I believe the distributions under the "Fractional Polarization" heading should use $h$ instead of $\bar{h}$.
My rationale is that the Boltzmann distribution goes off of the energy quanta, defined by $E = h\nu$. In the case of spin alignment, the characteristic frequency is $\nu = \bar{\gamma}B_0$. So, I believe the energy term should be $h\bar{\gamma}B_0$ in all of the equations in this section.
I believe the distributions under the "Fractional Polarization" heading should use $h$ instead of $\bar{h}$.
My rationale is that the Boltzmann distribution goes off of the energy quanta, defined by $E = h\nu$. In the case of spin alignment, the characteristic frequency is $\nu = \bar{\gamma}B_0$. So, I believe the energy term should be $h\bar{\gamma}B_0$ in all of the equations in this section.