CollisionDB: DataSet D108082

$e^{-} + H n = 3 \to H n = 9 + e^{-}$

Process	EEX: Excitation
Data type	cross section \| uploaded on 2023-02-08
Comment	Fit function and data were taken from Johnson et al. Equation (29). Errors: E<30threshold -> 100%, 30threshold<E<80threshold -> 60%, E>80threshold -> 20%.

Method	semi-empirical
Columns	E /eV sigma /cm²
Threshold	1.343 eV
Ref	B26: L.C. Johnson, "Approximations for collisional and radiative transition rates in atomic hydrogen", Astrophysical Journal 174, 227-236 (1972). [10.1086/151486]
Data	Download (data from fit)

Fitted Data

Fit Function
Details

\begin{aligned} σ_{e x}^{n > 2 \to m > n} (E) & = \frac{1.76 \times 10^{- 16} A_{1}^{2} I}{A_{3} E} [1 - e^{- A_{3} A_{4} \frac{E}{I}}] \\ [A_{5} (\ln (\frac{E}{I}) + \frac{I}{2 E}) + (A_{6} - A_{5} \ln \frac{2 A_{1}^{2}}{A_{3}}) (1 - \frac{I}{E})] \end{aligned}

Python

def h_eex_johnson(E, A1, A2, A3, A4, A5, A6, I):
    """
    This function calculates electron impact excitation cross sections (in cm2) of 
    H n > 2 to m > n , with exception of n=2 to n=3.
    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
    """
    sigma = 1.76e-16*A1**2/(A3*E/I)*(1-np.exp(-1*A3*A4*E/I)) * (A5*(np.log(E/I)+1/(2*E/I)) + 
                    (A6-A5 * np.log(2*A1**2/A3))*(1-1/(E/I)))
    return sigma

Fit Precision

0.6 %

Fit Coefficients

A1	3.000e+00
A2	8.889e-01
A3	3.457e-01
A4	1.969e-01
A5	1.590e+00
I	1.343e+00

x-range

1.3432098765432097 –

DataSet D108082

e−+Hn=3→Hn=9+e−

Fitted Data

$e^{-} + H n = 3 \to H n = 9 + e^{-}$