  We use the quasiparticle random phase approximation with a few Skyrme density
functionals to calculate strength functions in the Jpi = 0+, 1-, and 2+
channels for even Ca, Ni, and Sn isotopes, from the proton drip line to the
neutron drip line. We show where and how low-lying strength begins to appear as
N increases. We also exhibit partial energy-weighted sums of the transition
strength as functions of N for all nuclei calculated, and transition densities
for many of the interesting peaks. We find that low-energy strength increases
with N in all multipoles, but with distinctive features in each. The low-lying
0+ strength near the neutron at large N barely involves protons at all, with
the strength coming primarily from a single two-quasineutron configuration with
very large spatial extent. The low-lying 1- strength is different, with protons
contributing to the transition density in the nuclear interior together with
neutrons at large radii. The low-lying 2+ transition strength goes largely to
more localized states. The three Skyrme interactions we test produce similar
results, differing most significantly in their predictions for the location of
the neutron drip line, the boundaries of deformed regions, energies of and
transition strengths to the lowest 2+ states between closed shells, and
isovector energy-weighted sum rules.
