Cross section of ionization of atom by electrons per Lotz-Drevin

In this law, we are talking about the interaction of an atom and an electron, which ionizes an atom. Equivalent electrons on the outer shell of the ionized atom are electrons with the same principal and orbital quantum numbers. In this case, the Lotz-Drewin approximation for the ionization cross section is considered.

Notation:

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

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

cross_section

cross_section of ionization.

Symbol:

sigma

Latex:

\(\sigma\)

Dimension:

area

ionization_energy

energy of ionization of atoms.

Symbol:

E_i

Latex:

\(E_\text{i}\)

Dimension:

energy

electron_energy

energy of ionizing electrons.

Symbol:

E

Latex:

\(E\)

Dimension:

energy

first_coefficient

A coefficient used in the calculation.

Symbol:

A

Latex:

\(A\)

Dimension:

dimensionless

second_coefficient

A coefficient used in the calculation.

Symbol:

B

Latex:

\(B\)

Dimension:

dimensionless

electron_count

A nonnegative_number of equivalent electrons on the outer shell of the ionized atom.

Symbol:

N

Latex:

\(N\)

Dimension:

dimensionless

law

sigma = 2.66 * pi * a_0^2 * N * IE_h^2 / E_i^2 * A * (E / E_i - 1) / (E / E_i)^2 * log(1.25 * B * E / E_i)

Latex:

\[\sigma = \frac{2.66 \pi a_0^{2} N \mathrm{IE}_\text{H}^{2}}{E_\text{i}^{2}} \frac{A \left(\frac{E}{E_\text{i}} - 1\right)}{\left(\frac{E}{E_\text{i}}\right)^{2}} \log \left( 1.25 B \frac{E}{E_\text{i}} \right)\]