  We report the first coupled-cluster study of Auger decay in heavy metals. The
zinc atom is used as a case study due to its relevance to the Auger emission
properties of the $^{67}$Ga radionuclide. Coupled-cluster theory combined with
complex basis functions is used to describe the transient nature of the
core-ionized zinc atom. We also introduce second-order M{\o}ller-Plesset
perturbation theory as an alternative method for computing partial Auger decay
widths. Scalar-relativistic effects are included in our approach for computing
Auger electron energies by means of the spin-free exact two-component
one-electron Hamiltonian, while spin-orbit coupling is treated by means of
perturbation theory. We center our attention on the K-edge Auger decay of zinc
dividing the spectrum into three parts (K-LL, K-LM, and K-MM) according to the
shells involved in the decay. The computed Auger spectra are in good agreement
with experimental results. The most intense peak is found at an Auger electron
energy of 7432 eV, which corresponds to a $^1$D$_2$ final state arising from
K-L$_2$L$_3$ transitions. Our results highlight the importance of relativistic
effects for describing Auger decay in heavier nuclei. Furthermore, the effect
of a first solvation shell is studied by modeling of Auger decay in the
hexaaqua-zinc (II) complex. We find that K-edge Auger decay is slightly
enhanced by the presence of the water molecules as compared to the bare atom.
