Relativistic effects in many-body systems of finite size,internal structure,and internal motions: I. “Self-acceleration” of astrophysical systems

It is proved that the post-Newtonian general relativistic center of rest mass of a bounded physical system composed of a number of bodies characterized by finite dimensions, arbitrary internal structure, and arbitrary internal motions cannot in general move uniformly, contrary to what was conventionally accepted up to now. Mathematical expressions are derived and discussed describing, in terms of the above characteristics of the bodies, the position and velocity vectors of the center of rest mass of the system and the force, which is responsible for its nonuniform motion, with respect to the uniformly moving post-Newtonian general relativistic center of inertial mass of the physical system. In the special case of a binary star it is shown that the center of rest mass should describe, around the uniformly moving center of inertial mass, an ellipse of the same period and eccentricity as those of the Newtonian elliptical orbit of the relative motion. The length of the axes of this ellipse depends on the internal characteristics of the members of the binary star, and the motion of the center of rest mass becomes important when these characteristics are strong enough. Finally, it is proved that in every effort for describing theoretically a binary system, the internal characteristics of the members of which are ignored, and for accurate measurements of their positions and velocities, the above fictitious motion of the center of rest mass has to be taken into account; otherwise, the results of the measurements will not be consistent with the theoretical predictions.     

Relativistic finite baryon size effect and the mass limit for neutron stars

We revise our previous calculation of the finite baryon size effect on the mass limit for neutron stars by making the formulation be relativistic. The result is still consistent with the observational data.Communicated by: A. Schäfer     

Relativistic many-body and QED effects on the hyperfine structure of lithium-like ions

The hyperfine splitting of the ground state of three-electron ions is studied in detail with the help of the multi-configuration Dirac-Fock method. We study the role of the magnetic electron-electron interaction and of the negative energy continuum. An all-order evaluation of some vacuum polarization corrections is performed. The Bohr-Weisskopf effect is evaluated in a simple model.     

The Sachs moment and finite size effects in muonic hyperfine structure

In calculations of finite size effect in muonic hyperfine structure, the meson exchange part of nuclear magnetism has so far not been taken explicitly into account. We investigate this effect for the Sachs moment and show that the reduction factor is approximately the same as for the orbital part. Consequences for theoretical values of the h.f.s. constant A₁ are discussed for the special nucleus ²⁰⁹Bi.     

String tension,gluebal masses and finite size effects in lattice SU(3)

We estimate the string tension by looking at Wilson loops and measuring the correlation between Wilson lines at g² = 1.0 for lattice SU(3). The bound $\text{Λ}{}_{\mathrm{<mtext>L</mtext>}}\text{σ}\text{?0.0087 ± 0.0011}$ is larger than the previous results. The mass of the 0⁺⁺ glueball is also estimated. The finite size effects on these quantities are shown to be large by comparing results on a 6³ × 10 lattice with those on 9⁴ lattice.     

Anisotropy of cyclotron masses,many-body effects and X-ray emission spectra in Pd

The calculation of intensity distribution in X-ray M-emission bands of Pd was carried out by the RAPW method. The anisotropy of cyclotron masses was theoretically studied, the contributions into renormalization of the cyclotron masses of electron-phonon interactions and spin fluctuations were estimated.     

Relaxation studies in fermion systems: Nonlinear and finite size effects

The time evolution of some non-equilibrium fermion model systems is studied by a numerical solution of the Uehling-Uhlenbeck equation in both its complete and linearized forms. The solutions are analyzed in terms of general properties of the corresponding linear eigenvalue problem. The dependence of the relaxation process on the size and the symmetry of the perturbation are investigated for spatially infinite homogeneous systems and for particles bound in an external harmonic oscillator potential as a model example for finite systems.     

Relativistic and many-body effects in K, L, and M shell ionization energy for elements with and the determination of the 1s Lamb shift for heavy elements

We report on a calculation of K, L and M inner-shell ionization energy in atoms with atomic numbers in the range . Many-body effects are evaluated for all n =1, 2, and 3 hole states. Those include correlation and effects due to the auto-ionizing nature of the hole states (Auger shift). For high Z we add recent corrected nuclear polarization, and several second-order vacuum polarization corrections. K and L ionization energies are compared with experimental X-ray absorption edges measurements. Excellent agreement with rare gazes and metal vapor measurements is found. We also compare our calculations with X-ray transition energies for all K and L lines that involve K, L and M holes. Finally we use K X-ray lines to deduce an hydrogenlike 1 s Lamb shift for several heavy elements, with far better accuracy than has been obtained by direct measurements of hydrogenlike ions. Received: 25 February 1998 / Accepted: 31 March 1998     

The size of finite size effects in lattice gauge theories

If a quantum field is enclosed in a spatial box of finite volume, its mass spectrum depends on the box size L. For field theories in the continuum Lüscher has shown to all orders in perturbation theory that for large L this dependence is related to certain scattering amplitudes of the infinite volume theory. We derived the corresponding relations for lattice field theories. Assuming their validity for lattice gauge theory outside the perturbative region the magnitude of finite size effects on the spectrum is determined by a glueball coupling constant. This quantity is estimated by strong coupling methods.     

Rotational spectrum,structure and internal motions of the ethylene-OCS weakly bound dimer

The rotational spectra of five isotopomers of the ethylene-OCS dimer have been observed by Fourier transform microwave spectroscopy and its structure was determined. The dipole moment components and rotational constants for this complex are consistent with a stacked geometry in which the OCS lies above the ethylene molecular plane, approximately parallel to the C=C bond. Two internal motions of the monomer subunits split each rotational transition into four components. The larger tunneling splittings have been analysed to give a twofold barrier for the internal motion of the ethylene subunit about its c inertial axis of 16(3) cm^?1. The results are compared with calculations with a semi-empirical model employing electrostatic, dispersion and repulsion interactions.     

