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In this brief review paper I outline the relevance of the single-particle states for the research in nuclear structure. They can be detected and studied by several experimental methods, like direct reactions, inelastic electron scattering, and so on. On the other hand, their properties are directly linked to the structure of nuclei and they can probe different aspects of the correlations that characterizes the nuclear systems. After a short introduction to the link between nuclear structure and properties of single-particle states, the general theoretical framework for the study of single-particle states is presented. The different experimental probes that can be used in detecting the single-particle states are then described, together with the corresponding theoretical methods. Finally, the presentation focuses on the particle-vibration scheme for the study of the single-particle states beyond the mean field level of approximation and some recent progresses in this field are discussed.

The relation between the broken rotational symmetry of a system and the topology of its Fermi surface is studied for the two-dimensional system with the quasiparticle interaction f(p, p') having a sharp peak at |p − p'| = q0. It is shown that, in the case of attraction and q0 = 2pF the first instability manifesting itself with the growth of the interaction strength is the Pomeranchuk instability. This instability appearing in the L = 2 channel gives rise to a second order phase transition to a nematic phase. The Monte Carlo calculations demonstrate that this transition is followed by a sequence of the first and second order phase transitions corresponding to the changes in the symmetry and topology of the Fermi surface. In the case of repulsion and small values of q0, the first transition is a topological transition to a state with the spontaneously broken rotational symmetry, namely, corresponding to the nucleation of L ≃ π(pF/q0 − 1) small hole pockets at the distance pF − q0 from the center and the deformation of the outer Fermi surface with the characteristic multipole number equal to L. At q0 → 0, when the model under study transforms to the two-dimensional Nozieres model, the multipole number characterizing the spontaneous deformation is L → ∞, whereas the infinitely folded Fermi curve acquires the Hausdorff dimension D = 2 which corresponds to the state with the fermion condensate.

The Energy Density Functional (EDF) theory is extremely successful within the effective force approach, noticeably the Skyrme or Gogny forces, in reproducing the nuclear binding energies and other nuclear properties along the whole mass table. The EDF is in this case represented formally as the Hartree-Fock (HF) mean field of an effective force, and the associated single particle states can be considered the eigenstates of the corresponding effective mean field. In general, the phenomenological single particle spectrum is not accurately reproduced. To overcome this difficulty one can improve the functional in order to incorporate in the mean field additional correlations in an effective way. In an alternative viable scheme one can introduce explicitly many-body correlations which affect the single particle motion at both dynamic and static levels. In particular, the particle-vibration coupling scheme modifies the positions of the individual single particle energies. In this case one also introduce the fragmentation of the single particle states, a feature that cannot be described at the mean field level. At the same time the so-introduced correlations modify the static single particle potential, and the single particle states that diagonalize the corresponding density matrix are not the orbitals of a mean field with occupation numbers 1 (occupied orbitals) and 0 (unoccupied orbitals) anymore. In this paper we show that both static and dynamic effects on the single particle motion can be introduced within a previously developed scheme, based on the conserving approximations, and that the static part can be identified with the so-called tadpole term introduced by Khodel in the self-consistent theory of finite Fermi systems. The treatment remains at the formal level, but we hope that several aspects of the particle-vibration coupling scheme will be clarified.

Several phenomena occurring in neutron stars are affected by the elementary excitations that characterize the stellar matter. In particular, low-energy excitations can play a major role in the emission and propagation of neutrinos, neutron star cooling and transport processes. In this paper, we consider the elementary modes in the star region where both proton and neutron components are superfluid. We study the overall spectral functions of protons, neutrons and electrons on the basis of the Coulomb and nuclear interactions. This study is performed in the framework of the Random Phase Approximation, generalized to superfluid systems. The formalism we use ensures that the Generalized Ward's Identities are satisfied. We focus on the coupling between neutrons and protons. On one hand this coupling results in collective modes that involve simultaneously neutrons and protons, on the other hand it produces a damping of the excitations. Both effects are especially visible in the spectral functions of the different components of the matter. At high density while the neutrons and protons tend to develop independent excitations, as indicated by the spectral functions, the neutron-proton coupling still produces a strong damping of the modes., 9 pages 6 figures, accepted in Physical Review C. arXiv admin note: substantial text overlap with arXiv:1708.03794

We calculate the binding energy of pure neutron matter up to third order in the Brueckner-Bethe-Goldstone hole-line expansion, employing various modern nucleon-nucleon potentials. At that order all results appear well converged to within a few percent up to a density of $0.8\phantom{\rule{0.28em}{0ex}}{\mathrm{fm}}^{\ensuremath{-}3}$. We analyze the potentials in terms of the strength of their hard core. Comparison with results of other theoretical methods is made.

