An extremely simple form for the energy density of a nuclear many-body system is derived from the two-body nucleon-nucleon interaction. This theory, which yields excellent results for energies and density distributions of finite nuclei, is used to determine the ground state configuration of matter at sub-nuclear density. As the baryon density is increased, nuclei become progressively more neutron rich until neutrons eventually escape, yielding a Coulomb lattice of bound neutron and proton clusters surrounded by a dilute neutron gas. The clusters enlarge and the lattice constant decreases with increasing density, approaching a completely uniform state near nuclear density.

An equation of state is developed for densities from nuclear density (3 x 1014 g cm−3) to about 1016 g cm−3. The repulsive interaction between baryons dominates and empirical arguments for its existence are given. This interaction is attributed to vector meson exchange, and is derived from classical field theory whereupon a Yukawa potential results. The potential actually assumed is a modification of the Reid potential. Arguments are given that the baryons will not form a crystal lattice. The actual calculations were done using Pandharipande's method. The particles present at high density certainly include nucleons, Λ and Σ. The presence of Δ is questionable but that of π is likely. Results are given for the concentration of various species. With the more likely assumption about interactions, the concentration of each permissible species of particle is about equal at ϱ = 1016 g cm−3. The relation between energy and density is nearly independent of the assumptions on the species permitted and the energy is about 3 GeV particle−1 at ϱ = 1016 g cm−3. The relation between pressure and energy density is given, which yields a sound velocity equal to c at a few times 1015 g cm−3. Results for the structure of neutron stars are given. The maximum mass is about 2 solar masses and the maximum moment of inertia 1045 g cm2.

The variational method for calculating energy of quantum fluids, and its applications to the Bose liquid 4He, Fermi neutron gas, and liquid 3He are discussed. The correlation functions are parameterized by their healing distance, and can depend on the states occupied by the correlated particles in the model wave function. They are calculated by constrained variation of lowest order contributions. The healing distance has a prescribed value in lowest order calculations, whereas it is sufficiently large in hopefully exact energy calculations. The direct many-body cluster diagrams are summed with successive approximations of an integral equation. The contribution of exchange diagrams is shown to decrease rapidly with the number of exchanges, and their sums are truncated after the energy has converged to within a few percent.

The nuclear Thomas-Fermi model which is based on nuclear matter calculations has been successfully applied to the study of the bulk properties of nuclei. It is ideally suited for extrapolation into the region of very neutron-rich and of superheavy nuclei. It is therefore a valuable approach for r-process calculations as well as for the study of neutron star matter at subnuclear densities.

The statistical bootstrap theory of hadrons predicts a particle level density which increases with mass like ϱ(m) = cmaexp bm. The motivation for this level density is explored and then it is used to derive an equation of state for zero-temperature ultra-dense (> 1017 g cm−3) matter. The nature, uses, and limitations of the equation of state are discussed.

The qualitative features of the equation of state of matter at supernuclear densities are deduced through a careful examination of the nature of particle interactions at short distances and by the introduction of an ‘effective mass spectrum.’ it is found that the equation of state begins to take on a particularly simple form (the ‘asymptotic form’) at a relatively low matter density of 1017 g cm−3. A brief review of various approaches to calculate the equation of state for a neutron star is also given.

Arguments are given for pions becoming an important constituent of neutron star matter at densities greater than a critical density lying between 5 × 1014 and 1015 g cm−3. It is anticipated that this will lead to a substantial softening of the equation of state.

We evoke the possible existence of hypercollapsed tightly bound nuclear isomers, due to the existence of an attractive ‘heart’ deep inside the repulsive core.

We consider the structure of atoms and atomic chains in the presence of ultra-strong magnetic fields as might be found in pulsars or neutron stars. Some consequences of these models for neutron star surfaces are mentioned.

Using the many-body techniques appropriate for quantum crystals it is shown that the deep interior of a neutron star is most likely an orderly arrangement of neutrons, protons and hyperons forming a solid. It is shown that a liquid or gas arrangement would produce higher energy. If so, a neutron star can be viewed as two solids (crust and core) permeated by a layer of ordinary or (perhaps) superfluid liquid. Astronomical evidence is in favor of such a structure: the sudden jumps in the periods of the Crab and Vela pulsars that differ by a factor of ∼ 102 can be easily explained by the star-quake model. If the Crab is less massive than Vela (i.e., if it is not dense enough to have a solid core), the star-quakes take place in the crust whereas for Vela they occur in the core.

