1207.7099 (Gustav R. Jansen)

Spherical coupled-cluster theory for open-shell nuclei    [PDF]

Gustav R. Jansen

A microscopic description of nuclei is important to understand the nuclear shell-model from fundamental principles. This cannot be achieved without an effective approximation scheme, especially if three-nucleon forces are included. The purpose of thus article is to define and evaluate an approximation scheme that can be used to study nuclei that are described as two particles attached to a closed (sub-)shell nucleus. The equation-of-motion coupled-cluster formalism has been used to obtain ground and excited state energies. This method is based on the diagonalization of a non-Hermitian matrix obtained from a similarity transformation of the many-body nuclear Hamiltonian. A chiral interaction at the next-to-next-to-next-to leading order (n${}^3$lo) using a cutoff at 500 MeV was used. The ground state energies of ${}^6$Li and ${}^6$He were in good agreement with a no-core shell-model calculation using the same interaction. Several excited states were also produced with overall good agreement. Only the $J^\pi=3^+$ excited state in ${}^6$Li showed a sizeable deviation. The ground state energies of ${}^{18}$O, ${}^{18}$F and ${}^{18}$Ne were converged, but underbound compared to experiment. Also the calculated spectra were converged and comparable to both experiment and shell-model studies in this region. Some excited states in ${}^{18}$O were high or missing in the spectrum. Converged results were obtained for all nuclei and the method can be used to describe nuclear states with simple structure. Especially the ground state energies were very close to an exact diagonalization. To obtain a closer match with experimental data, effects of three-nucleon forces, the scattering continuum as well as additional configurations in the coupled-cluster approximations, are necessary.

View original: http://arxiv.org/abs/1207.7099