We calculate modified Urca neutrino emission rates in the dense nuclear matter in neutron star cores. We find that these rates are strongly enhanced in the beta-stable matter in regions of the core close to the direct Urca process threshold. This enhancement can be tracked to the use of the in-medium nucleon spectrum in the virtual nucleon propagator. We describe the in-medium nucleon scattering in the non-relativistic Bruckner-Hartree-Fock framework taking into account two-body as well as the effective three-body forces, although the proposed enhancement does not rely on a particular way of the nucleon interaction treatment. Finally we suggest a simple approximate expression for the emissivity of the n-branch of the modified Urca process that can be used in the neutron stars cooling simulations with any nucleon equation of state of dense matter., 8 pages, 3 figures; accepted for publication in PLB. In v.2 misprint in eq.(9) corrected and discussion of cooling curves expanded

Thermal conductivity and shear viscosity of npe$\mu$ matter in non-superfluid neutron star cores are considered in the framework of Brueckner-Hartree-Fock many-body theory. We extend our previous work (Shternin, Baldo and Haensel, 2013) by analysing different nucleon-nucleon potentials and different three-body forces. We find that the use of different potentials leads up to one order of magnitude variations in the values of the nucleon contribution to transport coefficients. The nucleon contribution dominates the thermal conductivity, but for all considered models the shear viscosity is dominated by leptons., Comment: 4 pages, 2 figures; in v.2 misprints in eqs. (5)-(9) corrected

The accurate computation of nuclear matter properties, such as its binding energy, is still a challenge to nuclear theory, largely because the quark substructure of nucleons creates a strong repulsion at short distances that renders a straightforward perturbative calculation impossible. In this work, the authors study the Brueckner-Bethe-Goldstone expansion of dense Fermi systems in terms of hole-line contributions, of the associated Goldstone diagrams, to the binding energy of nuclear matter. They use various modern nucleon-nucleon potentials of high precision. In all cases the three-hole-line contributions are sufficiently small suggesting that the expansion converges. Yet, the empirical saturation properties of nuclear matter are not reproduced for any potential. This means that very strong nuclear three-body forces are required in order to achieve satisfactory saturation properties of nuclear matter, and that such forces are essential for all considered potentials.

Within a microscopic approach the structure of Neutron Stars is usually studied by modelling the homogeneous nuclear matter of the core by a suitable Equation of State, based on a many-body theory, and the crust by a functional based on a more phenomenological approach. We present the first calculation of Neutron Star overall structure by adopting for the core an Equation of State derived from the Brueckner-Hartree-Fock theory and for the crust, including the pasta phase, an Energy Density Functional based on the same Equation of State, and which is able to describe accurately the binding energy of nuclei throughout the mass table. Comparison with other approaches is discussed. The relevance of the crust Equation of state for the Neutron Star radius is particularly emphasised., Comment: 14 pages, 6 figures, accepted version

It has been found in previous works [M. Baldo and K. Fukukawa, Phys. Rev. Lett. 113, 241501 (2014); K. Fukukawa, M. Baldo, G. F. Burgio, L. Lo Monaco and H.-J. Schulze, Phys. Rev. 92, 065802 (2015)] that the nucleon–nucleon potential of [Y. Fujiwara, M. Kohno, C. Nakamoto and Y. Suzuki Phys. Rev. C 64, 054001 (2001); Y. Fujiwara et al., Phys. Rev. C 65, 014002 (2001)] gives an accurate saturation point in symmetric nuclear matter once the three hole-line contributions are included in the Brueckner–Bethe–Goldstone expansion without the addition of three-body forces in the nuclear Hamiltonian. The potential is based on a quark model of nucleons and on the quark–quark interaction together with quark exchange processes. These features introduce an intrinsic nonlocality of the nucleon–nucleon interaction. In order to clarify the role of the quark degrees of freedom and of the nonlocality in the saturation, we perform a comparative study of this potential and the traditional meson exchange models, exemplified in the CD-Bonn potential. We find that at the Brueckner–Hartree–Fock approximation, which corresponds to the two hole-line level of approximation, the dominant modification of the nucleon–nucleon interaction with respect to CD-Bonn is incorporated in the s-wave channels, where the quark degrees of freedom should be more relevant, in particular for the short range quark exchange processes. However, when the three hole-line contribution is included, we find that the higher partial waves play a relevant role, mainly in the term that describes the effect of the medium on the off-shell propagation of the nucleon.

