Constraining a possible time variation of the gravitational constant through "gravitochemical heating" of neutron stars

A hypothetical time variation of the gravitational constant G would cause neutron star matter to depart from beta equilibrium, due to the changing hydrostatic equilibrium. This induces nonequilibrium beta processes, which release energy that is invested partly in neutrino emission and partly in internal heating. Eventually, the star arrives at a stationary state in which the temperature remains nearly constant, as the forcing through the change of G is balanced by the ongoing reactions. Using the surface temperature of the nearest millisecond pulsar, PSR J0437-4715, inferred from ultraviolet observations, we estimate two upper limits for this variation: (1) |.G/G|< 2 x 10(-10) yr(-1), if direct Urca reactions are allowed, and (2) |.G/G|< 4 x 10(-12) yr(-1), considering only modified Urca reactions. The latter is among the most restrictive obtained by other methods.     

Phase transitions in nucleonic matter and neutron-star cooling

A new scenario for neutron-star cooling is suggested by the correspondence between pion condensation, induced by critical spin-isospin fluctuations, and the metal-insulator phase transition in a 2D electron gas. Above the threshold density for pion condensation, the neutron single-particle spectrum acquires an insulating gap that quenches neutron contributions to neutrino production. In the liquid phase just below the transition, the fluctuations play dual roles by (i) creating a multisheeted neutron Fermi surface that extends to low momenta and activates the normally forbidden direct Urca cooling mechanism, and (ii) amplifying the nodeless P-wave neutron superfluid gap while suppressing S-wave pairing. Lighter stars without a pion-condensed core undergo slow cooling, whereas enhanced cooling occurs in heavier stars via direct Urca emission from a thin shell of the interior.     

Superfluid nucleon matter in and out of equilibrium and weak interactions

The Larkin-Migdal approach to a cold superfluid Fermi liquid is generalized for a nonequilibrium system. The Schwinger-Keldysh diagram technique is applied. The developed formalism is applicable to the pairing in the states with arbitrary angular momenta. We consider the white body radiation problem by calculating probabilities of different direct reactions from a piece of a fermion superfluid. The closed diagram technique is formulated in terms of the full Green’s functions for systems with the pairing correlation. The cutting rules are used to classify the diagrams representing one-nucleon, two-nucleon, etc. processes in the matter. The important role of multi-piece diagrams for the vector-current conservation is demonstrated. In the case of equilibrated systems, dealing with dressed Green’s functions, we demonstrate correspondence between calculations in the Schwinger-Kadanoff-Baym-Keldysh formalism and the ordinary Matsubara technique. As an example we consider neutrino radiation from the neutron pair breaking and formation processes in case of a singlet pairing. Necessary correlation effects are included. The in-medium renormalization of normal and anomalous vertices is performed.     

Pairing in asymmetric two-component fermion matter

We analyze the possibilities of pairing between two different fermion species in asymmetric matter at low density. While the direct interaction allows pairing only for very small asymmetries, the pairing mediated by polarization effects is always possible, with a pronounced maximum at finite asymmetry. We present analytical results up to second order in the low-density parameter k_Fa.     

Raman coupling and cooper pairing in cold atomic Fermi gases

We consider a cold two-species atomic Fermi gas confined in a trap. We combine the Hainan coupling between the states (we assume them to be the states with different spins) with the Cooper pairing of atoms with these different spins. This opens up a new prospect for investigation of interplay between various phenomena involving Raman coupling (e.g., atom lasers, dark-state polaritons) and effects caused by Cooper pairing of particles (e.g., superfluidity). We have obtained a threshold of transition from oscillatory to amplifying behavior of matter waves.     

Nuclear superfluidity and cooling time of neutron stars

We discuss how the nuclear superfluidity affects the thermalisation time of the inner crust of neutron star in the case of a rapid cooling process. The thermal response of the inner crust matter is calculated supposing two pairing scenarios: one corresponding to the BCS approximation and the other to many-body techniques including polarisation effects. It is shown that these two pairing scenarios, which reflect the present uncertainty in the pairing properties of infinite neutron matter, give very different values for the thermalisation time of the crust.     

Hyperonic neutron stars: reconciliation between nuclear properties and NICER and LIGO/VIRGO results

Using an extended version of quantum hadrodynamics,I propose a new microscopic equation of state(EoS)that is able to correctly reproduce the main properties of symmetric nuclear matter at the saturation density,as well as produce massive neutron stars and satisfactory results for the radius and the tidal parameter.I show that this EoS can reproduce at least a 2.00 solar mass neutron star,even when hyperons are present.The constraints about the radius of a 2.00 M_⊙ and the minimum mass that enables a direct Urea effect are also checked.     

