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

The stability of the linear chain structure of three ff clusters for 12C against the bending and fi ssion 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 ff initial con fi guration, it is found that the linear chain structure is stable when the rotational frequency is within the range of 2.0- 2.5 MeV. Beyond this range, the fi nal states are not stable against fi ssion. By examining the density distributions and the occupation of single-particle levels, however, these fi ssions 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 3.5 MeV, but the fi ssion still occurs when the rotational frequency approaches 4.0 MeV.