The Barcelona-Catania-Paris-Madrid (BCPM) functional recently proposed to describe nuclear structure properties of finite nuclei is generalized as to include a realistic effective mass. The resulting functional is as good as the previous one in describing binding energies, radii, deformation properties, etc and, in addition, the description of Giant Quadrupole Resonance energies is greatly improved., 8 pages, 5 figures

A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on the direct solution of the Dyson equation with PC corrected mass operator, is presented. It is used for finding the odd-even mass difference between even Pb and Sn isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather highly accurate predictions for these mass differences already at the mean-field level. In the case of the lead chain, account for the PC corrections induced by the low-laying phonons $2^+_1$ and $3^-_1$ makes agreement of the theory with the experimental data significantly better. For the tin chain, the situation is not so definite. In this case, the PC corrections make agreement better in the case of the addition mode but they spoil the agreement for the removal mode. We discuss the reason of such a discrepancy., Comment: 10 pages, 3 figures, 11 tables. arXiv admin note: substantial text overlap with arXiv:1710.09159

A method to evaluate the particle-phonon coupling (PC) corrections to the single-particle energies in semi-magic nuclei, based on a direct solving the Dyson equation with PC corrected mass operator, is used for finding the odd-even mass difference between 18 even Pb isotopes and their odd-proton neighbors. The Fayans energy density functional (EDF) DF3-a is used which gives rather high accuracy of the predictions for these mass differences already on the mean-field level, with the average deviation from the existing experimental data equal to 0.389 MeV. It is only a bit worse than the corresponding value of 0.333 MeV for the Skyrme EDF HFB-17 which belongs to a family of Skyrme EDFs with the highest overall accuracy in describing the nuclear masses. Account for the PC corrections induced by the low-laying phonons $2^+_1$ and $3^-_1$ significantly diminishes the deviation of the theory from the data till 0.218 MeV., Comment: 6 pages, 3 figures, 3 tables

The thermal evolution of Neutron Stars is affected by the elementary excitations that characterize the stellar matter. In particular, the low-energy excitations, with a spectrum linear in momentum, can play a major role in the emission and propagation of neutrinos. In this paper, we focus on the elementary modes in the region of proton superfluidity, where the neutron component is expected to have a very small or zero pairing gap. We study the overall spectral functions of protons, neutrons and electrons on the basis of the Coulomb and nuclear interactions. This study is performed in the framework of the Random Phase Approximation, generalized in order to describe the response of a superfluid system. The formalism we use ensures that the Generalized Ward's Identities are satisfied. Despite their relative small fraction, the protons turn out to modify the neutron spectral function as a consequence of the nuclear neutron-proton interaction. This effect is particularly evident at the lower density, just below the crust for a density close to the saturation value, while at increasing density the neutrons and the protons are mainly decoupled. The proton spectral function is characterized by a pseudo-Goldstone mode below $ 2\Delta $, twice the pairing gap, and a pair-breaking mode above $ 2\Delta $. The latter merges in the sound mode of the normal phase at higher momenta. The neutron spectral function develops a collective sound mode only at the higher density. The electrons have a strong screening effect on the proton-proton interaction at the lower momenta, and decouple from the protons at higher momenta., Comment: 6 figures, to appear in Phys. Rev. C

Odd-even double mass differences (DMD) of magic nuclei are found within the approach starting from the free $NN$ interaction with account for particle-phonon coupling (PC) effects. We consider three PC effects: the phonon induced effective interaction, the renormalization of the "ends" due to the $Z$-factor corresponding to the pole PC contribution to the nucleon mass operator and the change of the single-particle energies. The perturbation theory in $g^2_L$, where $g_L$ is the vertex of the $L$-phonon creation, is used for PC calculations. PC corrections to single-particle energies are found self-consistently with an approximate account for the tadpole diagram. Results for magic $^{40,48}$Ca, $^{56,78}$Ni, $^{100,132}$Sn and $^{208}$Pb nuclei are presented. For lighter part of this set of nuclei, from $^{40}$Ca till $^{56}$Ni, the cases divide approximately in half between those where the PC corrections to DMD values make agreement with the data better and the ones with the opposite result. In the major part of the cases of worsening of description of DMD, a poor applicability of the perturbation theory for the induced interaction is the most probable reason of the phenomenon. For intermediate nuclei, $^{78}$Ni and $^{100}$Sn, there is no sufficiently accurate data on masses of nuclei necessary for finding DMD values. Finally, for heavier nuclei, $^{132}$Sn and $^{208}$Pb, PC corrections always make agreement with the experiment better.

