Pairing In Neutron Matter Research Articles

Singlet and Triplet pairing in neutron matter

Singlet and Triplet pairing in neutron matter

Variational and parquet-diagram calculations for neutron matter. III. S -wave pairing

We apply parquet-diagram summation methods for the calculation of the superfluid gap in $S$-wave pairing in neutron matter for realistic nucleon-nucleon interactions such as the Argonne $v_6$ and the Reid $v_6$ potentials. It is shown that diagrammatic contributions that are outside the parquet class play an important role. These are, in variational theories, identified as so-called "commutator contributions". Moreover, using a particle-hole propagator appropriate for a superfluid system results in the suppression of the spin-channel contribution to the induced interaction. Applying these corrections to the pairing interaction, our results agree quite well with Quantum Monte Carlo data.

Conventional and Unconventional Pairing and Condensates in Dilute Nuclear Matter

This contribution will survey recent progress toward an understanding of diverse pairing phenomena in dilute nuclear matter at small and moderate isospin asymmetry, with results of potential relevance to supernova envelopes and proto-neutron stars. Application of ab initio many-body techniques has revealed a rich array of temperature-density phase diagrams, indexed by isospin asymmetry, which feature both conventional and unconventional superfluid phases. At low density there exist a homogeneous translationally invariant BCS phase, a homogeneous LOFF phase violating translational invariance, and an inhomogeneous translationally invariant phase-separated BCS phase. The transition from the BCS to the BEC phases is characterized in terms of the evolution, from weak to strong coupling, of the pairing gap, condensate wave function, and quasiparticle occupation numbers and spectra. Additionally, a schematic formal analysis of pairing in neutron matter at low to moderate densities is presented that establishes conditions for the emergence of both conventional and unconventional pairing solutions and encompasses the possibility of dineutron formation.

Spin-polarized neutron matter: Critical unpairing and BCS-BEC precursor

We obtain the critical magnetic field required for complete destruction of $S$-wave pairing in neutron matter, thereby setting limits on the pairing and superfluidity of neutrons in the crust and outer core of magnetars. We find that for fields $B \ge 10^{17}$ G the neutron fluid is non-superfluid -- if weaker spin-1 superfluidity does not intervene -- a result with profound consequences for the thermal, rotational, and oscillatory behavior of magnetars. Because the dineutron is not bound in vacuum, cold dilute neutron matter cannot exhibit a proper BCS-BEC crossover. Nevertheless, owing to the strongly resonant behavior of the $nn$ interaction at low densities, neutron matter shows a precursor of the BEC state, as manifested in Cooper-pair correlation lengths {being} comparable to the interparticle distance. We make a systematic quantitative study of this type of BCS-BEC crossover in the presence of neutron fluid spin-polarization induced by an ultra-strong magnetic field. We evaluate the Cooper pair wave-function, quasiparticle occupation numbers, and quasiparticle spectra for densities and temperatures spanning the BCS-BEC crossover region. The phase diagram of spin-polarized neutron matter is constructed and explored at different polarizations.

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 1S0 pairing in β-equilibrium nuclear matter; the second one due to the anisotropic neutron-neutron 3PF2 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.

Self-consistent description of the inner crust of a neutron star within a realistic semimicroscopic model

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.

S-pairing in neutron matter: I. Correlated basis function theory

S-wave pairing in neutron matter is studied within an extension of correlated basis function (CBF) theory to include the strong, short range spatial correlations due to realistic nuclear forces and the pairing correlations of the Bardeen, Cooper and Schrieffer (BCS) approach. The correlation operator contains central as well as tensor components. The correlated BCS scheme of [S. Fantoni, Nucl. Phys. A 363 (1981) 381], developed for simple scalar correlations, is generalized to this more realistic case. The energy of the correlated pair condensed phase of neutron matter is evaluated at the two-body order of the cluster expansion, but considering the one-body density and the corresponding energy vertex corrections at the first order of the Power Series expansion. Based on these approximations, we have derived a system of Euler equations for the correlation factors and for the BCS amplitudes, resulting in correlated nonlinear gap equations, formally close to the standard BCS ones. These equations have been solved for the momentum independent part of several realistic potentials (Reid, Argonne v 14 and Argonne v 8 ′ ) to stress the role of the tensor correlations and of the many-body effects. Simple Jastrow correlations and/or the lack of the density corrections enhance the gap with respect to uncorrelated BCS, whereas it is reduced according to the strength of the tensor interaction and following the inclusion of many-body contributions.

A realistic model of superfluidity in the neutron star inner crust

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.

S01Superfluid Phase Transition in Neutron Matter with Realistic Nuclear Potentials and Modern Many-Body Theories

The 1S0 pairing in neutron matter is studied using realistic two- and three-nucleon interactions. The auxiliary field diffusion Monte Carlo method and correlated basis function theory are employed to get quantitative and reliable estimates of the gap. The two methods are in good agreement up to the maximum gap density and both point to a slight reduction with respect to the standard BCS value. In fact, the maximum gap is about 2.5 MeV at kF approximately 0.8 fm(-1) in BCS and 2.2-2.4 MeV at kF approximately 0.6 fm(-1)in correlated matter. In general, the computed medium polarization effects are much smaller than those previously estimated within all theories. Truncations of Argonne to simpler forms give the same gaps in BCS, provided the truncated potentials have been refitted to the same data set. The three-nucleon interaction provides an additional increase of the gap of about 0.35 MeV.

