After having crossed an absorbing cloud, the intensity of a source, I , is received by the observer as I() = I , where is the optical depth of the cloud.
Let's connect to the physical parameters.
N : column density
a( : line absorption coefficient
: broadening function
l : lower level of the atomic transition
k : upper level of the atomic transition
: rest wavelength of the transition
gl : statistical weight of the lower level
gk : statistical weight of the upper level
akl : spontaneous transition probability
flk = upward oscillator strength