arXiv subjects

C. Fuchs

Publications and source records attributed to C. Fuchs.

At least 37 records · Page 2Linked to original sources

arXiv2007

Nuclear matter in the crust of neutron stars derived from realistic NN interactions

Properties of inhomogeneous nuclear matter are evaluated within a relativistic mean field approximation using density dependent coupling constants. A parameterization for these coupling constants is presented, which reproduces the properties of the nucleon self-energy obtained in Dirac Brueckner Hartree Fock calculations of asymmetric nuclear matter but also provides a good description for bulk properties of finite nuclei. The inhomogeneous infinite matter is described in terms of cubic Wigner-Seitz cells, which allows for a microscopic description of the structures in the so-called ``pasta-phase'' of nuclear configurations and provides a smooth transition to the limit of homogeneous matter. The effects of pairing properties and finite temperature are considered. A comparison is made to corresponding results employing the phenomenological Skyrme Hartree-Fock approach and the consequences for the Thomas-Fermi approximation are discussed.

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arXiv2007

Semiclassical expansion of quantum characteristics for many-body potential scattering problem

In quantum mechanics, systems can be described in phase space in terms of the Wigner function and the star-product operation. Quantum characteristics, which appear in the Heisenberg picture as the Weyl's symbols of operators of canonical coordinates and momenta, can be used to solve the evolution equations for symbols of other operators acting in the Hilbert space. To any fixed order in the Planck's constant, many-body potential scattering problem simplifies to a statistical-mechanical problem of computing an ensemble of quantum characteristics and their derivatives with respect to the initial canonical coordinates and momenta. The reduction to a system of ordinary differential equations pertains rigorously at any fixed order in $\hbar$. We present semiclassical expansion of quantum characteristics for many-body scattering problem and provide tools for calculation of average values of time-dependent physical observables and cross sections. The method of quantum characteristics admits the consistent incorporation of specific quantum effects, such as non-locality and coherence in propagation of particles, into the semiclassical transport models. We formulate the principle of stationary action for quantum Hamilton's equations and give quantum-mechanical extensions of the Liouville theorem on the conservation of phase-space volume and the Poincaré theorem on the conservation of $2p$ forms. The lowest order quantum corrections to the Kepler periodic orbits are constructed. These corrections show the resonance behavior.

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arXiv2006

Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter based on improved approximation schemes

We present Dirac-Brueckner-Hartree-Fock calculations for isospin asymmetric nuclear matter which are based on improved approximations schemes. The potential matrix elements have been adapted for isospin asymmetric nuclear matter in order to account for the proton-neutron mass splitting in a more consistent way. The proton properties are particularly sensitive to this adaption and its consequences, whereas the neutron properties remains almost unaffected in neutron rich matter. Although at present full Brueckner calculations are still too complex to apply to finite nuclei, these relativistic Brueckner results can be used as a guidance to construct a density dependent relativistic mean field theory, which can be applied to finite nuclei. It is found that an accurate reproduction of the Dirac-Brueckner-Hartree-Fock equation of state requires a renormalization of these coupling functions.

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arXiv2006

Density resummation of perturbation series in a pion gas to leading order in chiral perturbation theory

The mean field (MF) approximation for the pion matter, being equivalent to the leading ChPT order, involves no dynamical loops and, if self-consistent, produces finite renormalizations only. The weight factor of the Haar measure of the pion fields, entering the path integral, generates an effective Lagrangian $δ\mathcal{L}_{H}$ which is generally singular in the continuum limit. There exists one parameterization of the pion fields only, for which the weight factor is equal to unity and $δ\mathcal{L}_{H}=0$, respectively. This unique parameterization ensures selfconsistency of the MF approximation. We use it to calculate thermal Green functions of the pion gas in the MF approximation as a power series over the temperature. The Borel transforms of thermal averages of a function $\mathcal{J}(χ^αχ^α)$ of the pion fields $χ^α$ with respect to the scalar pion density are found to be $\frac{2}{\sqrtπ}\mathcal{J}(4t)$. The perturbation series over the scalar pion density for basic characteristics of the pion matter such as the pion propagator, the pion optical potential, the scalar quark condensate $<{\bar{q}}q>$, the in-medium pion decay constant ${\tilde{F}}$, and the equation of state of pion matter appear to be asymptotic ones. These series are summed up using the contour-improved Borel resummation method. The quark scalar condensate decreases smoothly until $T_{max}\simeq 310$ MeV. The temperature $T_{max}$ is the maximum temperature admissible for thermalized non-linear sigma model at zero pion chemical potentials. The estimate of $T_{max}$ is above the chemical freeze-out temperature $T\simeq 170$ MeV at RHIC and above the phase transition to two-flavor quark matter $T_{c} \simeq 175$ MeV, predicted by lattice gauge theories.

