Nuclear mean field on and near the drip lines

We discuss two subjects related to the structure of nuclei near the drip lines. The first is the vanishing of N=20 magic structure in Z<<N=20 nuclei. Large-scale state-of-the-art shell-model calculations with 2s1d and lower 2p1f shells are shown to present a unified description of N=20 isotones with Z=10-20, covering both stable and unstable nuclei. The calculations demonstrate that, although the N=20 closed-shell structure remains for Z≥14, the N=20 closed-shell structure vanishes naturally towards nuclei with Z≤12, giving rise to various anomalous features including those in 32Mg and 31Na. It is suggested that, in these nuclei, the deformed mean field overcomes the shell gap created by the spherical mean potential. Furthermore, the almost perfect agreement with a recent experiment is presented for the B(E2; 0+1→2+1) value of 32Mg. The second part is devoted to the mean field for loosely bound neutrons. The variational shell model (VSM) is explained with an application to the anomalous ground state of 11Be. The VSM has been proposed recently to describe the structure of neutron-rich unstable nuclei. Contrary to the failure of spherical Hartree-Fock, the anomalous 1/2+ ground state and its neutron halo are reproduced with Skyrme SIII interaction. This state is bound due to dynamical coupling between the core and the loosely bound neutron which oscillates between 2s1/2 and 1d5/2 orbits. The direct neutron capture is discussed briefly in its relation to the neutron halo. (orig.)