International Journal of Modern Physics E

In these lectures, I will attempt a pedagogical and qualitative introduction to the theory of equilibrium and thermalization of quark-gluon plasmas. I assume only that the reader is familiar with quantum field theory at zero temperature and with QCD as the theory of the strong interactions. I focus on the limit of small α_s, which in principle should be relevant at extremely high temperature because of asymptotic freedom, and in any case provides a clean theoretical context in which to discuss a variety of phenomena. Topics discussed include the basic equilibrium formalism for finite-temperature quantum field theory, Debye screening, electric deconfinement, magnetic confinement, dimensional reduction, plasma waves, kinetic theory, hydrodynamic properties such as viscosity, the Landau–Pomeranchuk–Migdal effect, thermalization in (arbitrarily high energy) heavy ion collisions, and QCD plasma instabilities.

In this series of three lectures, we discuss several aspects of high energy scattering among hadrons in Quantum Chromodynamics. The first lecture is devoted to a description of the parton model, Bjorken scaling and the scaling violations due to the evolution of parton distributions with the transverse resolution scale. The second lecture describes parton evolution at small momentum fraction x, the phenomenon of gluon saturation and the Color Glass Condensate (CGC). In the third lecture, we present the application of the CGC to the study of high energy hadronic collisions, with emphasis on nucleus-nucleus collisions. In particular, we provide the outline of a proof of high energy factorization for inclusive gluon production.

Starting with the example of the quantum mechanical harmonic oscillator, we develop the concept of euclidean lattice field theory. After describing Wilson's formulation of quantum chromodynamics on the lattice, we will introduce modern lattice QCD actions which greatly reduce lattice artefacts or are even chiral invariant. The substantial algorithmic improvements of the last couple of years will be shown which led to a real breakthrough for dynamical Wilson fermion simulations. Finally, we will present some results of present simulations with dynamical quarks and demonstrate that nowadays even at small values of the quark mass high precision simulation results for physical quantities can be obtained.

A brief revision of different relativistic hadronic models, including the original sigma-omega model, models with nonlinear meson terms, density dependent coupling parameters and the quark-meson coupling, are presented. The inclusion of short range correlations is discussed. Dense stellar matter is described within the relativistic hadronic models introduced. We build the EoS for cold and warm hadronic and hybrid stars and discuss the star properties obtained within the different approaches. The low density thermodynamical and dynamical instabilities of stellar matter of interest for the discussion of the crust of neutron stars are investigated.

The infrared behavior of Landau gauge QCD vertex functions is investigated employing a skeleton expansion of the Dyson–Schwinger and Renormalization Group equations. Results for the ghost-gluon, three-gluon, four-gluon and quark-gluon vertex functions are presented. Positivity violation of the gluon propagator, and thus gluon confinement, is demonstrated. Results of the Dyson–Schwinger equations for a finite volume are compared to corresponding lattice data. It is analytically demonstrated that a linear rising potential between heavy quarks can be generated by infrared singularities in the dressed quark-gluon vertex. The selfconsistent mechanism that generates these singularities necessarily entails the scalar Dirac amplitudes of the full vertex and the quark propagator. These can only be present when chiral symmetry is broken, either explicitly or dynamically.

Lowering the string scale in the TeV region provides a theoretical framework for solving the mass hierarchy problem and unifying all interactions. The apparent weakness of gravity can then be accounted by the existence of large internal dimensions, in the submillimeter region, and transverse to a braneworld where we must be confined. I review the main properties of this scenario and its implications for observations at both particle colliders, and in non-accelerator gravity experiments.

The possible structure of the QCD phase diagram is discussed focusing on color superconducting quark matter in the region of low temperatures and moderately large densities which could be relevant for compact stars.

It is clear that the order of the deconfining phase transition in QCD at nonzero temperature and density (with realistic quark masses) is of great experimental interest. The importance of the transition at zero baryon density with only two (degenerate) quark flavors is perhaps less evident. As a matter of fact, the order of the transition in this case is still an open problem and corresponds to the last question mark in the zero-density phase diagram of QCD. We argue that establishing the nature of the transition in this case is also a crucial test for numerical simulations of lattice QCD, allowing precise estimates of the possible systematic errors related to the choice of fermion-simulation algorithm and of discretized formulation for fermions.

