Nonlinear Derivative Model Research Articles

The Non-Linear Derivative (NLD) model for the in-medium hyperons & antihyperons dynamics

The in-medium properties of hyperons and antihyperons are studied with the Non-Linear Derivative (NLD) model and focus is made on the momentum dependence of strangeness optical potentials[1]. The NLD model is based on the Relativistic Mean Field (RMF) approximation to Relativistic Hadrodynamics (RHD) approach of nuclear systems, but it incorporates an explicit momentum dependence of mean-fields. The extension of the NLD model to the baryon and antibaryon octet is based on SU(6) and G-parity arguments. It is demonstrated that with a proper choice of momentum cut-offs, the Λ and Σ optical potentials are consistent with recent studies of the chiral effective field theory and Ξ optical potentials are consistent with Lattice-QCD calculations, over a wide momentum region. We also present NLD predictions for the in-medium momentum dependence of antiΛ, antiΣ and antiΞ hyperons. This work is important for future experimental studies, like CBM, PANDA at FAIR and is relevant to nuclear astrophysics as well.

Momentum dependent mean-fields of (anti)hyperons

We investigate the in-medium properties of hyperons and anti-hyperons in the framework of the Non-Linear Derivative (NLD) model. We focus on the momentum dependence of in-medium strangeness optical potentials. The NLD model is based on the simplicity of the well-established Relativistic Mean-Field (RMF) approximation, but it incorporates an explicit momentum dependence on a field-theoretical level. The extension of the NLD model to the (anti)baryon-octet is formulated in the spirit of SU(6) and G-parity arguments. It is shown that with an appropriate choice of momentum cut-offs the Λ, Σ and Ξ optical potentials are consistent with recent studies of the chiral effective field theory and Lattice-QCD calculations over a wide momentum region. In addition, we present NLD predictions for the in-medium momentum dependence of Λ‾-, Σ‾- and Ξ‾-hyperons. This work is important for future experimental studies such as CBM, PANDA at the Facility for Antiproton and Ion Research (FAIR). It is relevant for nuclear astrophysics too.

Momentum dependent mean-fields of hyperons & antihyperons

The in-medium properties of hyperons and antihyperons are studied with the Non-Linear Derivative (NLD) model and focus is made on the momentum dependence of strangeness optical potentials. The NLD model is based on the Relativistic Mean Field (RMF) approximation to Relativistic Hadrodynamics (RHD) approach of nuclear systems, but it incorporates an explicit momentum dependence of mean-fields. The extension of the NLD model to the baryon and antibaryon octet is based on SU(6) and G-parity arguments. It is demonstrated that with a proper choice of momentum cut-offs, the Λ and Σ optical potentials are consistent with recent studies of the chiral effective field theory(χ -EFT) and optical potentials are consistent with Lattice-QCD calculations, over a wide momentum region. We also present NLD predictions for the in-medium momentum dependence of ∧¯, ∑¯ and Ξ¯ hyperons. This work is important for future experimental studies, like CBM, PANDA at FAIR and is relevant to nuclear astrophysics as well.

NLD Equation of State for compressed, hot and relativistic nuclear matter

We investigate the properties of compressed and hot hadronic matter within the Non-Linear Derivative (NLD) formalism. The novel feature of the NLD model is an explicit momentum dependence of the mean-fields, which is regulated by cut-off’s of natural hadronic scale. It is covariantly and thermodynamical-consistently formulated at the basis of a field-theoretical level. We show that the NLD model describes adequately all the empirical information of cold nuclear matter as function of density (equation of state) and, in particular, as function of particle momenta (optical potential). Finally, we present predictions of the NLD approach for hot and compressed hadronic matter in terms of the Equation of state as function of density and temperature. These studies are relevant for the forthcoming experiments at FAIR@GSI. They are also important for astrophysical purposes, e.g., static neutron stars and dynamic neutron star binary systems.

