  Having a detailed theoretical knowledge of the low-energy structure of the
heavy odd-mass nucleus $^{197}$Au is of prime interest as the structure of this
isotope represents an important input to theoretical simulations of collider
experiments involving gold ions performed worldwide at relativistic energies.
In the present article, therefore, we report on new results on the structure of
$^{197}$Au obtained from state-of-the-art multi-reference energy density
functional (MR-EDF) calculations. Our MR-EDF calculations were realized using
the Skyrme-type pseudo-potential SLyMR1, and include beyond mean-field
correlations through the mixing, in the spirit of the Generator Coordinate
Method (GCM), of particle-number and angular-momentum projected triaxially
deformed Bogoliubov quasi-particle states. Comparison with experimental data
shows that the model gives a reasonable description of $^{197}$Au with in
particular a good agreement for most of the spectroscopic properties of the
$3/2_1^+$ ground state. From the collective wave function of the correlated
state, we compute an average deformation $\bar{\beta}(3/2_1^+)=0.13$ and
$\bar{\gamma}(3/2_1^+)=40^\circ$ for the ground state. We use this result to
construct an intrinsic shape of $^{197}$Au representing a
microscopically-motivated input for precision simulations of the associated
collider processes. We discuss, in particular, how the triaxiality of this
nucleus is expected to impact $^{197}$Au+$^{197}$Au collision experiments at
ultrarelativistic energy.