Cosmic rays have always been an important tool to study particle interactions and astrophysics. In this article, we are going to review the main results from this field in the energy range from 10¹⁶ to 10²⁰ eV. Important results from the KASCADE and Pierre Auger Experiments are going to be shown and discussed. Some perspectives for the near future concerning new measurements are going to be presented.

A gauge-invariant saddle point expansion for the Yang–Mills vacuum transition amplitude on the basis of the squeezed approximation to the vacuum wave functional is outlined. This framework allows the identification of gauge-invariant infrared degrees of freedom which arise as dominant sets of gauge field orbits and provide the principal input for an essentially analytical treatment of soft amplitudes. The analysis of the soft modes sheds new light on how vacuum fields organize themselves into collective excitations and yields a gauge-invariant representation of instanton and meron effects as well as a new physical interpretation for Faddeev–Niemi knots.

An approximate holographic dual of QCD is constructed and shown to reproduce the empirical linear trajectories of universal slope on which the square masses of radially and orbitally excited hadrons join. Conformal symmetry breaking and other IR effects are described exclusively by deformations of the anti-de Sitter background metric. The predictions for the light hadron spectrum include new relations between ground state masses and trajectory slopes and are in good overall agreement with experimental data.

In order to analyze optimization issues related to the non-perturbative optimized perturbation theory method we consider the effective potential as well as the fermionic mass for the 2d Gross–Neveu model. A direct comparison within the large-N approximation shows that the results obtained from the effective potential optimization are more efficient unless one uses the renormalization group to improve the mass.

We study the phase diagram of the 3d massless Gross–Neveu model with different numbers of fermionic species, N. Using the Optimized Perturbation Theory technique, the free energy is evaluated at finite temperature and chemical potential. The analytical results allow us to calculate critical quantities for any value of N and, in the present work, we choose de values N = 1,3,4,10. In addition, we determine the evolution of the tricritical points, in the temperature versus chemical potential plane for these different values of N.

We analyze the role of renormalization group (RG) running of the coupling and fermion masses in perturbative Yukawa theory at finite density. The dependence of the RG flow on the number of fermion flavors is discussed. Results for the fermionic contribution to the two-loop pressure at zero temperature and finite density are presented for N_F = 4, and finite fermion mass effects are shown to be an important correction.

We have recently performed a relativistic O(q⁴) chiral expansion of the two-pion exchange NN potential, and explored its configuration space content by fitting the theoretical expressions to parametrized simply formulas. In order to test the applicability of our parametrized potential, we studied the pion plus production in proton-neutron scattering at threshold an compare our results to the ones given by Reid 93 and v18 potentials. We shown that our results are very close to the v18 potential, which means that the potential is reliable and trustful.

In these proceedings a stochastic particle (1+1)-dimensional model which mimics high energy evolution and scattering in QCD at fixed impact parameter is presented. The model exhibits a saturation mechanism similar to gluon saturation in QCD as well as all the qualitative features expected in QCD at fixed impact parameter, concerning both the mean-field aspects and the effects of fluctuations, and appears to be in the universality class of the reaction-diffusion process, as also expected for QCD. The evolution equations for the scattering amplitude generated by this model appear as a natural generalization of the Balitsky-JIMWLK equations in which both target and projectile are symmetrically treated. The structural aspects of the model may inspire future searches for corresponding structures in QCD.

In this work the DIS measurements of the proton structure function at high energy from the dipole model in momentum space are reproduced. The dipole-proton forward scattering amplitude is modeled using the knowledge of asymptotic solutions of the Balitsky–Kovchegov equation, describing high-energy QCD in the presence of saturation effects.

We apply the subtractive renormalization method to the nucleon-nucleon interaction at Next-to-Next-to-Leading order (NNLO). Here we show the results for some uncoupled peripheral waves.

In the present work we investigate one possible variation on the usual static pulsars: the inclusion of rotation. We use a formalism proposed by Hartle and Thorne to calculate the properties of rotating pulsars with all possible compositions. All calculations were performed for zero temperature and also for fixed entropy equations of state.

