3D solution of Hartree-Fock-Bogoliubov equations for drip-line nuclei

Abstract

We investigate the possibility of describing triaxial quadrupole deformations for nuclei close to the two-neutron drip line by the Hartree-Fock Bogoliubov method taking into account resonances in the continuum. We use a Skyrme interaction to describe the HarteeFock hamiltonian and a density-dependent zero-range interaction to evaluate the pairing field. The mean-field equations are solved in a three-dimensional cubic mesh. We study the stability of the two-neutron separation energies and of the description of the nuclear surface as a function of the number of active mean-field orbitals and of the size of the mesh. The even Ni isotopes are used as a test case and the accuracy as a function of quadrupole deformation is studied by performing constrained calculations. A first application to the study of the two-neutron separation energies in Ni isotopes up to the drip line is presented.

Symmetry-unrestricted Skyrme–Hartree–Fock–Bogoliubov calculations for exotic shapes in nuclei from 64Ge to 84Mo

“…For convenience, we here recapitulate the two basis method [13,14,16,17] adopted as the algorithm of our computer code. In this method, the imaginarytime evolution method is combined with a diagonalization of the HFB Hamiltonian matrix to construct the canonical basis.…”

“…For the pairing (particle-particle) channel, we use the density-dependent zero-range interaction [13,14,17,[23][24][25][26][27][28][29][30], which has been successful in describing, for instance, the odd-even staggering effects in charge radii,…”

“…Recently, Terasaki, Heenen, Flocard and Bonche [13,14] have removed the restriction of spherical symmetry in solving the coordinate-space Skyrme-HFB equations in order to investigate the possibility to get three-dimensional (3D) deformed solutions in neutron rich nuclei. In their works, a Skyrme interaction is used to describe the Hartree-Fock (HF) Hamiltonian while a density dependent zero-range interaction is used for the pairing channel.…”

“…Recently, on the basis of the Skyrme HF plus BCS calculations with no restriction on the nuclear shape, Takami, Yabana and Matsuo [21,22] suggested that the oblate ground state of 68 Se is extremely soft against the Y 33 triangular deformation, and that the low-lying "spherical" minimum coexisting with the prolate ground state in 80 Zr has the Y 32 tetrahedral shape. As the first application of a fully 3D, symmetry-unrestricted Skyrme HFB method with the use of the densitydependent, zero-range pairing interaction [13,14,17,[23][24][25][26][27][28][29][30], we investigate in this paper shape coexistence and possibility of non-axial octupole deformations in proton rich N = Z nuclei in the A = 64 − 84 region and examine the above predictions. These nuclei are especially interesting objects to study, since proton and neutron deformed shell effects act coherently and rich possibilities arise for coexistence and competition of different shapes (see [31] for earlier references).…”

Continuum linear response in coordinate space Hartree–Fock–Bogoliubov formalism for collective excitations in drip-line nuclei

“…The coordinate space HFB has been applied extensively and clarifying some aspects of pairing effects on the ground state properties including the halo and the skin [7,8,[10][11][12][13][14][15][16][17]. Descriptions of deformed exotic nuclei are also under current developments [18][19][20][21][22]. The coordinate space HFB has been also used together with the relativistic mean-field models [23][24][25].…”