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.
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