The linear sigma model at finite baryonic density with a massive classical vector field is investigated considering that all the bosonic fields develop non zero expected classical values, eventually corresponding to dynamical symmetry breakings. The densities involving baryons are calculated using the solutions of the Dirac equation coupled to the classical vector and scalar field. The stability and ground state conditions are analyzed with particular (variational-like) prescriptions. Some aspects of relevance for states containing anti-hadrons and also for the restoration of chiral symmetry are discussed.

We solve numerically the two first order differential equations obtained by Tooper for polytropic compact stars. These equations depend on the polytropic index n related to the adiabatic index Γ = 1 + 1/n and on a parameter σ that manifests the relativistic content of the polytropic equation of state (EOS). In this work we investigate the effect of increasing σ for two polytropic EOS: the case of a nonrelativistic Fermi gas (n = 1.5) and the relativistic one (n = 3.0). We show that for large values of σ, where the sound velocity is not small in comparison to the velocity of light, the matter density is more concentrated in the center of the star and as a consequence the star mass also is: this effect is quite strong in the case of the relativistic fermi gas.

A complementary way to investigate the Hadron-Quark-Gluon Phase transition in heavy ion collisions is to analyze properties of dense astrophysical objects, i.e. neutron stars. A neutron star can be simply described as a giant nucleus. However, due to the enormous gravitational contraction, it can reach densities up to several times the density found in the Pb nucleus. This property allows the formation of a core made up of free quarks and gluons. Once this new phase is formed, the new state drastically changes the neutron star macroscopic properties, such as its mass and radius. In the present work, we follow a route opposite to the common sense, investigating the properties of the phase transition by analyzing neutron star properties of mass and radius. This observations can determine the density where the transition can occur or the order of the transition using some sort of reverse engineering. As a consequence, the values of the bag constant or the strong coupling constant can be inferred.

We study the thermodynamics of two flavor color superconducting (2SC) quark matter within a nonlocal chiral quark model, using both instantaneous and covariant nonlocal interactions. For applications to compact stars, we impose conditions of electric and color charge neutrality as well as β equilibrium and construct a phase transition to the hadronic matter phase described within the Dirac–Brueckner–Hartree–Fock (DBHF) approach. We obtain mass-radius relations for hybrid star configurations which fulfill modern observational constraints, including compact star masses above 2M_⊙.

The next generation of gravitational wave observatories are promissing candidates to make the first detections. Once the detection occurs the GW characteristics permit to extract some information about the gravitational wave source. In the present work we focus on waves produced by neutron stars which can give stringent constraints on the nuclear matter equation of state. The microscopic description is based on a nonlinear field-theoretical model in order to construct such an equation of state. The model has free parameters, which from actual knowledge may not be pinned down by direct nuclear matter experiments. An important example is the hyperon-sigma meson coupling constant, currently determined by the spin-isospin SU(6) scheme. The coupling constant is of significant relevance for the structure of the equation of state, controlling its rigidity and, consequently, the properties of neutron stars and gravitational wave signals. We show, in this work, how one can constrain the hyperon-sigma meson coupling constant assuming the detection of a gravitational wave.

The strange quark matter (SQM) hypothesis states that it is possible that the ground state of cold baryonic matter is a plasma composed roughly of equal numbers of up, down and strange quarks. This stability scenario is even more favorable if quarks are in a color flavor locked (CFL) state, in which quarks form pairs resembling the superconductivity Cooper pairs. We present calculations on the basis of the MIT Bag Model for the stability windows for SQM in the CFL state and for the energy of strangelets at non-zero temperatures, comparing with the unpaired SQM. We also discuss some astrophysical implications of such results.

We investigate the role of the strange σ*, ϕ and δ meson fields on the delineation of main properties of neutron stars using a parameterized Lagrangian density model in the effective baryon and meson sectors. We assume, strange quarks are localized within the hyperon fields, which carry the strangeness content of the model. Our main goal is to analyze stability conditions of neutron stars with large amount of strangeness per baryon. Our main result indicates the inclusion of the strange (anti-)quark containing meson field σ*, besides ϕ and δ into nuclear matter, turn the equation of state stiffer this way increasing the gravitational mass of the neutron star.

