The power

of a light beam traversing an atomic vapor is attenuated to a value

. The transmission

can be parametrized in terms of the absorption coefficient

and the vapor column length

according to the Lambert-Beer law as

.

The absorption coefficient

depends on the detuning of the light frequency

from the atomic resonance frequency

. Under the assumption of pure Doppler broadening, the absorption coefficient near the resonance frequency of a transition from a ground state

to an excited state

is given by

where

is the atomic density,

the wavelength of the transition,

the lifetime of the excited state, and the Doppler width is

,

with the vapor temperature

*T* and the atomic mass

, and where

are the relative intensities of the hyperfine components with

being the nuclear spin. The symbols on the right of the last equation represent Racah 6-

symbols.

The atomic density is inferred from the vapor pressure

by assuming the ideal gas relations. The vapor pressure is parametrized in the Clausius-Clapeyron form

, which assumes a thermodynamic equilibrium between the bulk metal and its vapor, and where the constants

and

* *depend on the isotope and on the state of aggregation (solid or liquid) of the bulk (see

Vapor Pressure and Density of Alkali Metals for details).

Spectra are then obtained by summing the contributions (1) of all allowed hyperfine components

of the transition with resonance frequencies given by the hyperfine structure of the coupled states.