DataSet D108068

\[\mathrm{e}^- + \mathrm{H} \; n=2 \rightarrow \mathrm{H} \; n=10 + \mathrm{e}^-\]

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<30*threshold -> 100%, 30*threshold<E<80*threshold -> 60%, E>80*threshold -> 20%.
Methodsemi-empirical
Columns
  1. E /eV
  2. sigma /cm2
Threshold3.264 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]
DataDownload (data from fit)

Fitted Data

Fit Function
Details		 \[\begin{align*} \sigma_{ex}^{n>2 \rightarrow m>n}(E) &= \frac{1.76 \times 10^{-16}A_1^2I}{A_2E} \Bigg[ 1 - e^{-A_3A_2 \frac{E}{I}} \Bigg] \\ & \Bigg[A_4 \bigg(\ln\bigg(\frac{E}{I}\bigg) + \frac{I}{2E}\bigg) + \bigg(A_5 - A_4\ln\frac{2A_1^2}{A_2}\bigg)\bigg(1 - \frac{I}{E} \bigg) \Bigg] \end{align*}\]
Python 
def h_eex_johnson(E, A1, A2, A3, A4, A5, 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/(A2*E/I)*(1-np.exp(-1*A3*A2*E/I)) * (A4*(np.log(E/I)+1/(2*E/I)) +
                    (A5-A4 * np.log(2*A1**2/A2))*(1-1/(E/I)))
    return sigma
Fit Precision0.6 %
Fit Coefficients 
A1
 2.000e+00
A2
 9.600e-01
A3
 6.534e-01
A4
 3.209e-02
A5
 1.747e-01
I
 3.264e+00
x-range 3.264 –