In this work we determine the critical density values of the phase transition between the hadronic to the CFL superconducting quark matter. The Delta resonances and the complete spin-1/2 baryonic octet are considered in the hadronic phase and it is observed that the delta matter inclusion in baryonic phase modifies significantly the critical conditions for the phase transition. Also, we discuss the role of the color superconducting gap on the structure properties of a formed hybrid neutron stars.

During the observation of the 4th November 2003 large solar flare, a new and intense spectral component was observed with a maximum lying in the terahertz range. The origin of such component is still unknown, constituting a problem that goes beyond the application of canonical models used to describe the well-known microwave spectrum observed at frequencies below 100 GHz. In this work we investigate a possible contribution to the terahertz synchrotron emission in solar flares from positrons produced by Drell–Yan process in proton-proton collisions in the solar atmosphere.

We have predicted (contribution to this issue) an isovector component of the light scalar meson sector by using the chiral symmetry transformation formalism. On the basis of this result, we study dense hadronic matter in a generalized relativistic mean field approach with σ, ω and ρ mesons as well as nonlinear self-couplings of the I = 1 component of a light scalar meson field and compare its predictions for neutron star properties with results from different models for nuclear matter found in the literature.

We investigate the production of disoriented chiral condensates in ultra high energy collisions and look for an intrinsic signature they could produce in ongoing and future cosmic ray experiments. This is implemented by studying the atmospheric showers generated after the chiral symmetry breakdown. We also speculate on the nature of the events and its connection with Centauro and anti-Centauro observations. Some preliminary results are presented.

We describe the ππS-wave in D⁺→ π⁺π⁻π⁺ decays using a unitary model for the ππ Final State Interactions (FSI). The three body decay is treated as a quasi two-body process where, at the weak vertex, the D meson decays into a resonance and a pion. The weak part of the decay amplitude is evaluated using the effective weak Hamiltonian within the factorization approximation.

The strangeness content of the nucleon electric and magnetic form factors is analyzed in a version of the meson cloud model, including the kaon and the scalar κ mesons. We compare our results with the recent measurements performed at TJNAF.

The scalar form factor of the nucleon in configuration space as well as its σ-term were evaluated some time ago in the framework of chiral symmetry. We investigate their dependence on the pion mass, aiming at the behavior of the σ-term at the chiral limit. Using the results for light pions, the nucleon mass as a function of the pion mass is evaluated. We also present the results for the scalar form factor for heavy pions.

Solutions for the amplitudes that give accurate description of pp and scattering at high energies are investigated, with particular attention given to the properties of their zeros and slopes, whose determination is required for the study of the Coulomb interference region. Proper extrapolations of these quantities to the LHC energies are important for the analysis of the forthcoming experiments.

We extend the use of derivative dispersion relations to the study of slopes of the real and imaginary amplitudes in pp and elastic scattering. The new relations are tested against the solutions for the amplitudes obtained in the analysis of the high energy data. Extensions beyond the forward direction are investigated.

The photoproduction helicity amplitudes for the positive parity excited baryons are analyzed in the context of the 1/N_c expansion of QCD.

We study the decay ω(782) → π⁺π⁻π⁰, which can contribute as an intermediate process to the photodisintegration of ³H and of ⁴He. In the calculation of this amplitude, performed by means of chiral effective Lagrangians, we study the role of the contact term and the ρ(770) resonance contributions. Dalitz plots are built with different values for the ρ mass and width. Our best result is obtained without the contact term.

QCD spectral sum rules is used to test the nature of the meson X(3872), assumed to be an exotic four-quark state with J^PC = 1⁺⁺. For definiteness, the current proposed recently by Maiani et al¹ is used, at leading order in α_s, considering the contributions of higher dimension condensates. The value M_X = (3.94 ± 0.17) GeV is found which is compatible, within the errors, with the experimental candidate X(3872). The uncertainties of our estimates are mainly due to the one from the c quark mass.