Screening effects on pairing in nuclear matter

The properties of the1S0 pairing in neutron and nuclear matter are discussed in the framework of the generalized gap equation. The self-energy and vertex corrections are treated on the same footing. It is found that the two effects lead to a strong suppression of the pairing in neutron matter, whereas they largely cancel out each other in nuclear matter due to the dominant attractive effect of the proton particle-hole bubble insertion.

Screening effects on 1S 0 pairing in nuclear matter

The properties of the 1S 0 pairing in neutron and nuclear matter are discussed in the framework of the generalized gap equation. The self-energy and vertex corrections are treated on the same footing. It is found that the two effects lead to a strong suppression of the pairing in neutron matter, whereas they largely cancel out each other in nuclear matter due to the dominant attractive effect of the proton particle-hole bubble insertion.

New method in bardeen-cooper-schrieffer theory: Tiplet pairing in superfluid dense neutron matter

On the basis of the method outlined in the first part of this review, the properties of superfluid dense neutron matter are analyzed in the density region where the spin of a Cooper pair and its total angular momentum are S=1 and J=2, respectively. An analytic solution to the problem of 3 P 2 pairing in neutron matter is presented. Basic features of the structure and of the energy spectrum of superfluid phases are discussed. Degeneracy that is absolutely dissimilar to that which is associated with the phase transformation of the order parameter in the S-pairing problem is a distinct feature of the structure of the aforementioned phases. It appears that one or even a few numbers characterizing the weight of components associated with different values of the projection M of the total angular momentum J=2 of a Cooper pair can be chosen arbitrarily, while the others adjust to them in accordance with universal laws. As a result, the structure of any phase depends neither on the density, nor on the temperature, nor on any other input parameter. The phases found here form two groups degenerate in energy. One of these groups comprises phases for which the sign of the order parameter remains unchanged over the entire Fermi surface, while the other consists of phases whose order parameter has a zero. The energy splitting between the phases from the different groups is calculated analytically as a function of temperature. The relative magnitude of this splitting changes from approximately 3% at T=0 to zero in the vicinity of the critical point T c. The role of tensor forces in dense neutron matter is analyzed. It is shown that the mixing of the orbital angular momenta L=1 and L=3 of Cooper pairs that is induced by tensor forces completely removes degeneracy peculiar to the 3 P 2-pairing problem—the number of phases and their structure at a given temperature are tightly fixed, while the energy spectrum of the phases splits completely.

Nucleon-nucleon phase shifts and pairing in neutron matter and nuclear matter

We consider ${}^{1}{S}_{0}$ pairing in infinite neutron matter and nuclear matter and show that in the lowest order approximation, where the pairing interaction is taken to be the bare nucleon-nucleon interaction in the ${}^{1}{S}_{0}$ channel, the pairing interaction and the energy gap can be determined directly from the ${}^{1}{S}_{0}$ phase shifts. This is due to the almost separable character of the nucleon-nucleon interaction in this partial wave. These results put an interaction-independent upper limit on the value of the gap, and on the density where ${}^{1}{S}_{0}$ superfluidity disappears in neutron matter and nuclear 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.

Triplet pairing of neutrons in β-stable neutron star matter

3 P 2 pairing in neutron matter is investigated using the Bonn potential models. We find pairing energy gaps in pure neutron matter comparable to the results of previous investigators when the attractive tensor coupling is included. However, taking into account that in a neutron star we have matter at β equilibrium, we find that the 3 P 2- 3 F 2 energy gap is reduced considerably.

Chapter II. Superfluidity in Neutron Star Matter and Symmetric Nuclear Matter

Nucleon superfluids which are realized in neutron star interior and symmetric nuclear matter are studied with use of realistic nuclear forces, in the density domain from the subnuclear region to about 3ρ_0 (ρ_0 being the nuclear density). It is shown that characteristic aspects of nuclear forces manifest themselves in the appearance of several kinds of nucleon superfluids, which strongly depends on the density ρ. In this chapter emphasis is put on the pairing correlations where strong noncentral (tensor and spin-orbit) forces play important roles. A theoretical framework applicable to the nonzero angular-momentum pairing including the coupling due to tensor force is given by extending the usual BCS-Bogoliubov theory for the ^1S_0 pairing (the zero angular-momentum one). This formulation has been applied to the ^3P_2+^3F_2 pairing in neutron matter (the dominant component of neutron stars) and the ^3S_1+^3D_1 pairing in symmetric nuclear matter. In the former case, although spin-orbit force mainly contributes to the ^3P_2 attraction, the tensor coupling with the ^3F_2 component assists to realize the ^3P_2 superfluid. In the latter case, the tensor coupling to the ^3D_1 component plays a vital role to realize the ^3S_1 superfluid with a large energy gap. Results of the energy gaps calculated for such nonzero angular-momentum pairings, as well as those for the ^1S_0 pairing, are shown. We have found the realization of the following nucleon superfluids; the neutron ^3P_2 superfluid and the proton ^1S_0 one in the fluid core of neutron stars at ρ≃(0.7∼3)ρ_0, the neutron ^1S_0 superfluid in the inner crust of neutron stars at ρ≃(10^−3∼0.5)ρ_0, and the ^3S_1 superfluid in symmetric nuclear matter at a wide range of ρ including ρ_0, contrary to the ^1S_0 one realized at ρ≲ρ_0/2. The properties of these superfluids and their implications are also discussed.