The role of an effective mass in the ab initio BCS equation for a pairing gap in atomic nuclei has been analyzed.

Recent results obtained by solving the ab initio equation for the pairing gap in a slab of nuclear matter are reviewed. They conclusively prove a surface nature of nucleon pairing in nuclei. First, the effective pairing interaction in the vicinity of the slab surface makes a dominant contribution to the gap. Second, there is a sizable surface enhancement of the pairing gap Δ(X) itself. Finally, an analysis of spatial correlation features of the anomalous density matrix shows that the local correlation length at the slab surface is very small, about 1.5 fm, but, in the interior of the slab, it is rather large, about the slab thickness. These results are in qualitative agreement with those obtained recently by Pillet and his coauthors for spherical nuclei by using the phenomenological Gogny force. An increase in the concentration of Cooper pairs at the surface of nuclei was yet another result of their study, and our present analysis confirms this indirectly.

We have recently presented a new non-relativistic nuclear energy density functional which is constructed, not as usual, from an effective density dependent nucleon-nucleon force but directly introducing in the functional results from microscopic nuclear and neutron matter Bruckner G -matrix calculations at various densities. We add a purely phenomenological finite range part to account for surface properties. We take from the literature a density dependent zero range force to describe the pairing correlations. We find that only four to five adjustable parameters, spin-orbit included, suffice to reproduce nuclear binding energies and radii to the same accuracy as those obtained with some of the best effective forces for both spherical and deformed nuclei. The deformation properties of this new functional are in excellent agreement with the results computed using the Gogny D1S force.

The self-consistent semimicroscopic fully quantum approach developed recently for describing the structure of the inner crust of a neutron star within the Wigner-Seitz method is used to perform a systematic calculation of the properties of the system under study. Only the lowest layers of the crust in the vicinity of the point where a phase transition to a uniform state occurs are excluded from our consideration. Use is made of a realistic microscopic model that treats pairing in neutron matter with allowance for corrections of many-body theory to the Bardeen-Cooper-Schrieffer approximation.

A method is developed to consider the particle-phonon coupling (PC) effects in the calculation of the odd-even double mass differences (DMD) in semi-magic nuclei starting from the free $NN$-potential. The PC correction $\delta \Sigma^{\rm PC}$ to the mass operator $\Sigma$ is found in $g_L^2$-approximation, $g_L$ being the vertex of creating the $L$-phonon. The tadpole term of the operator $\delta \Sigma^{\rm PC}$ is taken into account. The method is based on a direct, without any use of the perturbation theory, solution of the Dyson equation with the mass operator $\Sigma(\epsilon){=}\Sigma_0{+}\delta \Sigma^{\rm PC}(\epsilon)$ for finding the single-particle energies and $Z$-factors. In its turn, they are used as an input for finding different PC corrections to the DMD values. Results for a chain of even semi-magic nuclei $^{200-206}$Pb show that the inclusion of the PC corrections makes agreement with the experimental data significantly better., Comment: 6 pages, 2 figures, 3 tables; ; v2 -- small corrections in the text; to be published in JETP Letters

The nuclear symmetry energy characterizes the variation of the binding energy as the neutron to proton ratio of a nuclear system is varied. This is one of the most important features of nuclear physics in general, since it is just related to the two component nature of the nuclear systems. As such it is one of the most relevant physical parameters that affect the physics of many phenomena and nuclear processes. This review paper presents a survey of the role and relevance of the nuclear symmetry energy in different fields of research and of the accuracy of its determination from the phenomenology and from the microscopic many-body theory. In recent years, a great interest was devoted not only to the Nuclear Matter symmetry energy at saturation density but also to its whole density dependence, which is an essential ingredient for our understanding of many phenomena. We analyze the nuclear symmetry energy in different realms of nuclear physics and astrophysics. In particular we consider the nuclear symmetry energy in relation to nuclear structure, astrophysics of Neutron Stars and supernovae, and heavy ion collision experiments, trying to elucidate the connections of these different fields on the basis of the symmetry energy peculiarities. The interplay between experimental and observational data and theoretical developments is stressed. The expected future developments and improvements are schematically addressed, together with most demanded experimental and theoretical advances for the next few years., Comment: 71 pages, 33 figures, accepted for publication by Progress in Particle and Nuclear Physics. arXiv admin note: text overlap with arXiv:1310.2896, arXiv:1205.2585, arXiv:nucl-ex/0610013, arXiv:1407.7625, arXiv:nucl-ex/0310024, arXiv:1101.3648, arXiv:1406.4546, arXiv:1309.5153, arXiv:1401.2074, arXiv:1210.3402, arXiv:1506.04687, arXiv:astro-ph/0407529 by other authors

