n
    param E: requested impact energy in keV/u
    type E: float, np.ndarray
    param Ai: original main quantum number 
    type Ai: integer
    """
    e = E/50
    s = A2 - A1
    D = np.exp(-1/(A1*A2*e**2))
    y = 1/(1 - D*np.log(18*s)/(4*s))
    zp = 2/(e*A1**2*((2-A1**2/A2**2)**0.5+1))
    zm = 2/(e*A1**2*((2-A1**2/A2**2)**0.5-1))
    
    B = 8/(3*s)*(A2/(s*A1))**3*(0.184-0.04/s**(2/3))*(1-0.2*s/(A1*A2))**(1+2*s)
    L = np.log((1+0.53*e**2*A1*(A2-2/A2))/(1+0.4*e))
    G = 0.5*(e*A1**2/(A2-1/A2))**3
    F = (1-0.3*s*D/(A1*A2))**(1+2*s)
    H = zm**2*np.log(1+2*zm/3)/(2*y + 3*zm/2) - zp**2*np.log(1+2*zp/3)/(2*y + 3*zp/2)
    sigma = 8.8e-17*A1**4*(B*D*L + F*G*H)/e
    return sigma