One of the main avenues addressed by radioactive ion beams is the evolution of nuclear structure as a function of neutron-to-proton asymmetry. From a theoretical point of view, exotic nuclei far from stability offer a unique test of those components of effective interactions that depend on the isospin degrees of freedom. Since effective interactions in heavy nuclei have been adjusted to stable nuclei and to selected properties of infinite nuclear matter, it is by no means obvious that the isotopic trends far from stability, predicted by commonly used effective interactions, are correct. Such investigations reach inevitably into the regime of weakly bound nuclei, and these are much more difficult to treat theoretically than well-bound systems [1]. Their Fermi energy lies very close to zero, and the decay channels must be taken into account explicitly. Correlations due to pairing, core polarization, and clustering become crucial. In a drip-line system, the pairing interaction and the presence of skin excitations (soft modes) could require going beyond the picture of a nucleon moving in a single-particle orbit [2,3,4,5,6]. The positive aspect of this situation is that drip-line nuclei are also critical probes to understand and to further develop the nuclear pairing force.
Surprisingly, rather little is known about the basic properties of the pairing force. Up to now, the microscopic theory of the pairing interaction has only seldom been applied in realistic calculations for finite nuclei. A ``first-principle" derivation of the pairing interaction from the bare NN force still encounters many problems such as, e.g., treatment of core polarization [7,8]. Hence, phenomenological pairing interactions are usually introduced. In most older nuclear structure calculations, the pairing Hamiltonian has been approximated by the state-independent seniority pairing force, or schematic multipole pairing interaction [9]. Such oversimplified forces, usually treated by means of the BCS approximation, perform remarkably well when applied to nuclei in the neighborhood of the stability valley, but they are inappropriate (and formally wrong) when extrapolating far from stability. The self-consistent mean-field models have meanwhile reached such a high level of precision that one needed to improve on the pairing part of the model. The presently most up-to-date models employ local paring forces parametrized as contact interactions [10,11,2]. More flexible forms attach a density dependence to the pairing strength [12,13,14]. There exist even more elaborate forms which include also gradient terms [15,16]. It is clear that some density dependence is needed. Nuclear matter calculations and experimental data on isotope shifts strongly suggest that pairing is a surface phenomenon and that the pairing interaction should be maximal in the surface region. It is not so obvious, however, how the actual density dependence should be parametrized in detail [2]. This is why neutron-rich nuclei play such an important role in this discussion. Indeed, because of strong surface effects, the properties of these nuclei are sensitive to the density dependence of pairing. Last, but not least, a good understanding of pairing is important for astrophysical applications where exotic nuclei play a crucial role and where the nuclear pairing interaction is also important for theories of superfluidity in neutron stars [17].
The main objective of this work is to investigate the role of density dependence of pairing interaction on properties of neutron-rich nuclei. The material contained in this study is organized as follows. The definitions pertaining to self-consistent densities and mean fields and a specification of interactions are given in Sec. 2. The analysis of HFB densities and mean-field potentials obtained in different pairing models is given in Sec. 3. The results of self-consistent calculations for pairing gaps, separation energies, and halos are discussed in Sec. 4. Finally, Sec. 5 contains the main conclusions of this work.