Experimental study of the pygmy dipole resonance in the (p,p$'\gamma$) reaction on $^{124}$Sn and its evolution in the Sn isotopic chain

The present thesis makes a specific focus on the experimental study of the pygmy dipole resonance (PDR) in $^{124}$Sn and its evolution with increasing number of neutrons for the $^{116-119,121,122}$Sn and $^{124}$Sn isotopes studied at the Oslo Cyclotron Laboratory. Proton- coincidences data were measured in the (p,p$'\gamma$) reaction exploiting the primary beam of 16 MeV protons. The Oslo method was applied in order to extract the average characteristics of $^{124}$Sn, such as the $\gamma$-ray strength function and the level density. The external data from neutron resonance experiments were utilized for collecting the systematics on the level density and the average radiative width at the neutron separation energy. These systematics were subsequently used to constrain the slope and normalization of both extracted characteristics. Several approaches to the normalization procedure were tested, and all the $\gamma$-ray strengths extracted were found to be in good agreement within the estimated systematic and statistical uncertainties with the external data, obtained with different experimental techniques. A peak-like structure was observed in the strength at $\approx$6.5 MeV, and this was found to be in agreement with other experimental data. The total dipole response of a nucleus was reconstructed from E$_{\gamma}\approx$1.6 MeV up to $\approx$ 18 MeV in order to extract the bulk characteristics of the PDR mode, such as the energy centroid and integrated strength. Moreover, the present work contributes with the fraction of the Thomas-Reiche-Kuhn sum rule (TRK) exhausted by the PDR in the $^{124}$Sn isotope to the systematics, previously obtained at the Oslo Cyclotron Laboratory for the lighter tin isotopes. The fraction of the TRK sum rule, extracted for the $\gamma$-ray strength function obtained with the approach similar to that used for the lighter Sn isotopes, points at an almost constant fraction of the total dipole strength, attributed to the PDR. Furthermore, the alternative normalization of the $\gamma$-ray strength function, proposed in the present work, results in the largest fraction ($\approx$ 2%) for $^{124}$Sn among all Sn isotopes studied. In addition, the distinguished components of the PDR were found to be shifted towards lower $\gamma$-energies as compared to the lighter Sn isotopes. In addition, the qualitative test of the generalized Brink-Axel hypothesis was carried out by studying the extracted strengths as functions of various initial and final excitation energies. The strength was found to be independent of the initial excitation energy with the correction for observed Porter-Thomas fluctuations. The $\gamma$-ray strength functions feeding the ground and the first excited states were found to deviate strongly from an average strength, especially for the low $\gamma$-energies. Such deviation was assumed to stem from numerous reasons, and one of the reasons implies that the Brink-Axel hypothesis does not hold for these states