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arXiv2006

The relativistic self-energy in nuclear dynamics

It is a well known fact that Dirac phenomenology of nuclear forces predicts the existence of large scalar and vector mean fields in matter. To analyse the relativistic self-energy in a model independent way, modern high precision nucleon-nucleon ($NN$) potentials are mapped on a relativistic operator basis using projection techniques. This allows to compare the various potentials at the level of covariant amplitudes were a remarkable agreement is found. It allows further to calculate the relativistic self-energy in nuclear matter in Hartree-Fock approximation. Independent of the choice of the nucleon-nucleon interaction large scalar and vector mean fields of several hundred MeV magnitude are generated at tree level. In the framework of chiral EFT these fields are dominantly generated by contact terms which occur at next-to-leading order in the chiral expansion. Consistent with Dirac phenomenology the corresponding low energy constants which generate the large fields are closely connected to the spin-orbit interaction in $NN$ scattering. The connection to QCD sum rules is discussed as well.

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arXiv2006

Underlying gauge symmetries of second-class constraints systems

Gauge-invariant systems in unconstrained configuration and phase spaces, equivalent to second-class constraints systems upon a gauge-fixing, are discussed. A mathematical pendulum on an $n-1$-dimensional sphere $S^{n-1}$ as an example of a mechanical second-class constraints system and the O(n) non-linear sigma model as an example of a field theory under second-class constraints are discussed in details and quantized using the existence of underlying dilatation gauge symmetry and by solving the constraint equations explicitly. The underlying gauge symmetries involve, in general, velocity dependent gauge transformations and new auxiliary variables in extended configuration space. Systems under second-class holonomic constraints have gauge-invariant counterparts within original configuration and phase spaces. The Dirac's supplementary conditions for wave functions of first-class constraints systems are formulated in terms of the Wigner functions which admit, as we show, a broad set of physically equivalent supplementary conditions. Their concrete form depends on the manner the Wigner functions are extrapolated from the constraint submanifolds into the whole phase space.

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arXiv2006

Dilepton production at HADES: theoretical predictions

Dileptons represent a unique probe for nuclear matter under extreme conditions reached in heavy-ion collisions. They allow to study meson properties, like mass and decay width, at various density and temperature regimes. Present days models allow generally a good description of dilepton spectra in ultra-relativistic heavy ion collision. For the energy regime of a few GeV/nucleon, important discrepancies between theory and experiment, known as the DLS puzzle, have been observed. Various models, including the one developed by the Tübingen group, have tried to address this problem, but have proven only partially successful. High precision spectra of dilepton emission in heavy-ion reactions at 1 and 2 GeV/nucleon will be released in the near future by the HADES Collaboration at GSI. Here we present the predictions for dilepton spectra in C+C reactions at 1 and 2 GeV/nucleon and investigate up to what degree possible scenarios for the in-medium modification of vector mesons properties are accessible by the HADES experiment.

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arXiv2006

Modelization of the EOS

This article summarizes theoretical predictions for the density and isospin dependence of the nuclear mean field and the corresponding nuclear equation of state. We compare predictions from microscopic and phenomenological approaches. An application to heavy ion reactions requires to incorporate these forces into the framework of dynamical transport models. Constraints on the nuclear equation of state derived from finite nuclei and from heavy ion reactions are discussed.

