- In the ideal case of atoms at rest.

- Let
be the normalized distribution of atoms with
velocity between
*v*and

*v*+ d*v*, then:

(8.1)

- In the program
__the velocity is assumed to be gaussian__, thus:

This full expression (1) is denoted as a ``Maxwell + damping wing'' or ``Voigtian'' profile in the program.

In the case of low column density ( 1)

can be approximated to:

= NS

(8.2) |

This simplified expression (2) is denoted as a ``Maxwellian'' profile in the program.

*In cases where the source has a (cosmological) velocity.*

Let z be the redshift of the source.

An absorption is measured in the spectrum at = corresponding to a rest wavelength .

This yields for the redshift of the cloud:

The velocity of the cloud relative to the source is:

In practice the program computes the absorption profile in the cloud reference frame

(