  Low-lying electric-dipole ($E1$) strength of a neutron-rich nucleus contains
information on neutron-skin thickness, deformation, and shell evolution. We
discuss the possibility of making use of total reaction cross sections on
$^{40}$Ca, $^{120}$Sn, and $^{208}$Pb targets to probe the $E1$ strength of
neutron-rich Ca, Ni, and Sn isotopes. They exhibit large enhancement of the
$E1$ strength at neutron number $N > 28$, $50$, and $82$, respectively, due to
a change of the single-particle orbits near the Fermi surface participating in
the transitions. The density distributions and the electric-multipole strength
functions of those isotopes are calculated by the Hartree-Fock+BCS and the
canonical-basis-time-dependent-Hartree-Fock-Bogoliubov methods, respectively,
using three kinds of Skyrme-type effective interaction. The nuclear and Coulomb
breakup processes are respectively described with the Glauber model and the
equivalent photon method in which the effect of finite-charge distribution is
taken into account. The three Skyrme interactions give different results for
the total reaction cross sections because of different Coulomb breakup
contributions. The contribution of the low-lying $E1$ strength is amplified
when the low-incident energy is chosen. With an appropriate choice of the
incident energy and target nucleus, the total reaction cross section can be
complementary to the Coulomb excitation for analysing the low-lying $E1$
strength of unstable nuclei.
