We use the quasiparticle random phase approximation with a few Skyrme density functionals to calculate strength functions in the J π = 0 + , 1 − , and 2 + channels for even Ca, Ni, and Sn isotopes, from the proton drip line to the neutron drip line. We show where and how low-lying strength begins to appear as N increases. We also exhibit partial energy-weighted sums of the transition strength as functions of N for all nuclei calculated, and transition densities for many of the interesting peaks.We find that low-energy strength increases with N in all multipoles, but with distinctive features in each. The low-lying 0 + strength near the neutron at large N barely involves protons at all, with the strength coming primarily from a single two-quasineutron configuration with very large spatial extent. The low-lying 1 − strength is different, with protons contributing to the transition density in the nuclear interior together with neutrons at large radii. The low-lying 2 + transition strength goes largely to more localized states. The three Skyrme interactions we test produce similar results, differing most significantly in their predictions for the location of the neutron drip line, the boundaries of deformed regions, energies of and transition strengths to the lowest 2 + states between closed shells, and isovector energy-weighted sum rules.
We present Hartree-Fock-Bogoliubov (HFB) calculations of the ground states of even Mg isotopes. A Skyrme force is used in the mean field channel and a density-dependent zero-range force in the pairing channel. 40 Mg and 20 Mg are predicted to be at the two-neutron and two proton drip-lines respectively. A detailed study of the quadrupole deformation properties of all the isotopes shows that the ground states of 36,38,40 Mg are strongly deformed with significantly different deformations for the neutrons and protons. Our study supports the disappearance of the N = 28 shell gap in the Mg and Si isotopes. : Nuclei far from stability; Hartree-Fock Bogoliubov method for deformed nuclei; S 2n iand quadrupole moments for Mg isotopes.
We use the canonical Hartree-Fock-Bogoliubov basis to implement a completely self-consistent quasiparticle-random-phase approximation with arbitrary Skyrme energy density functionals and density-dependent pairing functionals. The point of the approach is to accurately describe multipole strength functions in spherical even-even nuclei, including weakly-bound drip-line systems. We describe the method and carefully test its accuracy, particularly in handling spurious modes. To illustrate our approach, we calculate isoscalar and isovector monopole, dipole, and quadrupole strength functions in several Sn isotopes, both in the stable region and at the drip lines.phase approximation (RPA) or QRPA are usually carried out in coordinate space, facilitating treatment of decay channels and guaranteeing correct asymptotics. Surprisingly, as we discuss below, the rich literature on the RPA and QRPA, which includes many coordinate-space calculations, contains few treatments of the continuum that exploit the entire Skyrme functional in a fully self-consistent way.To avoid confusion, we state what we mean by a fully self-consistent RPA or QRPA calculation. First, the underlying mean-field calculation must be self-consistent in the usual sense. Next, the residual interaction used in the RPA or QRPA must be derived from the same force or energy functional that determines the mean field. An important consequence of this condition, and of other more detailed technical conditions discussed below, is that spurious excitations arising from symmetry breaking by the mean field have zero or nearly zero energy, leaving the physical intrinsic excitations completely uncontaminated by spurious motion. Finally, energy-weighted sum rules must be satisfied to high accuracy. We elaborate on these requirements below; Refs. [9, 10, 11] discuss ways in which RPA calculations commonly violate them.The literature applying RPA or QRPA to nuclear structure is huge, and a complete review is beyond the scope of our paper. We do, however, present an overview of the studies that are related in one way or another to nuclear density functionals, self consistency, pairing, and the key issue of the particle continuum.The standard version of QRPA, the so-called matrix formulation, is carried out in the configuration space [12, 13] of single-quasiparticle states. A number of papers treat collective states in spherical nuclei in the Skyrme-RPA and QRPA matrix formulation (see Refs. [13,14] and references cited therein), in which the positive-energy continuum is discretized, e.g. by solving the Hartree-Fock-Bogoliubov (HFB) and QRPA equations in a harmonic-oscillator singleparticle basis. Within this group, the first fully self-consistent calculations that properly account for continuum effects are those of Refs. [15,16], in which the localized canonical basis of coordinate-space HFB is used to calculate betadecay rates of neutron-rich r-process nuclei and Gamow-Teller strength distributions. Recently, fully self-consistent HFB+QRPA calculations have also been carr...
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.
hi@scite.ai
10624 S. Eastern Ave., Ste. A-614
Henderson, NV 89052, USA
Copyright © 2024 scite LLC. All rights reserved.
Made with 💙 for researchers
Part of the Research Solutions Family.