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arXiv2006

Medium effects on phi decays to dilepton and kaon-antikaon pairs in relativistic heavy ion reactions

We consider the role of rescattering of secondary kaons on the dilepton branching ratio of the phi meson. In-medium mass modifications and broadening of kaons and phi mesons are taken into account. We find in the framework of a Bjorken scenario for the time evolution of the expanding fireball that the phi yield from dimuons is moderately or at least only slightly enhanced compared to that from kaon-antikaon pairs. The relation to experimental yields measured by the NA49, NA50 and CERES Collaborations at CERN SPS and the PHENIX Collaboration at RHIC is discussed.

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arXiv2006

Model independent study of the nucleon self-energy in matter

Relativistic and non-relativistic modern nucleon-nucleon potentials are mapped on a relativistic operator basis using projection techniques. This allows to compare the various potentials at the level of covariant amplitudes were a remarkable agreement is found. In nuclear matter large scalar and vector mean fields of several hundred MeV magnitude are generated at tree level. This is found to be a model independent feature of the nucleon-nucleon interaction.

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arXiv2006

Constraints on the high-density nuclear equation of state from the phenomenology of compact stars and heavy-ion collisions

A new scheme for testing nuclear matter equations of state (EsoS) at high densities using constraints from neutron star phenomenology and a flow data analysis of heavy-ion collisions is suggested. An acceptable EoS shall not allow the direct Urca process to occur in neutron stars with masses below $1.5~M_{\odot}$, and also shall not contradict flow and kaon production data of heavy-ion collisions. Compact star constraints include the mass measurements of 2.1 +/- 0.2 M_sun (1 sigma level) for PSR J0751+1807, of 2.0 +/- 0.1 M_sun from the innermost stable circular orbit for 4U 1636-536, the baryon mass - gravitational mass relationships from Pulsar B in J0737-3039 and the mass-radius relationships from quasiperiodic brightness oscillations in 4U 0614+09 and from the thermal emission of RX J1856-3754. This scheme is applied to a set of relativistic EsoS constrained otherwise from nuclear matter saturation properties with the result that no EoS can satisfy all constraints simultaneously, but those with density-dependent masses and coupling constants appear most promising.

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arXiv2006

$D$-mesons and charmonium states in hot pion matter

We calculate the in-medium $D$ meson self-energies in a hot pion gas induced by resonance interactions with pions. The appropriate resonances in the {\it s},~ {\it p} and {\it d} waves of the $D$ meson-pion pair are represented by low lying scalar, vector and tensor $D^*$ mesons. At temperatures around 200 MeV the D-meson mass drops by $30~ \rm {MeV}$ and the scattering width grows up to $60~ \rm {MeV}$. Similar medium effects are found for the $D^*$ vector mesons. This opens and/or enhances the decay and/or dissociation channels of the charmonium states $Ψ^\prime$, $χ_c$ and $J/Ψ$ to $D \bar D,~D^* \bar D,~D \bar D^* ,~D^* \bar D^*$ pairs in pion matter.

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arXiv2005

Energy densities and equilibration in heavy ion collisions at sqrt(s) = 200 GeV with the quark-gluon string model

We study thermodynamic characteristica of ultra-relativistic Au+Au collisions at RHIC energy sqrt(s) = 200 GeV within the framework of a microscopic transport model, namely the quark-gluon string model (QGSM). The temporal evolution of the local energy density, transverse and longitudinal pressure and equilibration times are considered. In contrast to complete equilibration which is even in central reactions hardly achieved, pre-equilibrium stages with energy densities well above the critical energy density predicted by lattice QCD are established at short time scales. Corresponding energy density profiles at proper time tau = 1 fm/c compare well with hydrodynamical assumptions for initial energy density distributions.

