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The unique isomeric transition at 7.8 eV in $~^{229}\mathrm{Th}$ has amagnetic dipole ($M1$) and an electric quadrupole ($E2$) multipole mixing. Sofar, the $E2$ component has been widely disregarded. Here, we investigate thenuclear physics nature and the impact of the $E2$ decay channel for the nuclearcoupling to the atomic shell based on the newest theoretical predictions forthe corresponding reduced nuclear transition probabilities. Our results showthat the contribution of the $E2$ channel is dominant or at least of the sameorder of magnitude for internal conversion or electronic bridge transitionsinvolving the atomic orbitals $7p$, $6d$ and $5f$. Notable exceptions are theinternal conversion of the $7s$ electron and the electronic bridge between theelectronic states $7s$ and $7p$, for which the $M1$ component dominates by twoto three orders of magnitude. Caution is therefore advised when consideringisomeric excitation or decay via nuclear coupling to the atomic shell, as theinvolved orbitals determine which multipole transition component dominates.

The electric quadrupole channel of the 7.8 eV $~^{229}\mathrm{Th}$ transition