One-dimensional non-relativistic and relativistic Brownian motions: a microscopic collision model

We study a simple microscopic model for the one-dimensional stochastic motion of a (non-)relativistic Brownian particle, embedded into a heat bath consisting of (non-)relativistic particles. The stationary momentum distributions are identified self-consistently (for both Brownian and heat bath particles) by means of two coupled integral criteria. The latter follow directly from the kinematic conservation laws for the microscopic collision processes, provided one additionally assumes probabilistic independence of the initial momenta. It is shown that, in the non-relativistic case, the integral criteria do correctly identify the Maxwellian momentum distributions as stationary (invariant) solutions. Subsequently, we apply the same criteria to the relativistic case. Surprisingly, we find here that the stationary momentum distributions differ slightly from the standard Jüttner distribution by an additional prefactor proportional to the inverse relativistic kinetic energy.     

Ground-State Properties of Ca Isotopes and the Density Dependence of the Symmetry Energy

A relativistic mean field model is used to study the ground-state properties of neutron-rich nuclei in Ca isotopes. An additional isoscalar and isovector nonlinear coupling has been introduced in the relativistic mean field model, which could soften the symmetry energy, while keep the agreement with the experimental data. The sensitivity of proton and neutron density distributions and single particle states in Ca isotopes to the additional isoscalarisovector nonlinear coupling term is investigated. We found that the binding energies, the density distributions of single particle levels are strongly correlated with the density dependence of the symmetric energy in nuclear matter.     

p-Adic stochastics and Dirac quantization with negative probabilities

A new mathematical apparatus, ap-adic theory of probability, is applied to realize the hypothetical world based on negative probability distributions created by Dirac for the relativistic quantization of photons. Within thep-adic theory of probability, negative probability distributions are well defined (in the language of limits of relative frequencies, but with respect to ap-adic metric). We propose that the negative Gibbs distributions arising in relativistic quantization are described byp-adic Stochastics.on leave from Moscow Institute of Electronic Engineering, Moscow, Russia.     

Ground state properties of 16O, 40Ca and 48Ca in a relativistic Hartree theory of nuclear matter

A relativistic field theory model of nuclear matter is solved in a Hartree approximation for finite nuclei. We show that the theory predicts small shell effects for the charge-density distributions in magic nuclei and is in agreement with recent electron scattering data. The effects of the small component of the relativistic wave function are investigated as well as the role of the isospin-dependent force generated by the rho field.     

Fragmentation and particle production in interactions of 10.6 GeV/N gold nuclei with hydrogen, light and heavy targets

We have investigated the interactions of 10.6 GeV/n Au in nuclear emulsion. Two methods of separating interactions into those with hydrogen, light (C,N,O) and heavy (Ag,Br) target nuclei were used, giving almost identical results, which strengthened our confidence in the correctness of these methods. We also measured the angular distributions of singly and multiply charged relativistic particles emitted from the interaction vertices and the charges of the multiply charged projectile fragments. The fragmentation of the projectile Au nuclei and of the target nuclei were analyzed. The multiparticle production was studied as a function of the mass of the target nucleus. The multiplicity and the pseudorapidity distributions of relativistic singly charged particles were compared with the predictions of the RQMD Model. Received: 22 April 1998 / Published online: 8 September 1998     

Quasi‐Relativistic Heat Equation via Lévy Stable Distributions: Exact Solutions

We introduce and study an extension of the heat equation relevant to relativistic energy formula involving square root of differential operators. We furnish exact solutions of corresponding Cauchy (initial) problem using the operator formalism invoking one‐sided Lévy stable distributions. We note a natural appearance of Bessel polynomials which allow one to obtain closed form solutions for a number of initial conditions. The resulting diffusion is slower than the non‐relativistic one, although it still can be termed a normal one. Its detailed statistical characterization is presented in terms of exact evaluation of arbitrary moments and kurtosis and is compared with the non‐relativistic case.     

