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The E1 strength function for 15 stable and unstable Sn even-even isotopesfrom A=100 till A=176 are calculated using the self-consistent microscopictheory which, in addition to the standard (Q)RPA approach, takes into accountthe single-particle continuum and the phonon coupling. Our analysis shows twodistinct regions for which the integral characteristics of both the giant andpygmy resonances behave rather differently. For neutron-rich nuclei, startingfrom $^{132}$Sn, we obtain a giant E1 resonance which significantly deviatesfrom the widely-used systematics extrapolated from experimental data in the$\beta$-stability valley. We show that the inclusion of the phonon coupling isnecessary for a proper description of the low-energy pygmy resonances and thecorresponding transition densities for $A<$132 nuclei, while in the $A>132$region the influence of phonon coupling is significantly smaller. The radiativeneutron 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 thebeyond-(Q)RPA strength functions and shown to be sensitive to both thepredicted low-lying strength and the phonon coupling contribution. Thecomparison with the widely-used phenomenological Generalized Lorentzianapproach shows considerable differences both for the strength function and theradiative neutron capture cross section. In particular, for the neutron-rich$^{150}$Sn, the reaction cross section is found to be increased by a factorgreater than 20. We conclude that the present approach may provide a completeand coherent description of the $\gamma$-ray strength function for astrophysicsapplications. In particular, such calculations are highly recommended for areliable estimate of the electromagnetic properties of exotic nuclei.

Self-consistent calculations of the strength function and radiative neutron capture cross section for stable and unstable tin isotopes