= Most populated rotational level
{title2=$J_*=\sqrt{T/(2\theta_{\rm rot})}-1/2$}
The <rotational state populations> of a spin-free polar <linear rigid rotor> are proportional to $(2J+1)e^{-\theta_{\rm rot}J(J+1)/T}$. Differentiating their logarithm with respect to continuous $J$ gives the displayed maximum when it is nonnegative. The actual maximum must be selected among nonnegative integers by comparing adjacent populations. This population maximum generally differs from a maximum in measured <spectral line> intensity.
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