Support of generalized parton distributions in Bethe–Salpeter models of hadrons

The proper support of generalized parton distributions from relativistic constituent quark models with pointlike constituents is studied. The correct support is guaranteed when the vertex function does not depend on the relative minus-momentum. We show that including quark interactions in models with pointlike constituent quarks might lead to a support problem. A computation of the magnitude of the support problem in the Bonn relativistic constituent quark model is presented.     

UF_6分子价轨道相对论效应的理论电子动量谱学研究

用非相对论、标量相对论和二分量相对论三种不同的密度泛函方法对UF_6分子的电子结构进行了量子化学计算,并利用编写的程序计算出了三种方法下各个价轨道的电子动量谱,比较了三种方法计算的价轨道能级及动量分布的差异.结果表明,相对论效应不仅使UF_6的能级劈裂和移动,而且对部分价轨道电子动量分布有显著的影响.     

Criterion for long-wavelength electromagnetic instability of a homogeneous relativistic plasma

Electromagnetic instability of an unmagnetized homogeneous relativistic plasma with an anisotropic velocity distribution having a center of symmetry is analyzed. A stability criterion is derived for slowly varying long-wavelength perturbations. The criterion is formulated as a set of equalities that are not valid for ellipsoidal velocity distributions, but can be satisfied for other anisotropic distributions. The relativistic case is special only in that the rest mass is replaced with the relativistic one.     

Non-linear relativistic diffusions

We obtain a non-linear generalization of the relativistic diffusion. We discuss diffusion equations whose non-linearity is a consequence of quantum statistics. We show that the assumptions of the relativistic invariance and an interpretation of the solution as a probability distribution substantially restrict the class of admissible non-linear diffusion equations. We consider relativistic invariant as well as covariant frame-dependent diffusion equations with a drift. In the latter case we show that there can exist stationary solutions of the diffusion equation besides the equilibrium solution corresponding to the quantum or Tsallis distributions. We define the relative entropy as a function of the diffusion probability and prove that it is monotonically decreasing in time when the diffusion tends to equilibrium. We discuss its relation to the thermodynamic behavior of diffusing particles.     

Generalized isothermal models with strange equation of state

We consider the linear equation of state for matter distributions that may be applied to strange stars with quark matter. In our general approach the compact relativistic body allows for anisotropic pressures in the presence of the electromagnetic field. New exact solutions are found to the Einstein-Maxwell system. A particular case is shown to be regular at the stellar centre. In the isotropic limit we regain the general relativistic isothermal Universe. We show that the mass corresponds to the values obtained previously for quark stars when anisotropy and charge are present.      

Nonextensive statistical effects in the quark-gluon plasma formation at relativistic heavy-ion collisions energies

We investigate the relativistic equation of state of hadronic matter and quark-gluon plasma at finite temperature and baryon density in the framework of the non-extensive statistical mechanics, characterized by power-law quantum distributions. We impose the Gibbs conditions on the global conservation of baryon number, electric charge and strangeness number. For the hadronic phase, we study an extended relativistic mean-field theoretical model with the inclusion of strange particles (hyperons and mesons). For the quark sector, we employ an extended MIT-Bag model. In this context we focus on the relevance of non-extensive effects in the presence of strange matter.     

Charged Multiplicity Density and Number of Participant Nucleons in Relativistic Nuclear Collisions

The energy and centrality dependencies of charged particle pseudorapidity density in relativistic nuclearcollisions were studied using a hadron and string cascade model, JPCIAE. Both the relativistic p+p experimental dataand the PHOBOS and PHENIX Au+Au data at RHIC energy could be fairly reproduced within the framework ofJPCIAE model and without retuning the model parameters. The predictions for Pb + Pb collisions at the LHC energywere also given. We computed the participant nucleon distributions using different methods. It was found that thenumber of participant nucleons is not a well defined variable both experimentally and theoretically. Thus it may beinappropriate to use the charged particle pseudorapidity density per participant pair .as a function of the number ofparticipant nucleons for distinguishing various theoretical models.     

