Structure of even-even nuclei using a mapped collective Hamiltonian and the D1S Gogny interaction

Abstract

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 R42=E(41+)/E(21+) 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 γ and β excitations, and the energies of the 2+ γ vibrations accord well with experiment. The character of the 02+ state is interpreted as shape coexistence or β-vibrational excitations on the basis of relative quadrupole transition strengths. Bands are predicted with the properties of β vibrations for many nuclei having R42 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]

Testing Skyrme energy-density functionals with the quasiparticle random-phase approximation in low-lying vibrational states of rare-earth nuclei

“…And overall, neither of the QRPA calculations is as good as that of Ref. [54]. Figure 3 shows E2 transition strengths B(E2; 0 + gs → 2 + γ ), hereafter denoted B(E2) ↑, for the same isotopes.…”

“…Energies and transition strengths Figure 2 shows measured γ-vibration energies alongside the results of our two QRPA calculations and a collective-model calculation (with parameters determined from the Gogny energy functional) by Delaroche et al [54]. In all the plots the minimum energy occurs around A=162.…”

“…and [54] are not published. We include only those experimental data that are labeled γ-vibrations in Ref.…”

Breaking of axial symmetry in excited nuclei as identified in experimental data

“…A recent constrained HFB calculation using the Gogny D1S interaction by Delaroche et al [5] indicates broken axial symmetry for a large number of nuclei across the table of isotopes. A clustering of values around Q 0 ≈ 200fm 2 and cos (3γ ) ≈ 0.2 is a result of this calculation where in some cases the values including the predicted standard deviation do not include γ = 0 • i.e., cos (3γ ) = 1.…”

Fragment Yields Calculated in a Time-Dependent Microscopic Theory of Fission

“…Microscopic methods, where the nucleus is described starting from protons, neutrons, and an effective interaction between them, have been used to calculate a plethora of nuclear properties (see, e.g., [1,2,3] and references therein). Nuclear fission in particular, has been studied using microscopic approaches since the 1980's (e.g., [4,6,7,5,8]).…”