We derive the equation of state (EOS) of nuclear matter from are alistic constituent quark model for the nucleon-nucleon interaction. We use the Brueckner-Bethe-Goldstone approach with the inclusion of the three hole-line contribution. We find that the resulting EOS reproduces correctly the saturation point, moreover the symmetry energy at low density, its slope, and the incompressibility turn out to be compatible with phenomenology. We calculate the mass-radius relation for neutron stars, and find maximum values close to two solar masses, in agreement with recent observational data.

A self-consistent quantum approach to describe the inner crust structure of neutron stars is developed within the Wigner-Seitz (WS) approximation, based on the generalized energy functional method involving explicitly neutron and proton pairing correlations. The energy functional is constructed by matching the realistic phenomenological nuclear functional by Fayans et al. for describing the pseudonucleus in the center of the WS cell with the one calculated microscopically for neutron matter within the Brueckner approach with the Argonne v18 force. The microscopic description of the neutron superfluidity is based on the BCS approach with the same v18 force. Many-body theory corrections to the BCS method (the correlation and self-energy ones) are included in the calculation scheme in an approximate way. A wide region of average densities was investigated corresponding to the Fermi momentum values kF = 0.6–1.2 fm−1

A critical point determining the interphace between the outer and inner parts of the crust of a neutron star has been found using a previously developed self-consistent semi-microscopic method. The critical density ρd thus obtained is only slightly lower than the commonly accepted value. At the same time, the equilibrium structure of the crust near the critical point differs significantly from that obtained in known calculations.

A semi-microscopic self-consistent quantum approach developed recently to describe the inner crust structure of neutron stars within the Wigner-Seitz (WS) method with the explicit inclusion of neutron and proton pairing correlations is further developed. In this approach, the generalized energy functional is used which contains the anomalous term describing the pairing. It is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the WS cell with the one calculated microscopically for neutron matter. Previously the anomalous part of the latter was calculated within the BCS approximation. In this work corrections to the BCS theory which are known from the many-body theory of pairing in neutron matter are included into the energy functional in an approximate way. These modifications have a sizable influence on the equilibrium configuration of the inner crust, i.e. on the proton charge Z and the radius R_c of the WS cell. The effects are quite significant in the region where the neutron pairing gap is larger., Comment: 24 pages, 14 figures; LaTeX, submitted to EPJA

The effective pairing interaction corresponding to the Argonne nucleon-nucleon potential v18 is found within the local potential approximation for several values of the boundary energy E 0 that specifies the model subspace S 0. A detailed comparison with the analogous effective interaction calculated previously for the Paris nucleon-nucleon potential is performed. It is shown that the effective interactions obtained for the two different nucleon-nucleon potentials at the same value of E 0 are very close to each other. In the case of the Paris potential, a very wide subspace S′ complementary to S 0 was required in calculating the effective interaction (the corresponding cutoff momentum being k max = 160−180 fm−1), whereas a much narrower subspace S′ corresponding to k max = 10−12 fm−1 could be used in the case of the Argonne potential.

The structure of neutron stars is determined by the nuclear Equation of State well above the nuclear saturation density. Since only limited hints from heavy ion reactions at intermediate energy can be used to constraint the Equation of State, theoretical predictions are essential. Different microscopic many-body methods for symmetric matter as well as for pure neutron matter are compared to the aim of assessing the theoretical uncertainties. The possible transition to quark matter in the interior of neutron stars is then briefly discussed and it is argued that recent observational data, if confirmed, would point towards a stiffening of the quark Equation of State with respect to the asymptotic freedom regime.