Non-Linear Derivative Interactions in Relativistic Hadrodynamics

The Lagrangian of Relativistic Hadrodynamics (RHD) is extended by introducing non-linear derivative (NLD) operators into the interactions between the nucleon with the meson elds. As the novel feature of the NLD model, the nucleon selfenergy depends on both, on energy and density. Our approach contains a single cut-o parameter, which determines the density dependence of the nuclear equation of state (EoS) and the energy dependence of the nucleon-nucleus optical potential. The NLD formalism is compatible with results from microscopic nuclear matter calculations as well as with Dirac phenomenology.

Non-Linear Derivative Interactions in Relativistic Hadrodynamics

The Lagrangian of Relativistic Hadrodynamics (RHD) is extended by introducing non- linear derivative (NLD) operators into the interactions between the nucleon with the meson fields. As the novel feature of the NLD model, the nucleon selfenergy depends on both, on energy and density. Our approach contains a single cut-off parameter, which determines the density dependence of the nuclear equation of state (EoS) and the energy dependence of the nucleon-nucleus optical potential. The NLD formalism is compatible with results from microscopic nuclear matter calculations as well as with Dirac phenomenology.

Toward relativistic mean-field description of [formula omitted]–nucleus reactions

In this work we study the antinucleon–nucleus optical potential in the framework of the non-linear derivative (NLD) model with momentum dependent mean-fields. We apply the NLD model to interaction of antinucleons (N¯) in nuclear matter and, in particular, to antiproton scattering on nuclei. In nuclear matter a strong suppression of the N¯-optical potential at rest and at high kinetic energies is found and caused by the momentum dependence of relativistic mean-fields. The NLD results are consistent with known empirical N¯–nucleus observations and agree well with antiproton–nucleus scattering data. This makes the NLD approach compatible with both, nucleon and antinucleon Dirac phenomenologies. Furthermore, in nuclear matter an effective mass splitting between nucleons and antinucleons is predicted.

Momentum dependent mean-field dynamics of compressed nuclear matter and neutron stars

Nuclear matter and compact neutron stars are studied in the framework of the non-linear derivative (NLD) model which accounts for the momentum dependence of relativistic mean-fields. The generalized form of the energy-momentum tensor is derived which allows to consider different forms of the regulator functions in the NLD Lagrangian. The thermodynamic consistency of the NLD model is demonstrated for arbitrary choice of the regulator functions. The NLD approach describes the bulk properties of the nuclear matter and compares well with microscopic calculations and Dirac phenomenology. We further study the high density domain of the nuclear equation of state (EoS) relevant for the matter in $\beta$-equilibrium inside neutron stars. It is shown that the low density constraints imposed on the nuclear EoS and by the momentum dependence of the Schr\"odinger-equivalent optical potential lead to a maximum mass of the neutron stars around $M \simeq 2 M_{\odot}$ which accommodates the observed mass of the J1614-2230 millisecond radio pulsar.

Relativistic mean field model for nuclear matter with non-linear derivative couplings

We apply the non-linear derivative (NLD) model proposed recently by Gaitanos et al. to investigate the properties of nuclear matter and the mass-radius relation of neutron stars as well. Three cases with different energy-dependent non-linear terms in this model are chosen, in which comparison among the obtained results has been made. It is found that the calculated results are sensitive to the non-linear terms in the NLD model.

How deep is the antinucleon optical potential at FAIR energies

The key question in the interaction of antinucleons in the nuclear medium concerns the deepness of the antinucleon–nucleus optical potential. In this work we study this task in the framework of the non-linear derivative (NLD) model which describes consistently bulk properties of nuclear matter and Dirac phenomenology of nucleon–nucleus interactions. We apply the NLD model to antinucleon interactions in nuclear matter and find a strong decrease of the vector and scalar self-energies in energy and density and thus a strong suppression of the optical potential at zero momentum and, in particular, at FAIR energies. This is in agreement with available empirical information and, therefore, resolves the issue concerning the incompatibility of G-parity arguments in relativistic mean-field (RMF) models. We conclude the relevance of our results for the future activities at FAIR.