This source states that the absorption coefficient $\gamma$ is proportional to the difference in particle number density $\Delta n$ per unit volume between the initial and the final rotational state and also proportional to the dipole moment $\mu_T$ $$\gamma \propto \Delta n\cdot \mu_T$$ According to the Beer-Lambert Law the absoprtion coefficient is also equal to: $$\gamma=\log_{10}\bigg(\frac{I_0}{I}\bigg)\cdot \frac{1}{c\cdot l}$$ Where $I_0$ and $I$ are the incidental and transmitted intensity, $c$ is the concentration of the solution and $l$ the traveled length through the solution by the incidental beam.
From this Beert-Lambert law I woud deduce that the absorption coefficient is in terms of per 1 unit length and per 1 unit concentration.
I would assume that the difference in number density $\Delta n$ is analogous to the concentration of a solution.
But how is $\gamma$ then proportional to the $\Delta n$ if it should be per 1 unit of $\Delta n$ just as it is per 1 unit of sample concentration?