Cross section of ionization of atom by electrons per Granovsky

The Granovsky approximation for the ionization cross section is considered. As the electron energy increases, the velocities of primary and secondary electrons increase, the possibility of their recombination with ions decreases, and the ionization cross section area increases. However, at very high energies, the ionization cross section decreases, as the electrons fly past the atom without having time to ionize it, since the time spent by the electron near the atom decreases.

effective_cross_section

Effective cross_section of ionization of particles.

Symbol:

sigma_eff

Latex:

\(\sigma_\text{eff}\)

Dimension:

area

ionization_energy

Ionization energy.

Symbol:

sigma_i

Latex:

\(\sigma_\text{i}\)

Dimension:

energy

electron_energy

energy of ionizing electrons.

Symbol:

E

Latex:

\(E\)

Dimension:

energy

maximum_cross_section

Maximum cross_section of ionization.

Symbol:

sigma_max

Latex:

\(\sigma_\text{max}\)

Dimension:

area

maximum_electron_energy

Maximum energy of ionizing electrons.

Symbol:

E_max

Latex:

\(E_\text{max}\)

Dimension:

energy

law

sigma_eff = sigma_max * (E - sigma_i) / (E_max - sigma_i) * exp((E_max - E) / (E_max - sigma_i))

Latex:

\[\sigma_\text{eff} = \sigma_\text{max} \frac{E - \sigma_\text{i}}{E_\text{max} - \sigma_\text{i}} \exp{\left(\frac{E_\text{max} - E}{E_\text{max} - \sigma_\text{i}} \right)}\]