Cluster structures in $^{12}$C from global energy density functionals

TL;DR

This paper employs a global energy density functional approach within a beyond mean-field framework to analyze the cluster structures and spectroscopic properties of low-lying states in carbon-12, achieving results comparable to specialized microscopic models.

Contribution

It introduces a relativistic EDF-based microscopic method that successfully describes cluster structures and spectroscopic features in $^{12}$C, including the Hoyle state, using symmetry projection and configuration mixing.

Findings

Successfully reproduces main spectroscopic features of $^{12}$C

Achieves reasonable agreement with experimental form factors

Provides a unified microscopic description comparable to cluster models

Abstract

Spectroscopic properties of low-lying states and cluster structures in $^{12}$C are analyzed in a "beyond mean-field framework" based on global energy density functionals (EDFs). To build symmetry-conserving collective states, axially-symmetric and reflection-asymmetric solutions of the relativistic Hartree-Bogoliubov equations are first projected onto good values of angular momentum, particle number, and parity. Configuration mixing is implemented using the generator coordinate method formalism. It is shown that such a global microscopic approach, based on a relativistic EDF, can account for the main spectroscopic features of $^{12}$C, including the ground-state and linear-chain bands as well as, to a certain approximation, the excitation energy of the Hoyle state. The calculated form factors reproduce reasonably well the available experimental values, and display an accuracy comparable to that of dedicated microscopic cluster models.