We study the hadron-quark phase transition in the interior of neutron stars (NS). For the hadronic sector, we use a microscopic equation of state (EOS) involving nucleons and hyperons derived within the Brueckner-Bethe-Goldstone many-body theory, with realistic two-body and three-body forces. For the description of quark matter, we employ both the MIT bag model with a density dependent bag constant, and the color dielectric model. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses are never larger than 1.7 solar masses, no matter the model chosen for describing the pure quark phase., 11 pages, 5 figures, submitted to Phys. Rev. D

We study the hadron-quark phase transition in the interior of neutron stars (NS's). We calculate the equation of state (EOS) of hadronic matter using the Brueckner-Bethe-Goldstone formalism with realistic two-body and three-body forces, as well as a relativistic mean field model. For quark matter we employ the MIT bag model constraining the bag constant by using the indications coming from the recent experimental results obtained at the CERN SPS on the formation of a quark-gluon plasma. We find necessary to introduce a density dependent bag parameter, and the corresponding consistent thermodynamical formalism. We calculate the structure of NS interiors with the EOS comprising both phases, and we find that the NS maximum masses fall in a relatively narrow interval, $1.4 M_\odot \leq M_{\rm max} \leq 1.7 M_\odot$. The precise value of the maximum mass turns out to be only weakly correlated with the value of the energy density at the assumed transition point in nearly symmetric nuclear matter., Comment: 25 pages, Revtex4, 16 figures included as postscript

We review our knowledge on the properties of the nuclear medium that have been studied, along many years, on the basis of many-body theory, laboratory experiments and astrophysical observations. First we consider the realm of phenomenological laboratory data and astrophysical observations, and the hints they can give on the characteristics that the nuclear medium should possess. The analysis is based on phenomenological models, that however have a strong basis on physical intuition and an impressive success. More microscopic models are also considered, and it is shown that they are able to give invaluable information on the nuclear medium, in particular on its Equation of State. The interplay between laboratory experiments and astrophysical observations are particularly stressed, and it is shown how their complementarity enriches enormously our insights into the structure of the nuclear medium. We then introduce the nucleon-nucleon interaction and the microscopic many-body theory of nuclear matter, with a critical discussion about the different approaches and their results. The Landau Fermi Liquid theory is introduced and briefly discussed. As illustrative example, we discuss neutron matter at very low density, and it is shown how it can be treated within the many-body theory. A section is dedicated to the pairing problem. The connection with nuclear structure is then discussed, on the basis of the Energy Density Functional method. The possibility to link the physics of exotic nuclei and the astrophysics of neutron stars is particularly stressed. Finally we discuss the thermal properties of the nuclear medium, in particular the liquid-gas phase transition and its connection with the phenomenology on heavy ion reactions and the cooling evolution of neutron stars. The presentation has been taken for non-specialists and possibly for non-nuclear physicists., Comment: 90 pages, 29 figures, revised version

We study cold dense quark matter and hybrid neutron stars with a Dyson-Schwinger quark model and various choices of the quark-gluon vertex. We obtain the equation of state of quark matter in beta equilibrium and investigate the hadron-quark phase transition in combination with a hadronic equation of state derived within the Brueckner-Hartree-Fock many-body theory. Comparing with the results for quark matter with the rainbow approximation, the Ball-Chiu ansatz and the 1BC ansatz for the quark-gluon vertex lead to a reduction of the effective interaction at finite chemical potential, qualitatively similar to the effect of our gluon propagator. We find that the phase transition and the equation of state of the quark or mixed phase and consequently the resulting hybrid star mass and radius depend mainly on a global reduction of the effective interaction due to effects of both the quark-gluon vertex and gluon propagator, but are not sensitive to the vertex ansatz., Comment: 6 pages, 5 figures

We study the structure of newly born neutron stars (protoneutron stars) within the finite temperature Brueckner-Bethe-Goldstone theoretical approach including also hyperons. We find that for purely nucleonic stars both finite temperature and neutrino trapping reduce the value of the maximum mass. For hyperonic stars the effect is reversed, because neutrino trapping shifts the appearance of hyperons to larger baryon density and stiffens considerably the equation of state., 11 pages, 7 figures, submitted to Astronomy & Astrophysics

Within the Wigner-Seitz approximation, a self-consistent fully quantum-mechanical calculation of the structure of the inner crust of a neutron star is performed over a wide range of densities with allowance for superfluidity effects. Within the approach used, the Wigner-Seitz cell consists of a nuclear-like cluster surrounded by a nearly uniform neutron gas. An effective energy functional is constructed by matching, at the cluster surface, the realistic phenomenological nuclear functional for the cluster due to S. A. Fayans and his coauthors and the energy functional calculated microscopically for neutron matter. The microscopic component of the functional is calculated within the Brueckner method by using the v18 Argonne interaction.

