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Register a new userRenormalization group approach to neutron matter: quasiparticle interactions, superfluid gaps and the equation of state
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Achim Schwenk SUNYn Stony Brook
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Renormalization group methods can be applied to the nuclear many-body problem using the approach proposed by Shankar. We start with the two-body low momentum interaction V_{low k} and use the RG flow from the particle-hole channels to calculate the full scattering amplitude in the vicinity of the Fermi surface. This is a new straightforward approach to the many-body problem which is applicable also to condensed matter systems without long-range interactions, such as liquid 3He. We derive the one-loop renormalization group equations for the quasiparticle interaction and the scattering amplitude at zero temperature. The RG presents an elegant method to maintain all momentum scales and preserve the antisymmetry of the scattering amplitude. As a first application we solve the RG equations for neutron matter. The resulting quasiparticle interaction includes effects due to the polarization of the medium, the so-called induced interaction of Babu and Brown. We present results for the Fermi liquid parameters, the equation of state of neutron matter and the 1S0 superfluid pairing gap.
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We have developed a fully consistent framework for calculations in the Quasiparticle Random Phase Approximation (QRPA) with $NN$ interactions from the Similarity Renormalization Group (SRG) and other unitary transformations of realistic interactions. The consistency of our calculations, which use the same Hamiltonian to determine the Hartree-Fock-Bogoliubov (HFB) ground states and the residual interaction for QRPA, guarantees an excellent decoupling of spurious strength, without the need for empirical corrections. While work is under way to include SRG-evolved 3N interactions, we presently account for some 3N effects by means of a linearly density-dependent interaction, whose strength is adjusted to reproduce the charge radii of closed-shell nuclei across the whole nuclear chart. As a first application, we perform a survey of the monopole, dipole, and quadrupole response of the calcium isotopic chain and of the underlying single-particle spectra, focusing on how their properties depend on the SRG parameter $lambda$. Unrealistic spin-orbit splittings suggest that spin-orbit terms from the 3N interaction are called for. Nevertheless, our general findings are comparable to results from phenomenological QRPA calculations using Skyrme or Gogny energy density functionals. Potentially interesting phenomena related to low-lying strength warrant more systematic investigations in the future.
We show that the renormalization group decimation of modern nucleon potential models to low momenta results in a unique nucleon interaction V_{low k}. This interaction is free of short-ranged singularities and can be used directly in many-body calculations. The RG scaling properties follow directly from the invariance of the scattering phase shifts. We discuss the RG treatment of Fermi liquids. The RG equation for the scattering amplitude in the two particle-hole channels is given at zero temperature. The flow equations are simplified by retaining only the leading term in an expansion in small momentum transfers. The RG flow is illustrated by first studying a system of spin-polarized fermions in a simple model. Finally, results for neutron matter are presented by employing the unique low momentum interaction V_{low k} as initial condition of the flow. The RG approach yields the amplitude for non-forward scattering, which is of great interest for calculations of transport properties and superfluid gaps in neutron star interiors. The methods used can also be applied to condensed matter systems in the absence of long-ranged interactions.
The Equation of State (EoS) of dense matter represents a central issue in the study of compact astrophysical objects and heavy ion reactions at intermediate and relativistic energies. We have derived a nuclear EoS with nucleons and hyperons within the Brueckner-Hartree-Fock approach, and joined it with quark matter EoS. For that, we have employed the MIT bag model, as well as the Nambu--Jona-Lasinio (NJL) and the Color Dielectric (CD) models, and found that the NS maximum masses are not larger than 1.7 solar masses. A comparison with available data supports the idea that dense matter EoS should be soft at low density and quite stiff at high density.
{it Background.} We investigate possible correlations between neutron star observables and properties of atomic nuclei. Particularly, we explore how the tidal deformability of a 1.4 solar mass neutron star, $M_{1.4}$, and the neutron skin thickness of ${^{48}}$Ca and ${^{208}}$Pb are related to the stellar radius and the stiffness of the symmetry energy. {it Methods.} We examine a large set of nuclear equations of state based on phenomenological models (Skyrme, NLWM, DDM) and {it ab-initio} theoretical methods (BBG, Dirac-Brueckner, Variational, Quantum Monte Carlo). {it Results.} We find strong correlations between tidal deformability and NS radius, whereas a weaker correlation does exist with the stiffness of the symmetry energy. Regarding the neutron skin thickness, weak correlations appear both with the stiffness of the symmetry energy, and the radius of a $M_{1.4}$. {it Conclusion.} The tidal deformability of a $M_{1.4}$ and the neutron-skin thickness of atomic nuclei show some degree of correlation with nuclear and astrophysical observables, which however depends on the ensemble of adopted EoS.
Neutron star (NS) is a unique astronomical compact object where the four fundamental interactions have been revealed from the observation and studied in different ways. While the macroscopic properties of NS like mass and radius can be determined within the General Relativity using a realistic equation of state (EOS) of NS matter, such an EOS is usually generated by a nuclear structure model like, e.g., the nuclear mean-field approach to asymmetric nuclear matter. Given the radius of NS extended to above 10 km and its mass up to twice the solar mass, NS is expected to be tidally deformed when it is embedded in a strong tidal field. Such a tidal effect was confirmed unambiguously in the gravitation wave signals detected recently by the LIGO and Virgo laser interferometers from GW170817, the first ever direct observation of a binary NS merger. A nonrelativistic mean-field study is carried out in the present work within the Hartree-Fock formalism to construct the EOS of NS matter, which is then used to determine the tidal deformability, gravitational mass, and radius of NS. The mean-field results are compared with the constraints imposed for these quantities by the global analysis of the observed GW170817 data, and a strong impact by the incompressibility of nuclear matter on the hydrostatic configuration of NS is shown.
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