The shape of gold

Having a detailed theoretical knowledge of the low-energy structure of the heavy odd-mass nucleus $$^{197}\hbox {Au}$$ 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 at relativistic energies. In the present article, therefore, we report on new results on the structure of $$^{197}\hbox {Au}$$ 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 $$^{197}\hbox {Au}$$ 197 Au with in particular a good agreement for most of the spectroscopic properties of the $$3/2_1^+$$ 3 / 2 1 + ground state. From the collective wave function of the correlated state, we compute an average deformation $$\bar{\beta }(3/2_1^+)=0.13$$ β ¯ ( 3 / 2 1 + ) = 0.13 and $$\bar{\gamma }(3/2_1^+)=40^\circ $$ γ ¯ ( 3 / 2 1 + ) = 40 ∘ for the ground state. We use this result to construct an intrinsic shape of $$^{197}\hbox {Au}$$ 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 $$^{197}\hbox {Au}$$ 197 Au + $$^{197}\hbox {Au}$$ 197 Au collision experiments at ultrarelativistic energy.