the electronic spin ($\mathbf{S}=\nicefrac{1}{2}$) couples with the rotational angular momentum $\mathbf{N}$, thus splitting each rotational level $N_{K_a,\,K_c}$ into two fine-structure sub-levels. The fine-structure levels have either $J = N + \nicefrac{1}{2}$ or $J = N - \nicefrac{1}{2}$ quantum numbers, with the exception of the $N = 0$ level, for which only the $J = \nicefrac{1}{2}$ level exists. The total angular momentum $\mathbf{J}$ further couples with each nuclear spin ($I_{\ensuremath{\mathrm{N}}}$ and $I_{\ensuremath{\mathrm{D}}}=1$, $I_{\ensuremath{\mathrm{H}}}=\nicefrac{1}{2}$), giving rise to the so-called hyperfine structure (HFS). The angular momentum coupling scheme adopted takes into account the magnitude of the interaction (from strongest to weakest):

\[eq:coup\] $$\begin{aligned}
 \label{eq:subcoup}
                &\mathbf{J}    = &\mathbf{N}   + \mathbf{S}         \,, \\
                &\mathbf{F}_1  = &\mathbf{J}   + \mathbf{I}_{\ensuremath{\mathrm{N}}} \,, \\
                &\mathbf{F}_2  = &\mathbf{F}_1 + \mathbf{I}_{\ensuremath{\mathrm{H}}} \,, \\
                &\mathbf{F}    = &\mathbf{F}_2 + \mathbf{I}_{\ensuremath{\mathrm{D}}} \,.
            \end{aligned}$$

A more detailed accounts of the spectroscopy can be found in @bizzocchi2020nhd.

Doubly-deuterated amidogen radical
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The higher symmetry of with respect to requires additional considerations in the description of the energy levels manifold. belongs to the $C_{2v}$ symmetry point group and a $\pi$-rotation along the $b$ axis exchanges the two identical deuterium nuclei. Since deuterium is a boson, the total wave-function of must be symmetric upon the permutation of the 