DataSet D108109

\[\mathrm{e}^- + \mathrm{H} \; n=5 \rightarrow \mathrm{H}^{+} + 2\mathrm{e}^-\]

Process EIN: Ionization
Data type cross section | uploaded on 2023-02-08
Comment Fit function and data were taken from Johnson et al. Equation (35)Errors: E<5*Ionization -> 100%, 5*ionzation<E<208ionization -> 30%, E>20*ionization -> 10%.
Methodsemi-empirical
Columns
  1. E /eV
  2. sigma /cm2
Threshold0.544 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		 \[\begin{align*} \sigma_{ion}^{n>3}(E) = 1.76 \times 10^{-16}\frac{IA_1^2}{E} \bigg(1 - e^{-\frac{A_2E}{I}} \bigg) \Bigg[A_3 \ln \bigg( \frac{E}{I} \bigg) \\ + \bigg(A_4 - A_3\ln\big(2A_1^2\big)\bigg) \bigg(1 - \frac{I}{E} \bigg)^2 \Bigg] \end{align*}\]
Python 
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
Fit Precision1.0 %
Fit Coefficients 
A1
 5.000e+00
A2
 1.550e-01
A3
 3.101e+00
A4
 8.833e+01
I
 5.440e-01
x-range 0.544 –