The density-dependent finite-range Gogny force has been used to derive the effective Hamiltonian for the shell-model calculations of nuclei. The density dependence simulates an equivalent three-body force, while the finite range gives a Gaussian distribution of the interaction in the momentum space and hence leads to an automatic smooth decoupling between low-momentum and high-momentum components of the interaction, which is important for finite-space shell-model calculations. Two-body interaction matrix elements, single-particle energies, and the core energy of the shell model can be determined by the unified Gogny force. The analytical form of the Gogny force is advantageous to treat cross-shell cases, while it is difficult to determine the cross-shell matrix elements and single-particle energies using an empirical Hamiltonian by fitting experimental data with a large number of matrix elements. In this paper, we have applied the Gogny-force effective shell-model Hamiltonian to the $p$- and $sd$-shell nuclei. The results show good agreements with experimental data and other calculations using empirical Hamiltonians. The experimentally known neutron drip line of oxygen isotopes and the ground states of typical nuclei ${}^{10}\mathrm{B}$ and ${}^{18}\mathrm{N}$ can be reproduced, in which the role of three-body force is non-negligible. The Gogny-force-derived effective Hamiltonian has also been applied to the cross-shell calculations of the $sd\text{−}pf$ shell.

• Received 4 September 2018
• Revised 6 October 2018

DOI:https://doi.org/10.1103/PhysRevC.98.044320