  Given a $p$-adic field $K$ and a nilpotent uniform pro-$p$ group $G$, we
prove that all primitive ideals in the $K$-rational Iwasawa algebra $KG$ are
maximal, and can be reduced to a particular standard form. Setting
$\mathcal{L}$ as the associated $\mathbb{Z}_p$-Lie algebra of $G$, our approach
is to study the action of $KG$ on a Dixmier module $\widehat{D(\lambda)}$ over
the affinoid envelope $\widehat{U(\mathcal{L})}_K$, and to prove that all
primitive ideals can be reduced to annihilators of modules of this form.
