A systematic study of low energy nuclear structure at normal deformation is carried out using the Hartree-Fock-Bogoliubov theory extended by the generator coordinate method and mapped onto a five-dimensional collective quadrupole Hamiltonian. Results obtained with the Gogny D1S interaction are presented from drip line to drip line for even-even nuclei with proton numbers $Z=10$ to $Z=110$ and neutron numbers $N⩽200$. The properties calculated for the ground states are their charge radii, two-particle separation energies, correlation energies, and the intrinsic quadrupole shape parameters. For the excited spectroscopy, the observables calculated are the excitation energies and quadrupole as well as monopole transition matrix elements. We examine in this work the yrast levels up to $J=6$, the lowest excited $0^{+}$ states, and the two next yrare $2^{+}$ states. The theory is applicable to more than $90\%$ of the nuclei that have tabulated measurements. We assess its accuracy by comparison with experiments on all applicable nuclei where the systematic tabulations of the data are available. We find that the predicted radii have an accuracy of $0.6\%$, much better than can be achieved with a smooth phenomenological description. The correlation energy obtained from the collective Hamiltonian gives a significant improvement to the accuracy of the two-particle separation energies and to their differences, the two-particle gaps. Many of the properties depend strongly on the intrinsic deformation and we find that the theory is especially reliable for strongly deformed nuclei. The distribution of values of the collective structure indicator $R_{42}=E(4_1^{+})/E(2_1^{+})$ has a very sharp peak at the value 10/3, in agreement with the existing data. On average, the predicted excitation energy and transition strength of the first $2^{+}$ excitation are $12\%$ and $22\%$ higher than experiment, respectively, with variances of the order of $40–50\%$. The theory gives a good qualitative account of the range of variation of the excitation energy of the first excited $0^{+}$ state, but the predicted energies are systematically $50\%$ high. The calculated yrare $2^{+}$ states show a clear separation between $\gamma$ and $\beta$ excitations, and the energies of the $2^{+}$ $\gamma$ vibrations accord well with experiment. The character of the $0_2^{+}$ state is interpreted as shape coexistence or $\beta$-vibrational excitations on the basis of relative quadrupole transition strengths. Bands are predicted with the properties of $\beta$ vibrations for many nuclei having $R_{42}$ values corresponding to axial rotors, but the shape coexistence phenomenon is more prevalent. The data set of the calculated properties of 1712 even-even nuclei, including spectroscopic properties for 1693 of them, are provided in CEA Web site and EPAPS repository with this article [1].

• Received 22 September 2009

DOI:https://doi.org/10.1103/PhysRevC.81.014303