Statistical properties and photon strength functions of the <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi>Sn</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>112</mml:mn><mml:mo>,</mml:mo><mml:mn>114</mml:m

Here we report on the measurements of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mi>γ</a:mi></a:math>-ray strength functions and nuclear level densities of <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mmultiscripts><b:mi>Sn</b:mi><b:mprescripts/><b:none/><b:mrow><b:mn>112</b:mn><b:mo>,</b:mo><b:mn>114</b:mn></b:mrow></b:mmultiscripts></b:math> performed for the first time at the 9-MV Tandem accelerator facilities at Horia Hulubei Institute for Physics and Nuclear Engineering using the Oslo method. We extract thermodynamic properties and gross and fine properties of the pygmy dipole resonance for systematic comparison in the chain of Sn isotopes. The results are compared with microscopic models implemented in the TALYS reaction code and the fully microscopic quasiparticle-phonon model for the underlying nuclear structure of the dipole strength in <c:math xmlns:c="http://www.w3.org/1998/Math/MathML"><c:mmultiscripts><c:mi>Sn</c:mi><c:mprescripts/><c:none/><c:mrow><c:mn>112</c:mn><c:mo>,</c:mo><c:mn>114</c:mn></c:mrow></c:mmultiscripts></c:math>. The quasiparticle-phonon model results show the importance of complex configurations to the low-energy dipole response in the pygmy dipole resonance energy region. The experimental data are further included in the cross section and reaction rate calculations for the <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"><d:mrow><d:mo>(</d:mo><d:mi>n</d:mi><d:mo>,</d:mo><d:mi>γ</d:mi><d:mo>)</d:mo></d:mrow></d:math> reaction of the <e:math xmlns:e="http://www.w3.org/1998/Math/MathML"><e:mi>p</e:mi></e:math>-process nuclei <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mmultiscripts><f:mi>Sn</f:mi><f:mprescripts/><f:none/><f:mrow><f:mn>112</f:mn><f:mo>,</f:mo><f:mn>114</f:mn></f:mrow></f:mmultiscripts></f:math> showing a significant increase in reaction rates at high temperatures compared to existing nuclear databases.