We discuss novel dispersion relations in differential form, connecting real and imaginary parts of elastic scattering amplitudes and formally valid at any energy above the physical threshold. By means of fits to total cross section data from proton-proton and antiproton-proton scattering, we evaluate the corresponding ratio ρ between the real and imaginary parts of the forward amplitudes. We show that the results are exactly the same as those obtained through standard integral dispersion relations.

We use a configuration space expression and a procedure to tame its divergent behavior at short distances to evaluate the pion sigma-term. We obtain the result σ_π = 66.9 MeV, which is close to the espected value μ/2, where μ is the pion mass.

The ³P₀ model is a typical decay model which considers only OZI-allowed strong decays and considers a quark-antiquark pair creation in the presence of the initial state meson. The quark-antiquark pair is created with the vacuum quantum numbers. This model can also be obtained from the non-relativistic limit of the pair creation Hamiltonian. Applying the Reduced Hilbert Space formalism to the pair creation Hamiltonian will produce the characteristic expansion in powers of the wave function, where the ³P₀ model is the lowest order term of this expansion. This new model will correct ³P₀, which we call the Corrected ³P₀ model or C³P₀ model. The model will be applied to the light quarkonia decay sector.

We present the results of a novel model-independent fit to elastic proton-proton differential cross section data at . Taking into account the error propagation from the fit parameters, we determine the scattering amplitude in the impact parameter space (the proton profile function) and its statistical uncertainty region. We show that both the real and imaginary parts of the profile are consistent with two dynamical contributions, one from a central dense region, up to roughly 1 fm and another from a peripheral evanescent region from 1 to 3 fm.

In microscopic decay models, one attempts to describe hadron strong decays in terms of quark and gluon degrees of freedom. We begin by assuming that strong decays are driven by the same interquark Hamiltonian which determines the spectrum, and that it incorporates gaussian confinement. An A → BC decay matrix element of the JKJ Hamiltonian involves a pair-production current matrix elements times a scatering matrix element. Diagrammatically this corresponds to an interaction between an initial line and produced pair.

The infrared behavior of gluon and ghost propagators in Yang–Mills gauge theories is of central importance for the understanding of confinement in QCD. While analytic studies using Schwinger–Dyson equations predict the same infrared exponents for the SU(2) and SU(3) gauge groups, lattice simulations usually assume that the two cases are different, although their qualitative infrared features may be the same. We carry out a comparative study of lattice (Landau) propagators for both gauge groups. Our data were especially produced with equivalent lattice parameters to allow a careful comparison of the two cases.

Abelian dominance is manifested in the (continuum) perturbative regime through the fact that the running coupling constant, obtained from the ghost-gluon vertex in Maximally Abelian Gauge (MAG), depends only on the renormalization factor of the diagonal (or Abelian) gluon propagator, due to cancellation of the other renormalization factors. We investigate such a cancellation nonperturbatively using lattice numerical simulations and present some preliminary results for the running coupling constant.

We study the spectrum of gluon screening masses in lattice Yang–Mills theory as a function of the lattice size, for the gauge group SU(2) and near the deconfinement temperature. We obtain values for the mass ratios consistent with predictions from universality arguments.

We use a fast Monte Carlo generator to simulate the energy losses of jets initiated by light and heavy quarks traversing a dense medium. The study of the energy-energy correlation function shows that this variable is sensitive to the fact that jets initiated by heavy quarks suffer reduced quenching when compared to those initiated by light quarks.

We present a study of particle production yields measured in central Au-Au collision at RHIC in the framework of a relativistic mean field model. Our results are consistent with statistical thermal models, implying a high degree of chemical equilibrium.

Heavy Quarkonium states modifications in relativistic heavy ion collisions have been of great interest since the proposal by Matsui and Satz of J/ψ suppression as a signature of Quark-Gluon Plasma (QGP) formation. Recent studies suggest that the excited states χc, ψ(2S) and ϒ(3S) melt sequentially^1,2 and the amount of observed suppression depends on the state and medium conditions. Therefore, this suppression pattern may be used as a probe of the medium temperature. In this work we present preliminary results on the charmonium and bottomnium measurements performed by the STAR experiment at RHIC for p + p and Cu + Cu collisions at .

