Stability of the linear chain structure for $^{12}$C in covariant density functional theory on a 3D lattice

TL;DR

This study investigates the stability of the linear chain structure of three alpha clusters in carbon-12 using covariant density functional theory on a 3D lattice, revealing stability within specific rotational frequencies and addressing unphysical continuum effects.

Contribution

The paper introduces a damping function to remove unphysical continuum states in cranking covariant density functional theory, extending the understanding of linear chain stability in $^{12}$C.

Findings

Linear chain structure stable at rotational frequencies 2.0-2.5 MeV

Unphysical continuum occupation causes fission at higher frequencies

Stable linear chain persists up to about 3.5 MeV rotational frequency

Abstract

The stability of the linear chain structure of three $\alpha$ clusters for $^{12}$C against the bending and fission is investigated in the cranking covariant density functional theory, in which the equation of motion is solved on a 3D lattice with the inverse Hamiltonian and the Fourier spectral methods. Starting from a twisted three $\alpha$ initial configuration, it is found that the linear chain structure is stable when the rotational frequency is within the range of $\sim$2.0 MeV to $\sim$2.5 MeV. Beyond this range, the final states are not stable against fission. By examining the density distributions and the occupation of single-particle levels, however, these fissions are found to arise from the occupation of unphysical continuum with large angular momenta. To properly remove these unphysical continuum, a damping function for the cranking term is introduced. Eventually, the stable linear chain structure could survive up to the rotational frequency $\sim$3.5 MeV, but the fission still occurs when the rotational frequency approaches to $\sim$4.0 MeV.