In this paper, we have applied a local-scaling point transformation to the deformed three-dimensional Cartesian harmonic oscillator wave functions so as to allow for a modification of their unphysical asymptotic properties. In this way, we have obtained single-particle bases that remain infinite, discrete, and complete, but for which the wave functions have the asymptotic properties that are required by the canonical bases of Hartree-Fock-Bogoliubov theory. These bases preserve all the simplicity of the original harmonic-oscillator wave functions, and at the same time are amenable to very efficient numerical methods, such as Gauss-integration quadratures. They also allow for very simple calculations of local densities, which are at the core of self-consistent methods based on a Skyrme effective interaction.
The axial transformed harmonic oscillator basis has been implemented to achieve a fast and reliable method for solving the HFB equations with the correct asymptotic conditions. We have discussed several practical aspects of the implementation, like the treatment of pairing correlations, and tested the convergence and accuracy.
The formalism was developed for a general deformed transformed harmonic oscillator basis. Practical application within the configurational HFB formalism suggested a simplification to a purely spherical basis, however, as had been used in earlier calculations. We have nevertheless presented the general formalism because of its possible use in other applications.
As a first application of this new methodology, we have carried out HFB calculations using the SLy4 Skyrme force and a density-independent (volume) pairing force. The calculations were performed for the chain of even-Z Mg isotopes and for the light even-Z nuclei located near the two-neutron drip line. We have presented results for binding energies, quadrupole moments, and for the pairing properties of these nuclei.
Perhaps the most interesting outcome of our calculations is that nuclei that are formally beyond the two-neutron drip line, i.e., those with negative two-neutron separation energies, may have tangible half lives, provided (i) that they have localized ground states (negative Fermi energies), and (ii) their ground-state configurations are significantly different than those of the (daughter) nuclei with two less neutrons. According to our calculations, precisely such a situation occurs in the chains of isotopes with Z=10, 12, 14, 16 and 18. In these chains, the prolate configuration becomes unbound before (i.e., for a smaller neutron number) than the oblate configuration. That change in the ground state structure leads to negative two-neutron separation energies and thus to the exotic conditions given above.
This work has been supported in part by the Bulgarian National Foundation for
Scientific Research under project 
-809, by the Polish Committee for
Scientific Research (KBN) under Contract No. 2 P03B 040 14, by a computational
grant from the Interdisciplinary Centre for Mathematical and Computational
Modeling (ICM) of the Warsaw University, and by the National Science Foundation
under grant #s PHY-9600445, INT-9722810 and PHY-9970749.