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.

..
    TODO: find link
    TODO: move to `ionization` folder?

.. py:currentmodule:: symplyphysics.laws.chemistry.cross_section_of_ionization_of_atom_by_electron_by_granovsky

.. py:data:: effective_cross_section

    Effective :attr:`~symplyphysics.symbols.chemistry.cross_section` of ionization of particles.

Symbol:
    :code:`sigma_eff`

Latex:
    :math:`\sigma_\text{eff}`

Dimension:
    :code:`area`


.. py:data:: ionization_energy

    Ionization :attr:`~symplyphysics.symbols.basic.energy`.

Symbol:
    :code:`sigma_i`

Latex:
    :math:`\sigma_\text{i}`

Dimension:
    :code:`energy`


.. py:data:: electron_energy

    :attr:`~symplyphysics.symbols.basic.energy` of ionizing electrons.

Symbol:
    :code:`E`

Latex:
    :math:`E`

Dimension:
    :code:`energy`


.. py:data:: maximum_cross_section

    Maximum :attr:`~symplyphysics.symbols.chemistry.cross_section` of ionization.

Symbol:
    :code:`sigma_max`

Latex:
    :math:`\sigma_\text{max}`

Dimension:
    :code:`area`


.. py:data:: maximum_electron_energy

    Maximum :attr:`~symplyphysics.symbols.basic.energy` of ionizing electrons.

Symbol:
    :code:`E_max`

Latex:
    :math:`E_\text{max}`

Dimension:
    :code:`energy`


.. py:data:: law

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


    Latex:
        .. math::
            \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)}