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The $\gamma$-ray strength functions (GSF) and nuclear level densities (NLD)below the neutron threshold have been extracted for $^{111-113,116-122,124}$Snfrom particle-$\gamma$ coincidence data with the Oslo method. The evolution ofbulk properties of the low-lying electric dipole response has been investigatedon the basis of the Oslo GSF data and results of a recent systematic study ofelectric and magnetic dipole strengths in even-even Sn isotopes withrelativistic Coulomb excitation. The obtained GSFs reveal a resonance-like peakon top of the tail of the isovector giant dipole resonance, centered at$\approx$8 MeV and exhausting $\approx$2\% of the classical Thomas-Reiche-Kuhn(TRK) sum. In contrast to predictions of the relativistic quasiparticlerandom-phase and time-blocking approximation calculations (RQRPA and RQTBA), nomonotonous increase in the total low-lying $E1$ strength was observed in theexperimental data from $^{111}$Sn to $^{124}$Sn, demonstrating rather similarstrength distributions in these nuclei. The Oslo GSFs and NLDs were furtherused as inputs to constrain the cross sections and Maxwellian-averaged crosssections of $(n,\gamma)$ reactions in the Sn isotopic chain using TALYS. Theobtained results agree well with other available experimental data and therecommended values from the JINA REACLIB, BRUSLIB, and KADoNiS libraries.Despite relatively small exhausted fractions of the TRK sum rule, the low-lyingelectric dipole strength makes a noticeable impact on the radiativeneutron-capture cross sections in stable Sn isotopes. Moreover, theexperimental Oslo inputs for the $^{121,123}$Sn$(n,\gamma)$$^{122,124}$Snreactions were found to affect the production of Sb in the astrophysical$i$-process, providing new constraints on the uncertainties of the resultingchemical abundances from multi-zone low-metallicity Asymptotic Giant Branchstellar models.

Systematic study of the low-lying electric dipole strength in Sn isotopes and its astrophysical implications