We compute the hard diffractive hadroproduction of bosons W^± at high energies using Regge factorization and taking into account multiple Pomeron exchange corrections. The ratio of diffractive to non-diffractive W production agrees with the current Tevatron data and a prediction for the LHC is presented.

In the forthcoming nucleus-nucleus collisions at LHC we expect to see effects of the nonlinear (or saturation) regime of QCD. In this work we explore saturation effects on quarkonium production in nucleus-nucleus collisions, performing a quantitative analysis of the x_F distributions in these collisions with the Color Glass Condensate approach.

The color dipole model is traditionally applied to forward rapidities. Alternatively, we employ the dipole model to obtain backward rapidity distributions. We have chosen to work with dilepton production in pAu and pp collisions at RHIC and LHC energies. The results are best understood with the help of a nuclear modification factor R_pA as a function of transverse momentum and of rapidity. As it is found, dilepton production at backward rapidities is very dependent on nuclear effects.

In this work we use the program SPheRIO¹ (Smoothed Particle hydrodynamics evolution of Relativistic Ion collisions) to simulate the collision between two copper nuclei at 200 A GeV. SPheRIO is a numerical program that solves the hydrodynamics equations. We use the initial conditions provided by the program NeXus.².

We investigate the collective momentum anisotropy in relativistic heavy ion collisions in the BNL-RHIC energy regime with a three-dimensional hydrodynamical simulation code (SPHERIO) for different equations of state. We compare the widely used hadron gas-QGP bag model yielding a strong first order phase transition to other equations of state, which yield a smooth crossover as suggested by lattice QCD calculations.

In this work we discuss the strength of the trilinear Higgs boson coupling in composite models in a model independent way. The coupling is determined as a function of a very general ansatz for the fermionic self-energy, and turns out to be equal or smaller than the one of the Standard Model Higgs boson depending on the dynamics of the theory.

In this contribution we consider the influence of nonlinear gluon evolution in the production of prompt photons at the LHC pp collider. We consider the EHKQS parton distributions, which are based on the GLR-MQ evolution equations, and imply in an enhanced small-x gluon distribution at Q² ≤ 10 GeV² relative to the LO DGLAP gluon distribution. We find an enhancement of low-p_T photons for both single and double photon production. Consequences of this effect for the Quark-Gluon Plasma searches and for the QCD background to Higgs are also discussed.

A density dependent hadronic model and a common parametrization of the nonlinear Walecka model are used to obtain the lead neutron skin thickness through its proton and neutron density profiles. Our results are obtained within the Thomas–Fermi approximation. The neutron skin thickness is known to reflect the equation of state properties.

We study the Schwinger Model on the null-plane using the Dirac method for constrained systems. The fermion field is analyzed using the natural null-plane projections coming from the γ-algebra and it is shown that the fermionic sector of the Schwinger Model has only second class constraints. However, the first class constraints are exclusively of the bosonic sector. Finally, we establish the graded Lie algebra between the dynamical variables, via generalized Dirac bracket in the null-plane gauge, which is consistent with every constraint of the theory.

The problem of a fermion subject to a general mixing of vector and scalar screened Coulomb potentials in a two-dimensional world is analyzed and quantization conditions are found.

The problem of fermions in the presence of a pseudoscalar plus a mixing of vector and scalar potentials which have equal or opposite signs is investigated. We explore all the possible signs of the potentials and discuss their bound-state solutions for fermions and antifermions. The cases of mixed vector and scalar Pöschl–Teller-like and pseudoscalar kink-like potentials, already analyzed in previous works, are obtained as particular cases.

In this work we study the thermodynamic properties of an asymmetric system with arbitrary proton fraction, . We employ a Skyrme model in which surface and Coulomb effects are included phenomenologically to treat finite nuclei. We analyze the chemical and mechanical instabilities as a function of the asymmetry parameter. The coexistence surfaces (binodals) for different temperatures are constructed. We present applications to a set of finite nuclei, taking their critical parameters into account.

