Abstract
We investigate the influence of pairing correlations on some specific features of the clusterization process which occurs in a stellar matter composed of neutrons, protons and electrons, within a Skyrme-Lyon mean field approach. As it is known, in fact, nuclear matter presents a liquid-gas phase transition which appears at sub-saturation density, up to a critical temperature. Because of it, in compact-star matter one can encounter regions of instability against the formation of clusters, which can be characterized through the study of the free-energy curvature [1].

In our work, in particular, we test how pairing correlations may affect the isotopic composition of the clusters which may originate, in the supernova matter, from the spinodal mechanism. Moreover, as nucleon-nucleon correlations associated with clusterization play an important role also in determining the mean free path of neutrinos in the nuclear medium [2], we also discuss the impact of the considered pairing effects on neutrino scattering, which is of crucial importance for the star thermalization process.

[1] C. Ducoin, Ph. Chomaz and F. Gulminelli, Nucl. Phys. A 789, 1 (2007).
[2] G. Fabbri and F. Matera. Physical Review C 54. 4 (1996): 2031.