Hypernuclear physics for neutron stars

The role of hypernuclear physics for the physics of neutron stars is delineated. Hypernuclear potentials in dense matter control the hyperon composition of dense neutron star matter. The three-body interactions of nucleons and hyperons determine the stiffness of the neutron star equation of state and thereby the maximum neutron star mass. Two-body hyperon–nucleon and hyperon–hyperon interactions give rise to hyperon pairing which exponentially suppresses cooling of neutron stars via the direct hyperon URCA processes. Nonmesonic weak reactions with hyperons in dense neutron star matter govern the gravitational wave emissions due to the r-mode instability of rotating neutron stars.     

The pairing model

The consequences of the existence of pairing correlations in nuclei are discussed. Special attention is paid to the dynamical aspects of the pairing degree of freedom, as revealed by two-nucleon transfer reactions. These reactions constitute specific probes of the pairing collective modes.The mathematical framework in which the discussion is carried out is the BCS theory and the Random Phase Approximation.The borderline aspect of the subject, which lies between solid state and nuclear physics is emphasized, pointing out the similarities and differences between analogous phenomena of solid state and nuclear physics.     

Nonlocality effects on spin-one pairing patterns in two-flavor color superconducting quark matter and compact star applications

We study the influence of nonlocality in the interaction on two spin-one pairing patterns of two-flavor quark matter: the anisotropic blue-color pairing besides the usual two-color superconducting matter (2SCb), in which red and green colors are paired, and the color-spin locking phase (CSL). The effect of nonlocality on the gaps is rather large and the pairings exhibit a strong dependence on the form factor of the interaction, especially in the low-density region. The application of these small spin-one condensates for compact stars is analyzed: the early onset of quark matter in the nonlocal models may help to stabilize hybrid star configurations. While the anisotropic blue-quark pairing does not survive a big asymmetry in flavor space as imposed by the charge neutrality condition, the CSL phase as a flavor independent pairing can be realized as neutral matter in compact star cores. However, smooth form factors and the mismatch between the flavor chemical potential in neutral matter make the effective gaps of the order of magnitude ≃10 keV, and a more systematic analysis is needed to decide whether such small gaps could be consistent with the cooling phenomenology. The text was submitted by the authors in English.     

Conventional BCS,unconventional BCS,and non-BCS hidden dineutron phases in neutron matter

The nature of pairing correlations in neutron matter is re-examined. Working within the conventional approximation in which the nn pairing interaction is provided by a realistic bare nn potential fitted to scattering data, it is demonstrated that the standard BCS theory fails in regions of neutron number density, where the pairing constant λ, depending crucially on density, has a non-BCS negative sign. We are led to propose a non-BCS scenario for pairing phenomena in neutron matter that involves the formation of a hidden dineutron state. In low-density neutron matter, where the pairing constant has the standard BCS sign, two phases organized by pairing correlations are possible and compete energetically: a conventional BCS phase and a dineutron phase. In dense neutron matter, where λ changes sign, only the dineutron phase survives and exists until the critical density for termination of pairing correlations is reached at approximately twice the neutron density in heavy atomic nuclei.     

Comparison between microscopic and phenomenological nuclear pairing calculations

The isospin and density dependent effective pairing interaction is revisited by fitting the neutron gaps from the microscopic calculations for the neutron matter and the symmetric nuclear matter.The neutron pairing gaps for 1S0 channel for asymmetric nuclear matter are obtained from the BCS gap equation with a realistic bare nucleon-nucleon interaction in the Skyrme mean field.It is shown that the neutron gaps obtained from the new effective pairing interaction for the asymmetric nuclear matter are much imp...     

Multipole pairing states and the correspondence between two- and four-particle transfer reactions

Data for the ^58,60Ni(⁶Li, d) ^62,64Zn reactions, together with an analysis in terms of a simple multipole pairing model, indic that two-phonon states are extremely weakly excited. This result arises from the dominance of monopole pairing correlations in four-particle transfer reactions and explains the observed correspondence between two- and four-particle transfer reactions populating the same final nucleus.     