A self-consistent quantum approach to describe the inner crust structure of neutron stars is developed, within the Wigner–Seitz approximation. It is based on the generalized energy functional method involving explicitly neutron and proton pairing correlations. The energy functional is constructed by matching the realistic phenomenological functional by Fayans et al. for describing the nuclear-type cluster in the center of the Wigner–Seitz cell with the one calculated microscopically for neutron matter. It is shown that the neutron and proton superfluidity influences significantly the ground state structure of the inner crust.

The different superfluid states that can occur inside neutron stars are reviewed, both in the crust region and in the core. The role of correlations in determining the values of the pairing gaps is emphasized. Comparison is made on one hand with pairing in nuclear structure calculations in ordinary (terrestrial) nuclei, and on the other hand with hints from phenomenological analysis of observational data.

A self-consistent, completely quantum calculation of the structure of the inner crust of neutron stars is carried out in the Wigner-Seitz approximation with a realistic phenomenological nuclear energy functional, where pair correlations of neutrons and protons are included in the explicit form. It has been shown that the superfluidity of neutrons and protons affects the structure of the ground state of the crust.

The possibilities of pairing in a low-density, cold Fermi gas interacting either through the interaction with another fermionic species or through a bosonic gas are analysed. In the latter case, special attention is devoted to the study of the experimentally relevant situation of a two-dimensional system. Estimates for the gaps at zero temperature in experimental conditions are presented.

The surface nature of nuclear pairing is confirmed microscopically. A two-step approach is used in which the full Hilbert space S is split into the model subspace S 0 and the complementary one, S ′. The gap equation is solved in the model space in terms of the effective interaction V eff p which obeys the Bethe–Goldstone-type equation in the complementary subspace. The simplest nuclear systems with one-dimensional inhomogeneity are considered, i.e. semi-infinite nuclear matter and the nuclear slab. Numerical solution is carried out for the separable representation of the Paris NN-potential. The equation for the effective pairing interaction is solved directly, without use of any form of local approximation. A version of the local approximation, the local potential approximation, is suggested which works sufficiently well even in the surface region. The effective pairing interaction obtained in our calculations reveals a strong variation in the surface region changing from a strong attraction outside the nuclear matter to almost zero value inside. The effective interaction is found to be dependent on the chemical potential μ . At μ=−8 MeV , it reproduces qualitatively the phenomenological density-dependent effective pairing interaction, with the surface dominance, which was found previously in the self-consistent finite Fermi systems theory and in the new version of the energy functional method by Fayans et al. As | μ | decreases, the surface attraction becomes stronger. The gap equation was solved in semi-infinite matter and in the slab system with the help of the method by Khodel, Khodel and Clark which was suggested recently for nuclear matter. This method extended to non-homogeneous systems turned out to be very efficient in this case. The gap Δ found for both the systems exhibits a strong variation in the surface region with a pronounced maximum near the surface. The surface effect in Δ turned out to be μ -dependent being enhanced at small | μ |.

The density of nuclear matter in the interior of neutron stars can reach values, for the largest masses, which can be compatible with the onset of hadron deconfinement. For the study of this possibility the only viable method at present is the comparison between the available nucleon and quark Equations of State (EoS) at increasing baryon density. It is then possible to trace the transition to the deconfined phase or the appearence of a mixed phase. We present recent results on the structure of neutron stars based on this procedure. For the nucleon matter, the microscopic many-body theory of the Nuclear Equation of State is discussed in the framework of the Bethe-Brueckner-Goldstone method. The expansion is extended up to the three hole-line diagrams contribution. For the quark matter, different models are used to generate the quark EoS. Despite the maximum mass of neutron stars turns out to be only marginally sensitive to the considered quark EoS, it is found that the structure of neutron stars can drastically depend on the adopted model.

The microscopic many-body theory of the Nuclear Equation of State is discussed in the framework of the Bethe–Brueckner–Goldstone method. The expansion is extended up to the three hole-line diagrams contribution. The Brueckner equation for the two-body G-matrix and the Bethe–Fadeev equation for the three-body scattering matrix are solved both for the gap and continuous choices of the single particle potential. For symmetric and pure neutron matter strong evidence of convergence in the expansion is found. Once three-body forces are introduced, the phenomenological saturation point is reproduced. In order to study neutron stars static properties, the theory is extended to include strangeness, and the possible quark-gluon plasma component is described in the simplified MIT bag model. The results for the mass and radius of neutron stars are briefly discussed.

