Conclusions

This work contains the theoretical analysis of particle and pairing densities in neutron-rich nuclei and their dependence on the choice of pairing interaction. The main goal was to see the effect of pairing on spatial characteristics of nucleonic densities of nuclei far from stability, where the closeness of the particle continuum qualitatively changes the physical situation.

The main conclusion of our work is that, due to the self-consistent feedback between particle and pairing densities, the size of the neutron halo is strongly influenced by pairing correlations; hence by the pairing parametrization assumed. Consequently, experimental studies of neutron distributions in nuclei are extremely important for determining the density dependence of pairing interaction in nuclei. Our analysis suggests that the strong low-density dependence of the pairing force, simulated by taking very small values of $\alpha$ in DDDI, is unphysical. Therefore, predictions of very large halos in drip-line nuclei, obtained with $\alpha$=1/6 [24], should probably be revisited when more reliable information on pairing forces becomes available. The present experimental data are consistent with 1/2<$\alpha$<1. In this context, it is interesting to note that excellent fits to the data were obtained in Refs. [15,16] by taking $\alpha$=2/3. However, at present there is no theoretical argument why the density dependence should be even taken in a form of the power law. Clearly, a more precise determination of the density dependence (including the isovector dependence) is a challenging task for future theoretical work.

The authors would like to thank Jerry D. Garrett for many inspirational discussions on nuclear structure, nuclear pairing, and exotic nuclei. Jerry devoted a significant part of his scientific life to the question of pairing correlations and their manifestations in nuclear spectroscopy [31,32] and to new exciting physics brought by the development of radioactive beams [33]. Jerry was our close collaborator and a wonderful friend. We miss him dearly.

This research was supported in part by the U.S. Department of Energy under Contract Nos. DE-FG02-96ER40963 (University of Tennessee), DE-FG05-87ER40361 (Joint Institute for Heavy Ion Research), DE-AC05-00OR22725 with UT-Battelle, LLC (Oak Ridge National Laboratory), the Polish Committee for Scientific Research (KBN), and by the Bundesministerium für Bildung und Forschung (BMBF), Project No. 06 ER 808. We thank the Institute for Nuclear Theory at the University of Washington for its hospitality and the Department of Energy for partial support during the completion of this work.