Superfluid And BCS-BEC Crossover In Nuclear Matter

Recently, the study on Quantum Chromodynamics (QCD) phase structure is extend-ed to finite isospin density. The physical motivation to study QCD at finite isospin density,including isospin asymmetric nuclear matter and quark matter, lies in its relation to theinvestigation of compact stars and heavy ion collisions at intermediate energies.According to the BCS theory, in a weakly attractive-interacting Fermion system, theparticles near the Fermi surface are intended to form Cooper pairs, which leads to thespontaneous symmetry breaking of the system, and the corresponding ground state be-comes a superconductor/superfluid, which is denoted as BCS superconductor/superfluid.Two research directions in the study of nuclear matter at finite isospin density receivemore attention. One is the Bardeen/Cooper/Shriefer–Bose-Einstein condensation (BCS-BEC) crossover. At low temperature, the weakly correlated Cooper pairs in BCS super-conductor/superfluid may go over to the BEC superconductor/superfluid of two-particlebound states. Although the BCS limit and BEC limit are physically diferent from eachother, the change between them is found to be a smooth crossover. The other direction isthe possible phase transition induced by the mismatch between the two Fermi surfaces ofpairing particles. The Fermi surface mismatch will, on one hand, suppress the usual BCSCooper pairing, but on the other hand, support some unusual superconductor/superfluidstates, like the gapless Sarma state, inhomogeneous LOFF state and the mixed phase.In the frame of the density-dependent contact potential, we have investigated theBCS-BEC crossover and the superfluid-normal phase transition in isospin asymmetricnuclear matter with pairings in both I=0and I=1channels. The resulted conclusion isthat only neutron-proton pair could form a true bound state at extremely low density andthe neutron-neutron and proton-proton pairs could never form bound states at any densityand asymmetry. Another topic of the thesis is the phase structure of pion superfluid atfinite isospin and baryon density quark matter. In the frame of flavor S U(2) NJL model,we have constructed the phase diagram with a BCS-BEC crossover in the isospin andbaryon chemical potential plane, considering the competition of normal quark matter,usual BCS superfluid, gapless Sarma state and inhomogeneous LOFF state. The efectsof all these superfluid phases on the mass-radius relation of compact stars are studiedtoo. Moreover, we proposed the meson-meson scattering as a sensitive probe of the BCS- BEC crossover at quark level. In pion superfluid phase, the corresponding π-π scatteringamplitude, which is large at high isospin chemical potential, drops down monotonicallywith decreasing isospin chemical potential, and finally approaches zero at the border ofpion superfluid, indicating a BCS-BEC crossover in the pion superfluid.