We calculate the effects of induced interactions on the transition temperature to the BCS state in dilute Fermi gases. For a pure Fermi system with two species having equal densities, the transition temperature is suppressed by a factor $(4e{)}^{1/3}\approx 2.2$, and for $\nu$ fermion species, the transition temperature is increased by a factor $(4e{)}^{\nu /3-1}\approx {2.2}^{\nu -3\mathrm{}}$. For mixtures of fermions and bosons the exchange of boson density fluctuations gives rise to an attractive interaction, and we estimate the increase of the transition temperature due to this effect.

Ground-state energies and superfluid gaps are calculated for degenerate Fermi systems interacting via long attractive scattering lengths such as cold atomic gases, neutron, and nuclear matter. In the intermediate region of densities, where the interparticle spacing $\left(\sim {1/k}_F\right)$ is longer than the range of the interaction but shorter than the scattering length, the superfluid gaps and the energy per particle are found to be proportional to the Fermi energy and thus differ from the dilute and high-density limits. The attractive potential increase linearly with the spin-isospin or hyperspin statistical factor such that, e.g., symmetric nuclear matter undergoes spinodal decomposition and collapses whereas neutron matter and Fermionic atomic gases with two hyperspin states are mechanically stable in the intermediate density region. The regions of spinodal instabilities in the resulting phase diagram are reduced and do not prevent a superfluid transition.

We show that, for physically reasonable bulk and surface properties, the lowest energy state of dense matter consists of quark matter coexisting with nuclear matter in the presence of an essentially uniform background of electrons. We estimate the size and nature of spatial structure in this phase, and show that at the lowest densities the quark matter forms droplets embedded in nuclear matter, whereas at higher densities it can exhibit a variety of different topologies. A finite fraction of the interior of neutron stars could consist of matter in this new phase, which would provide new mechanisms for glitches and cooling.

▪ Abstract We review recent progress in the theory of neutron stars and compare its predictions with the observational data on masses, radii, and temperatures. The theory of neutron stars made up of neutrons, protons, and leptons is discussed in detail along with recent models of nuclear forces and modern many-body techniques. The possibilities of pion and kaon condensation in dense neutron star matter are considered, as is the possible occurrence of strange hyperons and quark-matter drops in the stellar core. The structure of mixed-phase matter in neutron stars, as well as the probable effect of phase transitions on the spin down of pulsars, is also discussed.