The elliptical motion of stars in close binary systems with a conservative mass exchange

The problem of the motion of a star in a close binary system with a conservative mass exchange is considered. In contrast to the well-known Paczynski-Huang model, a new model is used that defines the motion of close binary systems in the case of an elliptical orbit. The reactive forces and the force of gravity of stars by the overflowing jet are accounted for in the elliptic motion of the star. The calculations of elliptical orbits of close binary stars show that the effect of the reactive force on the evolution of the star orbit can be different. The changes of the major axis and eccentricity of the orbit of the second star are defined. The results are applied to the BF Aurigae star system and are given in the form of figures.     

Particles with internal structure: The geometry of classical motions and conservation laws

Classical models of elementary particles endowed with internal structure are constructed using the coadjoint orbit method. The geometry of minimal coupling is introduced and the Wong equations are recovered. Conservation laws are derived in the case of symmetric external Einstein-Yang-Mills fields. As a non-trivial example, classical motions in a B.P.S.T. instanton's field are investigated.     

Analytic modeling of tidal effects in the relativistic inspiral of binary neutron stars

To detect the gravitational-wave (GW) signal from binary neutron stars and extract information about the equation of state of matter at nuclear density, it is necessary to match the signal with a bank of accurate templates. We present the two longest (to date) general-relativistic simulations of equal-mass binary neutron stars with different compactnesses, C=0.12 and C=0.14, and compare them with a tidal extension of the effective-one-body (EOB) model. The typical numerical phasing errors over the ?22 GW cycles are Δ??±0.24 rad. By calibrating only one parameter (representing a higher-order amplification of tidal effects), the EOB model can reproduce, within the numerical error, the two numerical waveforms essentially up to the merger. By contrast, the third post-Newtonian Taylor-T4 approximant with leading-order tidal corrections dephases with respect to the numerical waveforms by several radians.     

Signatures of short-range many-body effects in the dielectric function of silicon for finite momentum transfer

We present an investigation of the dynamic structure factor and of the dielectric function epsilonM(Q,omega) of the prototypical semiconductor silicon for finite momentum transfer, combining inelastic x-ray scattering experiments and ab initio calculations. In contrast with optical spectra, for finite momentum transfer time-dependent density-functional theory in the adiabatic local-density approximation together with lifetime broadening describes the physics of valence excitations correctly. Major structures in the spectra, governed by short-range crystal and exchange-correlation local-field effects, are strongly influenced by a mixing of transitions of positive and negative energies, in striking difference to spectra for vanishing momentum transfer. This mixing gives rise to a pronounced Fano asymmetry.     

The influence of medium effects on the gross structure of hybrid stars

We investigate the influence of medium effects on the structure of hybrid stars, i.e. neutron stars possessing a quark matter core. We found that medium effects in quark matter reduce the extent of a pure quark matter phase in the interior of a hybrid star significantly in favor of a mixed phase of quark and hadronic matter. Over a wide range of the strong coupling constant — which parameterizes the influence of medium effects — quark matter is able to exist at least in a mixed phase in the interior of neutron stars.     

Relativistic effects in the calibration of electrostatic electron analyzers. II. Parallel plate and cylindrical mirror analyzers

Relativistic correction terms up to the second order are derived for the kinetic energy of an electron travelling along the central trajectory, which crosses the non-relativistic foci of electrostatic parallel plate and cylindrical mirror analyzers. The effects of fringing fields and source geometry are neglected. In both cases the magnitude of relativistic corrections depends on the geometry of the analyzer, but generally it is smaller than for the toroidal family of analyzers.     

Relativistic corrections to the gravitational radiation of a binary system and the fine structure of the spectrum

Relativistic corrections to the gravitational radiation emitted by a system of two point masses performing a quasielliptical motion are calculated in the Teukolsky formalism. It is shown that the radiation spectrum possesses a fine structure analogous to that of atomic spectra.     

Correlation effects,image charge effects and finite size in the macro-ion-electrolyte system: A field-theoretic approach

We consider a model of a macro-ion surrounded by small ions of an electrolyte solution. The finite size of ionic charge distributions of ions, and image charge effects are considered. From such a model it is possible to construct a statistical field theory with a single fluctuating field and derive physical interpretations for both the mean field and two-point correlation function. For point-like charges, at the level of a Gaussian (or saddle point) approximation, we recover the standard Poisson-Boltzmann equation. However, to include ionic correlation effects, as well as image charge effects of individual ions, we must go beyond this. From the field theory considered, it is possible to construct self-consistent approximations. We consider the simplest of these, namely the Hartree approximation. The Hartree equations take the form of two coupled equations. One is a modified Poisson-Boltzmann equation; the other describes both image charge effects on the individual ions, as well as correlations. Such equations are difficult to solve numerically, so we develop an (a WKB-like) approximation for obtaining approximate solutions. This, we apply to a uniformly charged rod in univalent electrolyte solution, for point like ions, as well as for extended spherically symmetric distributions of ionic charge on electrolyte ions. The solutions show how correlation effects and image charge effects modify the Poisson-Boltzmann result. Finite-size charge distributions of the ions reduce both the effects of correlations and image charge effects. For point charges, we test the WKB approximation by calculating a leading-order correction from the exact Hartree result, showing that the WKB-like approximation works reasonably well in describing the full solution to the Hartree equations. From these solutions, we also calculate an effective charge compensation parameter in an analytical formula for the interaction of two charged cylinders. Electronic supplementary material  Supplementary material in the form of a doc file available from the journal web page at and are accessible for authorised users.