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arXiv2005

Model independent study of the Dirac structure of the nucleon-nucleon interaction

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arXiv2005

Momentum, Density, and Isospin dependence of the Symmetric and Asymmetric Nuclear Matter Properties

Properties of symmetric and asymmetric nuclear matter have been investigated in the relativistic Dirac-Brueckner-Hartree-Fock approach based on projection techniques using the Bonn A potential. The momentum, density, and isospin dependence of the optical potentials and nucleon effective masses are studied. It turns out that the isovector optical potential depends sensitively on density and momentum, but is almost insensitive to the isospin asymmetry. Furthermore, the Dirac mass $m^*_D$ and the nonrelativistic mass $m^*_{NR}$ which parametrizes the energy dependence of the single particle spectrum, are both determined from relativistic Dirac-Brueckner-Hartree-Fock calculations. The nonrelativistic mass shows a characteristic peak structure at momenta slightly above the Fermi momentum $\kf$. The relativistic Dirac mass shows a proton-neutron mass splitting of $m^*_{D,n} m^*_{NR,p}$ which is in agreement with the results from nonrelativistic calculations.

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arXiv2005

Anisotropic flow of strange particles at RHIC

Space-time picture of the anisotropic flow evolution in Au+Au collisions at BNL RHIC is studied for strange hadrons within the microscopic quark-gluon string model. The directed flow of both mesons and hyperons demonstrates wiggle structure with the universal antiflow slope at |y| < 2 for minimum bias events. This effect increases as the reaction becomes more peripheral. The development of both components of the anisotropic flow is closely related to particle freeze-out. Hadrons are emitted continuously, and different hadronic species are decoupled from the system at different times. These hadrons contribute differently to the formation and evolution of the elliptic flow, which can be decomposed onto three components: (i) flow created by hadrons emitted from the surface at the onset of the collision; (ii) flow produced by jets; (iii) hydrodynamic flow. Due to these features, the general trend in elliptic flow formation is that the earlier mesons are frozen, the weaker their elliptic flow. In contrast, baryons frozen at the end of the system evolution have stronger v2.

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arXiv2005

Effective Nucleon Masses in Symmetric and Asymmetric Nuclear Matter

The momentum and isospin dependence of the in-medium nucleon mass are studied. Two definitions of the effective mass, i.e. the Dirac mass $m^*_D$ and the nonrelativistic mass $m^*_{NR}$ which parameterizes the energy spectrum, are compared. Both masses are determined from relativistic Dirac-Brueckner-Hartree-Fock calculations. The nonrelativistic mass shows a distinct peak around the Fermi momentum. The proton-neutron mass splitting in isospin asymmetric matter is $m^*_{D,n} m^*_{NR,p}$, which is consistent with nonrelativistic approaches.

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arXiv2005

Anisotropic flow of charged and identified hadrons in the quark-gluon string model for Au+Au collisions at sqrt(s) = 200 GeV

The pseudorapidity behaviour of the azimuthal anisotropy parameters v_1 and v_2 of inclusive charged hadrons and their dependence on the centrality has been studied in Au+Au collisions at full RHIC energy of sqrt(s) = 200 GeV within the microscopic quark-gluon string model. The QGSM simulation results for the directed flow v_1 show antiflow alignment within the pseudorapidity range |eta| < 2 in a fair agreement with the experimental v_1(eta) data, but cannot reproduce the further development of the antiflow up to |eta| around 3.5. The eta dependence of the elliptic flow v_2 extracted from the simulations agrees well with the experimental data in the whole pseudorapidity range for different centrality classes. The centrality dependence of the integrated elliptic flow of charged hadrons in the QGSM almost coincides with the PHOBOS experimental distribution. The transverse momentum dependence of the elliptic flow of identified and inclusive charged hadrons is studied also. The model reproduces quantitatively the low p_T part of the distributions rather good, but underestimates the measured elliptic flow for transverse momenta p_T > 1 GeV/c. Qualitatively, however, the model is able to reproduce the saturation of the v_2(p_T) spectra with rising p_T as well as the crossing of the elliptic flow for mesons and baryons.

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