The equation of state(EOS) of nuclear matter is studied up to the three-hole-line level of approximation in the Behte-Brueckner-Goldstone expansion. The results indicate a good convergence of the theory. The fact that the resulting EOS does not reproduce the empirical saturation point suggests that the three-body forces are most likely the main term missing in the nuclear Hamiltonian.

The possibility of neutron pairing in the $^1S_0$ channel is studied for dense neutron matter in a vicinity of the $\pi^0$ condensation point. The $^1S_0$ pairing gap $\Delta$ is shown to occur in a model with a pairing force induced by the exchange of a soft neutral pionic mode. The soft pion induced potential $V_{\pi}(r)$ is characterized by an attenuating oscillatory behavior in coordinate space, while in momentum space all $S$-wave matrix elements $V_{\pi}(p,p')$ are positive. The solution of the gap equation reveals strong momentum dependence.

We derive a new equation of state (EoS) for neutron stars (NS) from the outer crust to the core based on modern microscopic Brueckner-Hartree-Fock (BHF) calculations using the Argonne $v_{18}$ potential plus three-body forces computed with the Urbana model. To deal with the inhomogeneous structures of matter in the NS crust, we use the recent Barcelona-Catania-Paris-Madrid (BCPM) nuclear energy density functional that is directly based on the same microscopic BHF calculations, and which is able to reproduce the ground-state properties of nuclei along the periodic table. The EoS of the outer crust requires the masses of neutron-rich nuclei, which are obtained through Hartree-Fock-Bogoliubov calculations with the BCPM functional when they are unknown experimentally. To compute the inner crust, Thomas-Fermi calculations in Wigner-Seitz cells are performed with the same functional. Existence of nuclear pasta is predicted in a range of average baryon densities between $\simeq$0.067 fm$^{-3}$ and $\simeq$0.0825 fm$^{-3}$, where the transition to the core takes place. The NS core is computed from the nuclear EoS of the BHF calculation assuming non-exotic constituents (core of $npe\mu$ matter). In each region of the star, we discuss the comparison of the new EoS with previous EoSes for the complete NS structure, in particular, with the Lattimer-Swesty EoS and with the Shen et al. EoS widely used in astrophysical calculations. The new microscopically derived EoS fulfills at the same time a NS maximum mass of 2~$M_\odot$ with a radius of 10 km, and a 1.5~$M_\odot$ NS with a radius of 11.7 km., Comment: 23 pages, 17 figures, revised version accepted for publication in Astronomy & Astrophysics

Starting from a realistic constituent quark model for the nucleon-nucleon interaction, we derive the equation of state (EOS) of nuclear matter within the Bethe-Brueckner-Goldstone approach up to three-hole-line level, without need to introduce three-nucleon forces. To estimate the uncertainty of the calculations both the gap and the continuous choices for the single-particle potential are considered and compared. The resultant EOS is compatible with the phenomenological analysis on the saturation point, the incompressibility, the symmetry energy at low density and its slope at saturation, together with the high-density pressure extracted from flow data on heavy ion collisions. Although the symmetry energy is appreciably larger in the gap choice in the high-density region, the maximum neutron star masses derived from the continuous-choice EOS and the gap-choice EOS are similar and close to two solar masses, which is again compatible with recent observational data. Comparison with other microscopic EOS is presented and discussed., 15 pages, 11 figures, 8 tables

The U(1) gauge structure of torsion and dislocation in three dimensional Riemann-Cartan manifold have been studied. The local topological structure of dislocation have been presented by so-called topological method in which the quantum number is by Hopf indices and Brouwer degree. Furthermore, the relationship between the dislocation lines and Wilson lines of the U(1) gauge theory is discussed by using the Chern-Simons theory.

A realistic model is suggested based on the quasiparticle Lagrange version of the self-consistent Finite Fermi Systems theory supplemented with the microscopically calculated surface parameters of the Landau–Migdal interaction amplitude. The latter are expressed in terms of the off-shell T -matrix of free NN -scattering and show a strong dependence on the chemical potential of a nucleus under consideration in the drip line vicinity. This effect could result in shifting the neutron drip line position to very large values of the neutron excess.