β-decay studies approaching the N=20 island of inversion with a new shell-model Hamiltonian

β-decay properties of N=18-22, Z=10-14 nuclei are analyzed with a new shell-model Hamiltonian using the Gogny density-dependent interaction. The Gogny force which has been widely and successfully used in mean-field theory can provide reasonable two-body matrix elements for cross-shell calculations. The log ft values and β-decay level schemes are systematically studied using the D1S-Gogny interaction and compared with the SDPF-M results and experimental data. It is shown that the new Hamiltonian provides reliable results for β-decay along with subtle level schemes for this region. Shell-model calculations with Gogny interaction can lead to a successful description of nuclei in and around the N=20 island of inversion and supplements experiment where sufficient data are not available.