Total bremsstrahlung spectra in targets of Al,Ti, Sn and Pb produced by complete absorption of 90Sr β particles

Total bremsstrahlung (BS) spectra in thick targets of Al, Ti, Sn and Pb produced by complete absorption of ⁹⁰Sr β particles (0–546 keV) are reported in the photon energy region of 10–30 keV. The experimental BS spectral photon distributions were compared with the theoretical BS spectral photon distributions obtained from Elwert corrected (non‐relativistic) Bethe–Heitler theory, modified Elwert factor (relativistic) Bethe–Heitler theories for ordinary bremsstrahlung (OB) and the modified Elwert factor (relativistic) Bethe–Heitler theory, which include the polarization bremsstrahlung (PB) into OB in stripped atom approximation. It has been observed that the experimental results are showing better agreement with the modified Elwert factor (relativistic) Bethe–Heitler theory having the contribution of PB at photon energy from 10 to 30 keV. This indicates the importance of PB in BS spectra, while studying the spectral photon distributions produced by continuous β particles having energy range of 0–546 keV in thick metallic targets. Further, it is observed that the contribution of PB into OB increases with increase in atomic number of the target and decreases with increase in photon energy. Copyright © 2010 John Wiley & Sons, Ltd.     

Flow study in relativistic nuclear collisions by Fourier expansion of azimuthal particle distributions

We propose a new method to study transverse flow effects in relativistic nuclear collisions by Fourier analysis of the azimuthal distribution on an event-by-event basis in relatively narrow rapidity windows. The distributions of Fourier coefficients provide direct information on the magnitude and type of flow. Directivity and two dimensional sphericity tensor, widely used to analyze flow, emerge naturally in our approach, since they correspond to the distributions of the first and second harmonic coefficients, respectively. The role of finite particle fluctuations and particle correlations is discussed.     

Relativistic and distorted wave effects on Xe 4d electron momentum distributions

The relativistic and distorted wave effects are investigated for the electron momentum distributions of Xe 4d electrons.The theoretical results show good agreements with the experimental data measured previously with electron momentum spectroscopy. The distorted wave effect and the relativistic effect are found to play important roles in the low and high momentum regions, respectively.     

Gluon saturation and baryon stopping in the SPS, RHIC, and LHC energy regions

A new geometrical scaling method with a gluon saturation rapidity limit is proposed to study the gluon saturation feature of the central rapidity region of relativistic nuclear collisions. The net-baryon number is essentially transported by valence quarks that probe the saturation regime in the target by multiple scattering. We take advantage of the gluon saturation model with geometric scaling of the rapidity limit to investigate net baryon distributions, nuclear stopping power and gluon saturation features in the SPS and RHIC energy regions. Predictions for net-baryon rapidity distributions, mean rapidity loss and gluon saturation feature in central Pb+Pb collisions at the LHC are made in this paper.     

Maxwell-Jüttner distributions in relativistic molecular dynamics

In relativistic kinetic theory, which underlies relativistic hydrodynamics, the molecular chaos hypothesis stands at the basis of the equilibrium Maxwell-J ttner probability distribution for the four-momentum p^α. We investigate the possibility of validating this hypothesis by means of microscopic relativistic dynamics. We do this by introducing a model of relativistic colliding particles, and studying its dynamics. We verify the validity of the molecular chaos hypothesis, and of the Maxwell-J ttner distributions for our model. Two linear relations between temperature and average kinetic energy are obtained in classical and ultrarelativistic regimes.     

Theory of origin of hyperfine interactions in atomic systems

We shall review recent developments in the theory of magnetic hyperfine interactions, including the influence of many-body and relativistic effects and the finite spreads of nuclear charge and magnetic moment distributions. The present status of the understanding of these effects will be illustrated by analyzing a number of different systems including the alkali atoms, alkaline earth ions and several half-filled shell atomic and ionic systems.