  Nuclei at both the neutron- and proton-drip lines are studied. In the
cluster-core model, the halo-structure of all the observed and proposed cases
of neutron- or proton-halos is investigated in terms of simple potential energy
surfaces calculated as the sum of binding energies, Coulomb repulsion, nuclear
proximity attraction and the centrifugal potential for all the possible
cluster+core configurations of a nucleus. The clusters of neutrons and protons
are taken to be unbound, with additional Coulomb energy added for
proton-clusters. The model predictions agree with the available experimental
studies but show some differences with the nucleon separation energy
hypothesis, particularly for proton-halo nuclei. Of particular interest are the
halo-structures of $^{11}N$ and $^{20}Mg$. The calculated potential energy
surfaces are also useful to identify the new magic numbers and molecular
structures in exotic nuclei. In particular, N=6 is a possible new magic number
for very neutron-deficient nuclei, but Z=N=2 and Z=8 seem to remain magic even
for such nuclei, near the drip line.
