Narrow Results

The quark shell model has been successful in describing properties of hadrons. Because of color the quark shell model with 3n valence quarks has many more states which are singlet in color than the nuclear shell model with n valence nucleons. However, the quark interaction has been shown to favor two quarks coupled to spin zero and isospin zero and color , called diquarks. We show that the color singlet states in the quark shell model which have the maximal number of diquarks consistent with the Pauli symmetry are in one to one correspondence with the states of the nuclear shell model. We also investigate the implications of the quark interactions on the nuclear shell model interaction.

The solutions of the Wigner-transformed time-dependent Hartree–Fock–Bogoliubov equations are studied in the constant-Δ approximation, in spite of the fact that this approximation is known to violate both local and global particle-number conservation. As a consequence of this symmetry breaking, the longitudinal response function given by this approximation contains spurious contributions. A simple prescription for restoring both broken symmetries and removing the spurious strength is proposed. It is found that the semiclassical analogue of the quantum single-particle spectrum, has an excitation gap of 2Δ, in agreement with the quantum result. The effects of pairing correlations on the density response functions of three one-dimensional systems of different size are shown.

Results of the semi-microscopic self-consistent approach to describe the ground state properties of the inner crust of a neutron star developed recently within the Wigner-Seitz method with pairing effects taken into account are briefly reviewed.

We map out the temperature-density (T – n) phase diagram of an infinitely extended fermion system with pairwise interactions that support two-body (dimer) and three-body (trimer) bound states in free space. Adopting interactions representative of nuclear systems, we determine the critical temperature T_cs for the superfluid phase transition and the limiting temperature T_ce3 for the extinction of trimers. The phase diagram at subnuclear densities features a Cooper-pair condensate in the higher-density, low-temperature domain; with decreasing density there is a crossover to a Bose condensate of strongly bound dimers. The high-temperature, low-density domain is populated by trimers. The trimer binding energy decreases as the point (T,n) moves toward the domain occupied by the superfluid and vanishes at a critical temperature T_ce3 > T_cs. The ratio of the trimer and dimer binding energies is found to be a constant independent of temperature.

From the experimental data on odd-even staggering of masses, it has been shown that variation of pairing as a function of neutron number plays an important role in many distinctive features like occurrence of new shell closures, shell erosion, anomalous reduction of the energy of the first 2⁺ state and slower increase in the in the neutron-rich even-even nuclei in different mass regions. New predictions have been made in a model independent way.