Deformation of drip-line nuclei

Deformation of nuclei near the drip lines is a difficult and open problem in nuclear structure physics. It requires a simultaneous description of particle-hole, pairing, and continuum effects -- the challenge that only very recently can be addressed by mean-field methods. Deformability of nuclei plays a decisive role in determining particle separation energies and decay rates, and hence is crucial for a description of nuclear processes in a stellar environment.

Very recently we have developed methods [25,26] to approach this problem by using the local-scaling point transformation that allows us to modify asymptotic properties of the deformed harmonic oscillator wave functions. The resulting single-particle bases are very well suited for solving the HFB equations for deformed drip-line nuclei.

Calculations of a complete HFB mass table are now in progress and will be reported in separate publications [27,28]. Here we only show a sample of the results obtained for the SLy4 Skyrme interaction and the intermediate-type pairing force (15). A rather restricted size of the harmonic oscillator basis, limited to $N_{\mbox{\scriptsize {sh}}}$=14 spherical shells, was used, while the continuum states were included up to 60MeV. Figure 5 shows the two-neutron separation energies (top panel), the neutron pairing gaps (middle panel), and the deformations $\beta$ (bottom panel) for 1553 particle-bound even-even nuclei with Z$\leq$108 and N$\leq$188.

At the two-neutron drip line, one can see a very interesting effect of negative two-neutron separation energies for particle-bound (negative Fermi energy) nuclei. This is the result of a sudden change in configuration when approaching the drip line, that is caused by the fact that the ground-state configuration may become particle-unbound earlier than the excited one [25,27]. A similar effect occurs also in the heavy proton drip-line nuclei, where sequences of oblate ground states are obtained. Another effect at the proton drip line is related to long sequences of proton-magic (e.g., Z=50 and 82) isotopes intruding in the territory of unbound nuclei. This is the result of the vanishing pairing correlations, for which the proton Fermi energy coincides with the last occupied level, while in the neighboring nuclei it is located higher.

This research was supported in part by the U.S. Department of Energy underContractNos.DE-FG02-96ER40963 (University of Tennessee) and DE-AC05-00OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory), by the Polish Committee for Scientific Research (KBN) under Contract No. 5 P03B 014 21, and by computational grants from the Regionales Hochschulrechenzentrum Kaiserslautern (RHRK) Germany, European Center for Theoretical Studies (ECT*) in Trento, Italy, and Interdisciplinary Centre for Mathematical and Computational Modeling (ICM) of Warsaw University.