Pairing superfluidity in spin-orbit coupled ultracold Fermi gases

We review some recent progresses on the study of ultracold Fermi gases with synthetic spin-orbit coupling.In particular,we focus on the pairing superfluidity in these systems at zero temperature.Recent studies have shown that different forms of spin-orbit coupling in various spatial dimensions can lead to a wealth of novel pairing superfluidity.A common theme of these variations is the emergence of new pairing mechanisms which are direct results of spin-orbit-coupling-modified single-particle dispersion spectra.As different configurations can give rise to single-particle dispersion spectra with drastic differences in symmetry,spin dependence and low-energy density of states,spin-orbit coupling is potentially a powerful tool of quantum control,which,when combined with other available control schemes in ultracold atomic gases,will enable us to engineer novel states of matter.     

Two quasiparticle scattering and pairing in neutron matter with Skyrme interactions

Pairing matrix elements in neutron matter are computed employing Skyrme interactions under different approaches. We compare the pairing strengths calculated from the exact scattering amplitudes to those obtained as one neglects the integral kernel of the Bethe-Salpeter equation, and to the matrix element of the bare particle-particle interaction with and without rearrangement contribution. The effect upon the gap is analyzed in the frame of the simple weak coupling approximation, in order to indicate possible outcomes of more refined treatments of the pairing problem.     

Influence of isovector pairing and particle-number projection effects on spectroscopic factors for one-pair like-particle transfer reactions in proton-rich even-even nuclei

Isovector neutron-proton(np) pairing and particle-number fluctuation effects on the spectroscopic factors(SF) corresponding to one-pair like-particle transfer reactions in proton-rich even-even nuclei are studied. With this aim, expressions of the SF corresponding to two-neutron stripping and two-proton pick-up reactions, which take into account the isovector np pairing effect, are established within the generalized BCS approach, using a schematic definition proposed by Chasman. Expressions of the same SF which strictly conserve the particle number are also established within the Sharp-BCS(SBCS) discrete projection method. In both cases, it is shown that these expressions generalize those obtained when only the pairing between like particles is considered. First, the formalism is tested within the Richardson schematic model. Second, it is applied to study even-even proton-rich nuclei using the single-particle energies of a Woods-Saxon mean-field. In both cases, it is shown that the np pairing effect and the particle-number projection effect on the SF values are important, particularly in N =Z nuclei, and must then be taken into account.     

A Separable Pairing Force in Nuclear Matter

The method introduced by Duguet is adopted to derive a separable form of the pairing interaction in the ^1So channel from a bare or an effective nucleon-nucleon （NN） interaction in nuclear matter. With this approach the separable pairing interaction reproduces the pairing properties provided by its corresponding NN interaction. In this work, separable forms of pairing interactions in the ^1So channel for the bare NN interaction, Bonn potential and the Gogny effective interaction are obtained. It is found that the separable force of the Gogny effective interaction in the 1So channel has a clear link with the bare NN interaction. With such a simple separable form pairing properties provided by the Gogny force in nuclear matter can be reproduced.     

Superfluid states in β-stable nuclear matter

Two superfluid states of nuclear matter, which are supposed to play an important role in neutron stars, are discussed: the first one due to the proton-proton ¹ S ₀ pairing in β-equilibrium nuclear matter; the second one due to the anisotropic neutron-neutron ³ PF ₂ pairing in neutron matter. Since the two phases appear at high density of nuclear matter, the three-body forces were added to the pairing interaction and the strong correlation effects in the single-paricle spectrum. The energy gaps, obtained solving the extended BCS equations, significantly deviate from the values without medium effects so as to limit the role of these two superfluid states in the interpretation of phenomena occurring in the neutron-star core.     

Nuclear pairing: New perspectives

Nuclear pairing correlations are known to play an important role in various single-particle and collective aspects of nuclear structure. After the first idea by A. Bohr, B. Mottelson, and D. Pines on similarity of nuclear pairing to electron superconductivity, S.T. Belyaev gave a thorough analysis of the manifestations of pairing in complex nuclei. The current revival of interest in nuclear pairing is connected to the shift of modern nuclear physics towards nuclei far from stability; many loosely bound nuclei are particle-stable only due to the pairing. The theoretical methods borrowed from macroscopic superconductivity turn out to be insufficient for finite systems such as nuclei, in particular, for the cases of weak pairing and proximity of continuum states. We suggest a simple numerical procedure of exact solution of the nuclear pairing problem and discuss the physical features of this complete solution. We show also how the continuum states can be naturally included in the consideration bridging the gap between the structure and reactions. The path from coherent pairing to chaos and thermalization and perspectives of new theoretical approaches based on the full solution of pairing are discussed.