We present recent results on a systematic method to calculate transport coefficients for a meson gas (in particular, we analyze a pion gas) at low temperatures in the context of Chiral Perturbation Theory. Our method is based on the study of Feynman diagrams with a power counting which takes into account collisions in the plasma by means of a non-zero particle width. In this way, we obtain results compatible with analysis of Kinetic Theory with just the leading order diagram. We show the behavior with temperature of electrical and thermal conductivities and shear and bulk viscosities, and we discuss the fundamental role played by unitarity. We obtain that bulk viscosity is negligible against shear viscosity near the chiral phase transition. Relations between the different transport coefficients and bounds on them based on different theoretical approximations are also discussed. We also comment on some applications to heavy-ion collisions.

In the present work, we quantize a closed Friedmann–Robertson–Walker (FRW) model in the presence of a positive cosmological constant and radiation. It gives rise to a Wheeler–DeWitt equation for the scale factor which has the form of a Schrödinger equation for a potential with a barrier. We solve it numerically and determine the evolution of an initial wave-function.

We study the conditions for the formation and propagation of Korteweg – de Vries (KdV) solitons in relativistic fluid dynamics using an appropriate equation of state. It is known that in cartesian coordinates the combination of the Euler and continuity equations leads to the KdV equation. Recently it has been shown that this is true also in relativistic hydrodynamics. Here we show that a KdV-like equation can be obtained in relativistic hydrodynamics in spherical coordinates.

We present in this work a generalization of the solution of Gorenstein and Yang to the inconsistency problem of thermodynamics for systems with a temperature dependent Hamiltonian. We show that there are, in principle, an infinite number of solutions.

Electron scattering cross sections, including the eletromagnetic and weak neutral interactions with nuclei, are obtained from a microscopic relativistic model. Our calculation is important for heavy nuclei, for which unique experimental information on the neutron distribution is now under way.

We present a DHB approximation for excited hot nuclei and calculate the pairing gaps, binding energies, entropy and radii of several spherical and deformed nuclei. We show that the binding energy decreases as the temperature increases, as we would expect from the positive contribution of the thermal energy of the nucleons. The neutron, proton and charge radii of spherical nuclei increase as the temperature increases, while for the deformed ¹⁶⁸Er nucleus these quantities decrease up to T = 2 MeV, the temperature at which the deformation disappears, and increase above this temperature. The pairing interaction is taken into account self-consistently and studied as a function of the temperature: for the even Tin isotopes, the mean value of the neutron pairing gap is almost zero already at T = 1 MeV.

In the context of infinite nuclear matter, the equation of states obtained from the Walecka model turn out to be the same as those constructed from point-coupling models in which the nucleons interact with each other only when they are in contact.¹ Nonlinear point-coupling models have been applied sucessfully to describe infinite nuclear matter and finite nuclei spectra properties.² A theoretical support for this was presented on the basis of naturalness and naive dimensional analysis.³ For the usual linear Walecka model the infinite meson masses limit leads to a point-coupling model. From this, a quite natural question arises, whether the same kind of masses limit taken in a nonlinear Walecka model would provide a point-coupling model. We construct a modified nonlinear Walecka model Lagrangian in which the infinite meson masses limit can be taken exactly and leads to the contact nonlinear model. This modified nonlinear Walecka model includes higher order couplings. Although the modified and the nonlinear Walecka model at a mean field approach lead to distinct equations of state, the physically relevant content of the models are the same.

The nuclear matter at finite temperature is described in the relativistic mean field theory using linear and nonlinear interactions. The behavior of effective nucleon mass with temperature was numerically calculated. For the nonlinear NL3 interaction we also observed the striking decrease at temperatures well below the nucleon mass. The calculation of NL3 nuclear matter equation of state at finite temperature is still on progress.

The vast use of computers on scientific numerical computation makes the awareness of the limited precision that these machines are able to provide us an essential matter. A limited and insufficient precision allied to the truncation and rounding errors may induce the user to incorrect interpretation of his or her answer. In this work, we have developed a computational package to minimize this kind of error by offering arbitrary precision numbers and calculation. This is very important in Physics where we can work with numbers too small and too big simultaneously.