SELF-CONSISTENT MASS TABLE

Self-consistent methods based on density-dependent effective interactions have achieved a level of sophistication and precision which allows analyses of experimental data for a wide range of properties and for arbitrarily heavy nuclei. For instance, a self-consistent deformed mass table has been recently developed [14,15] based on the Skyrme energy functional. The resulting rms error on binding energies of 1700 nuclei is around 700 keV, i.e., is comparable with the agreement obtained in the shell-correction approaches.

Such calculations require a simultaneous description of p-h, pairing, and continuum effects - the challenge that only very recently could be addressed by mean-field methods. Very recently we have developed methods [16,17,18] to approach the problem of large-scale deformed HFB calculations by using the local-scaling point transformation that allows us to modify asymptotic properties of the deformed harmonic oscillator wave functions. Such calculations can be optimized to take advantage of parallel computing. (For example, it takes only one day to calculate the full self-consistent even-even mass table considering prolate, oblate, and spherical shapes!) This enables theorists to optimize effective interactions by adjusting their parameters to experimental binding energies and other observables. While the results of calculations of a complete HFB mass table will be reported in separate publications [18], Fig. 3 shows the calculated deformations $\vert\beta\vert$ for 1553 particle-bound even-even nuclei with Z$\leq$108 and N$\leq$188 obtained with the SLy4 Skyrme interaction and the intermediate-type pairing force (2).

  

Figure 3: Ground-state quadrupole deformations $\vert\beta\vert$obtained in large-scale deformed HFB calculations for particle-bound even-even nuclei with Z$\leq$108 and N$\leq$188. To produce such a mass/deformation table, it takes only one day on a modern parallel computer.

As one can see, there are several deformed regions around the neutron drip line where theory predicts significant deformations; hence the presence of rotational collectivity. The calculations also predict a very interesting effect of long sequences of semi-magic nuclei (e.g., Z=50 and N=82) intruding in the territory of unbound nuclei. This is the result of vanishing pairing correlations, for which the Fermi energy coincides with the last occupied level, while in the neighboring nuclei it is located higher.