The shape of gold

TL;DR

This paper provides a detailed theoretical analysis of the low-energy structure of the heavy odd-mass nucleus $^{197}$Au using advanced energy density functional calculations, offering insights into its shape and implications for collider experiments.

Contribution

The study applies state-of-the-art multi-reference energy density functional methods to accurately describe $^{197}$Au's structure and shape, including triaxial deformation effects.

Findings

Good agreement with experimental spectroscopic data

Computed average deformation parameters for the ground state

Insights into the impact of triaxiality on collider experiments

Abstract

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.