  The E1 strength function for 15 stable and unstable Sn even-even isotopes
from A=100 till A=176 are calculated using the self-consistent microscopic
theory which, in addition to the standard (Q)RPA approach, takes into account
the single-particle continuum and the phonon coupling. Our analysis shows two
distinct regions for which the integral characteristics of both the giant and
pygmy resonances behave rather differently. For neutron-rich nuclei, starting
from $^{132}$Sn, we obtain a giant E1 resonance which significantly deviates
from the widely-used systematics extrapolated from experimental data in the
$\beta$-stability valley. We show that the inclusion of the phonon coupling is
necessary for a proper description of the low-energy pygmy resonances and the
corresponding transition densities for $A<$132 nuclei, while in the $A>132$
region the influence of phonon coupling is significantly smaller. The radiative
neutron capture cross sections leading to the stable $^{124}$Sn and unstable
$^{132}$Sn and $^{150}$Sn nuclei are calculated with both the (Q)RPA and the
beyond-(Q)RPA strength functions and shown to be sensitive to both the
predicted low-lying strength and the phonon coupling contribution. The
comparison with the widely-used phenomenological Generalized Lorentzian
approach shows considerable differences both for the strength function and the
radiative neutron capture cross section. In particular, for the neutron-rich
$^{150}$Sn, the reaction cross section is found to be increased by a factor
greater than 20. We conclude that the present approach may provide a complete
and coherent description of the $\gamma$-ray strength function for astrophysics
applications. In particular, such calculations are highly recommended for a
reliable estimate of the electromagnetic properties of exotic nuclei.
