Cross section of interaction in recharge model

The effective cross section is a physical quantity characterizing the probability of transition of a system of two interacting particles to a certain final state, a quantitative characteristic of the acts of collision of particles of a stream hitting a target with target particles. The effective cross-section has the dimension of the area.

Notation:

1. \(a_0\) (a_0) is bohr_radius.

2. \(\mathrm{IE}_\text{H}\) (IE_h) is hydrogen_ionization_energy.

3. \(k_\text{B}\) (k_B) is boltzmann_constant.

4. \(e\) (e) is elementary_charge.

cross_section

cross_section of interaction of particles.

Symbol:

sigma

Latex:

\(\sigma\)

Dimension:

area

ionization_energy

Ionization energy of the particles.

Symbol:

E_i

Latex:

\(E_\text{i}\)

Dimension:

energy

molecular_mass

mass of a single gas particle.

Symbol:

m

Latex:

\(m\)

Dimension:

mass

pressure

Gas pressure.

Symbol:

p

Latex:

\(p\)

Dimension:

pressure

temperature

Gas temperature.

Symbol:

T

Latex:

\(T\)

Dimension:

temperature

electric_field_strength

electric_field_strength.

Symbol:

E

Latex:

\(E\)

Dimension:

voltage/length

law

sigma = pi * a_0^2 * IE_h / E_i * log(sqrt(3 * k_B * T / m) * sqrt(E_i / IE_h) * sigma * p * m / (2 * k_B * T * e * E))^2

Latex:

\[\sigma = \pi a_0^{2} \frac{\mathrm{IE}_\text{H}}{E_\text{i}} \log \left( \sqrt{\frac{3 k_\text{B} T}{m}} \sqrt{\frac{E_\text{i}}{\mathrm{IE}_\text{H}}} \frac{\sigma p m}{2 k_\text{B} T e E} \right)^{2}\]