Dipole excitations below the neutron separation threshold in neutron-rich Tin isotopes

Among the many ways to describe and predict the behaviour of a nucleus, we find the nuclear equation of state (EoS). This expression aims to account for the properties of nuclear matter from common run-off-the-mill nuclei, such as those found in nature, to neutron stars and nuclei far from stability synthesized in laboratories. Around the density nuclear matter would assume if it were infinite and constituted in equal parts by neutrons and protons, the nuclear equation of state can be expanded in a Taylor series: the first terms of this series define the behaviour of the equation of state. Of particular interest is the second order term, known as the symmetry energy. Because it is not experimentally accessible, though, a direct measurement cannot be performed and other observables have to be individuated. One of these observables is the dipole polarizability, indicated with α${}_D$ of the nucleus; this quantity correlates with the thickness of the neutron skin that forms around nuclei with a marked excess of neutrons and, thus, has the potential to put a constraint on the first order coefficient of symmetry energy's Taylor series expansion around the saturation density. This term is known as the "slope" and indicated with the letter L. The dipole polarizability can be obtained by integrating the strength of the nuclear response on all energies; this integral, though, is weighted by the energy: the response at lower energies plays, proportionally, a bigger role than that at higher ones. The aim of this work is to obtain a strength distribution for a neutron-rich isotope of Tin, ${}^{132}$Sn, and thus measure the dipole polarizability. To accomplish this, the data acquired at the GSI facility by the R${}^3$B collaboration, in Darmstadt, have been used and a novel method for profiling the strength of the dipole response of a nucleus from a noisy spectrum has been demonstrated to be promising and, furthermore, it is expected to be portable to other isotopes and experiments where a gamma array detector is used.