The applications of Nuclear Physics in Astrophysics and mainly on the study of supernova and neutron stars are widely and very important. Open problems still remain on the above research. The problems concern a) the construction of the equation of state of nuclear matter up to very high values of the baryon density b) the study of pairing correlations and the superconductivity and superfluidity phenomenon on nuclear matter and c) the neutrino emission process of supernova and hot neutron stars.
The nuclear structure study of finite nuclei is a fundamental activity in Theoretical Nuclear Physics. The mean field theory describes well the nuclear structure but experimental studies indicate that short-range correlations effects, between nucleons, must be taken into account. The study of the effect of short-range correlations is achieved by applying the many-body density matrix formalism. In general, the calculation of the density matrices, in Nuclear Physics, is very hard and complicated. The density-matrix can be evaluated by applying approximated methods. The knowledge of the many-body density matrices leads to the evaluation of the most important quantities of nuclear structure as the nuclear energy, the density and momentum distribution, the form factors, the quadrupole moments e.t.c.