We present a short Cook's tour of the possible effects of rotation coupled with superfluid properties of neutron star interiors. A suggestion is made to take advantage of forthcoming lunar occultations of the Crab Nebula in order to search for blackbody X-ray emission from the Crab pulsar.

The phase diagram of a charged Bose gas is drawn. The domains of existence of the solid, fluid and superfluid phases are discussed. It is predicted that superdense helium can be superfluid at densities higher than 106 g cm−3.

The implications of the Zeldovich model (baryons interacting through a massive vector field) for the problem of superluminal sound propagation and ferromagnetic transition are examined. In a classical baryon gas at high densities correlation effects lead to the pressure increasing faster than the energy, ultimately resulting in superluminal sound; crystallization phase transition appears however at comparable densities, thus competing with the onset of superluminal sound. For a high density fermi gas the domains of ferromagnetic transition are delineated, indicating a minimal and maximal density below and above which no ferromagnetic transition can be expected. The latter is further affected by relativistic effects requiring a different approach to the calculation of exchange energy and of the ferromagnetic phase.

The formation of a neutron star and the event observed as a supernova are presumed by most astrophysicists to be simultaneous. The theoretical difficulty of understanding this is compounded by a hierarchy of conflicting phenomena dominated by the possibility of effective neutrino transport of the heat of the neutron star formation to the outer envelope. A thermonuclear detonation of a carbon core may take place at just the right density such that both neutron star formation and neutrino assisted envelope ejection can occur together.

We examine what inferences can be made regarding neutron star structure from observations of micro- and macroglitch behavior. After considering various theories it seems plausible that crustquakes offer an explanation for the Crab microglitches, while corequakes can explain the Vela macroglitches. It is concluded that the Crab pulsar has a mass of less than 0.5 M⊙ and is ∼ 90% superfluid neutrons while the Vela pulsar may possess a solid neutron core and have a mass of ∼ 0.7 M⊙ with a superfluid neutron abundance of ∼ 15%.

Cooling rates are first calculated for neutron stars of about 1 M⊙ and 10 km radius, with magnetic fields from zero to about 1014 G, for two extreme cases of maximum and no superfluidity. The results show that most pulsars are so cold that thermal ionization of surface atoms would be negligible. Next, nucleon superfluidity and crystallization of heavy nuclei are treated more quantitatively, and more realistic hadron star models are chosen. Cooling rates are thus calculated for a stable hyperon star near the maximum mass limit, a medium weight neutron star, and a light neutron star with neutron-rich heavy nuclei near the minimum mass limit. Results show that cooling rates are a sensitive function of density. The lightest star is cooler than others in earlier stages but the trend is reversed later. The medium weight star is generally the coldest of all in lower temperature regions where the effect of superfluidity becomes significant. However, if a heavy star contains pions, its cooling will be even faster. The Crab pulsar and Vela pulsar, expected to be the two youngest, can be as hot as (2 ∼ 4) x 106 K (on the surface), comparable with the results obtained from internal frictional heating by Greenstein, if they are medium weight to heavy hadron stars. However, older pulsars are cold. In fact, at about a few million years, the age of average radio pulsars, the surface temperature becomes only several hundred to several thousand degrees. Thus, the earlier conclusions about cold pulsars are still valid. Cooling of a massive white dwarf star is also shown.

Information about the physical parameters of neutron stars is obtained from pulsar observations. The energy balance of the Crab Nebula and the Vela X remnant allows one to derive limits for the masses of the Crab and Vela pulsars. Glitch observations provide further clues on the masses of these two pulsars. The degree of confidence with which one should believe the derived numbers is pointed out. The possibility of observing neutron stars in binary systems as pulsating X-ray sources is discussed. Finally, the importance of observing redshifted gamma ray lines from the surface of neutron stars, and thus directly measuring either individual or statistical properties of these objects, is pointed out.