Concluding Remarks

In this paper, we have reported the development of an improved version of the configuration-space HFB method expanded in a transformed harmonic oscillator basis. In its current form, the method can be used reliably in systematic studies of wide ranges of nuclei, both spherical and axially deformed, extending all the way out to the nucleon drip lines. The key step was the development of a prescription for choosing a reliable transformation function to define the THO basis that does not require variational optimization. The current prescription only involves information from a preliminary configuration-space HFB calculation carried out in a harmonic oscillator basis. The transformation function is then tailored to correct the asymptotic properties of the HFB+HO results. The resulting HFB+THO theory accurately reproduces results of coordinate-space HFB theory, where available, and also reproduces the results obtained with an earlier version of the transformation that had to be optimized separately for each nucleus.

As a first application of the new HFB+THO methodology, we carried out a systematic study of all even-even nuclei having $Z$$\leq$108 and $N$$\leq$188. Variation after particle-number projection was approximately included using the Lipkin-Nogami method, with exact projection performed for the final self-consistent solutions. We focussed our discussion on those nuclei that are very near the nucleon drip lines, finding that in several regions of the periodic table there exist nuclei that are stable against one-particle emission but unstable against pair emission. We showed that invariably this is associated with a shape change in the ground state. For example, while two-particle emission to the configuration of the daughter with the same shape as the parent is forbidden, a decay to the ground state having a different shape can nevertheless occur. The associated change in shape may conceivably lead to sufficient hindrance of the decay, hence the longer lifetime. Consequently, it is conceivable that there exist nuclei that formally live beyond the neutron drip line but can be observed experimentally. This phenomenon, which had earlier been noted in calculations of light nuclei, is now seen to be a more common feature of nuclei near the neutron drip line.

In the description of very weakly-bound systems, small changes in the results can have important consequences, changing for example the precise locations of the drip lines. It is important, therefore, to continue to improve the current HFB+THO methodology to accommodate effects not presently being included. Particularly important could be effects that arise beyond mean field. It is also important to develop the new HFB+THO formalism for application to odd-mass systems, including the effects of Pauli blocking. But most crucial, in our opinion, is to develop new-generation energy density functionals that will allow for more reliable predictions of the properties of exotic nuclei. Work along these various lines is currently underway.