Systematic study of deformed nuclei at the drip lines and beyond

Abstract

An improved prescription for choosing a transformed harmonic oscillator (THO) basis for use in configuration-space Hartree-Fock-Bogoliubov (HFB) calculations is presented. The new HFB+THO framework that follows accurately reproduces the results of coordinate-space HFB calculations for spherical nuclei, including those that are weakly bound. Furthermore, it is fully automated, facilitating its use in systematic investigations of large sets of nuclei throughout the periodic table. As a first application, we have carried out calculations using the Skyrme Force SLy4 and volume pairing, with exact particle number projection following application of the Lipkin-Nogami prescription. Calculations were performed for all even-even nuclei from the proton drip line to the neutron drip line having proton numbers Z = 2, 4, . . . , 108 and neutron numbers N = 2, 4, . . . , 188. We focus on nuclei near the neutron drip line and find that there exist numerous particle-bound even-even nuclei (i.e., nuclei with negative Fermi energies) that have at the same time negative two-neutron separation energies. This phenomenon, which was earlier noted for light nuclei, is attributed to bound shape isomers beyond the drip line.

Axially deformed solution of the Skyrme–Hartree–Fock–Bogolyubov equations using the transformed harmonic oscillator basis. The program HFBTHO (v1.66p)

“…Several examples of deformed HFBTHO calculations, recently implemented on parallel computers, are given in Ref. [23]. By creating a simple load-balancing routine that allows one to scale the problem to 200 processors, it was possible to calculate the entire deformed even-even nuclear mass table in a single 24 wall-clock hour run (or approximately 4,800 processor hours).…”

“…In the code HFBTHO (v1.66p), function f (R) is chosen as in Ref. [23]. It transforms the incorrect Gaussian asymptotic behavior of deformed HO wave functions into the correct exponential form.…”

“…Recently, a new prescription for choosing the THO basis has been proposed and employed in self-consistent large-scale calculations [23]. For a given nucleus, the new prescription requires as input the results from a relatively simple HFB+HO calculation, with no variational optimization.…”

Nuclear energy density optimization: Large deformations

“…A cut-off of E cut = 60 MeV was used to truncate the quasi-particle space [36]. To prevent the collapse of pairing, we used the Lipkin-Nogami procedure according to [37].…”

Cluster formation and the virial equation of state of low-density nuclear matter

“…We note that the equation of state calculation of Buchler and Coon [19] is close in strategy to the virial equation of state, but it takes into account Pauli blocking on the phase shifts and thus uses a model NN interaction. Moreover, there are a variety of Skyrme-type [20,21,22] and relativistic mean-field [23,24,25] parametrizations of the nuclear energy functional, which are used to calculate ground-state energies and densities of intermediate-mass and heavy nuclei. However, it is not clear what form to take for the energy functional for a gas of nucleons at low densities, where the system forms clusters and the binding energy per nucleon is density-independent with E/A ≈ −16 MeV.…”