Instantaneous Bethe-Salpeter Equation and Its Exact Solution

We present an approach to solve Bethe-Salpeter (BS) equations exactly without any approximation if the kernel of the BS equations exactly is instantaneous, and take positronium as an example to illustrate the general features of the exact solutions. The key step for the approach is from the BS equations to derive a set of coupled and well-determined integration equations in linear eigenvalue for the components of the BS wave functions equivalently, which may be solvable numerically under a controlled accuracy, even though there is no analytic solution. For positronium, the exact solutions precisely present corrections to those of the corresponding Schrödinger equation in order v¹ (v is the relative velocity) for eigenfunctions, in order v² for eigenvalues, and the mixing between S and D components in J^PC=1^-- states etc., quantitatively. Moreover, we also point out that there is a questionable step in some existent derivations for the instantaneous BS equations if one is pursuing the exact solutions. Finally, we emphasize that one should take the O(v) corrections emerging in the exact solutions into account accordingly if one is interested in the relativistic corrections for relevant problems to the bound states.     

Theoretical study on the 1s22s-1s2 np transitions for Ni25+ ion

The transition energies, wavelengths and oscillator strengths for the 1s²2s-1s² np (n ? 9) transitions of Ni²⁵⁺ ion are calculated. In calculation of the energies, we not only take account of the firstorder corrections from relativistic and mass-polarization effects, but also estimate the higher-order relativistic contribution and QED correction by introducing the effective nuclear charge. The results agree with experimental data available in literature satisfactorily. Grotrian diagram showing these transitions is given.     

A single-particle nonlocal potential for taking into account quantum-electrodynamic corrections in calculations of the electronic structure of atoms

A new single-particle effective potential is proposed. This potential allows one to take into account quantum-electrodynamic (QED) corrections in relativistic calculations of many-electron ions and neutral atoms. In particular, it can be used in the Dirac-Fock (DF) method, the relativistic density functional, the multiconfiguration DF method, and the relativistic method of superposition of configurations. The potential is constructed without fitting parameters. Self-energy corrections have been calculated for a number of neutral alkali atoms and Li-like ions to check the quality of the nonlocal potential proposed. Comparison with the data in the literature on the QED corrections obtained in nonempirical calculations based on the use of QED perturbation theory is performed.     

Impact of ${\cal O}(\alpha)$ radiative corrections on CC03 physics at LEP

In this work we report about the effect that the improved knowledge of electroweak radiative corrections, via the recent calculations of four-fermion processes with corrections in double pole approximation, has on WW physics at LEP2. Particular emphasis is given to the effects on differential distributions and their impact on the experimental observables. This study is based on generator comparisons using the new codes from the 2000 LEP2 Montecarlo workshop and allows new, important insights on the effects full radiative corrections have on W physics observables. The results presented here explain why it is so important to take these new calculations into account for precision measurements at LEP2. Received: 3 August 2001 / Revised version: 20 November 2001 / Published online: 18 January 2002     

A simple model for scalar relativistic corrections to molecular total atomisation energies

ABSTRACT

Scalar relativistic corrections to atomisation energies of first- and second-row molecules can be rationalised in terms of a simple additive model, linear in changes in atomic s populations. In a sample of 200 first-and second-row molecules, such a model can account for over 98% of the variance (99% for the first-row subset). The remaining error can be halved again by adding a term involving the change in atomic p populations: those coefficients need not be fitted but can be fixed from atomic electron affinity calculations. This model allows a fairly accurate a priori estimate for the importance of scalar relativistic corrections on a reaction energy, at essentially zero computational cost. While this is not a substitute for explicit calculation of Douglas–Kroll–Hess (DKH) or exact two-component (X2C) relativistic corrections, the model offers an interpretative tool for the chemical analysis of scalar relativistic contributions to reaction energies.     

Calculation of the Relativistic Correction in Terms of the Oscillator Representation

A procedure is proposed for the calculation of the corrections associated with the relativistic motion and spin interaction of particles in a system of a few bodies. The relativistic corrections for the Coulomb and Cornell potentials are determined from the relativistic generalization of the Schrödinger equation. The slope of the Regge trajectory and the masses of mesons are calculated taking the relativistic correction into account.     

Spatial-dispersion and relativistic effects in the optical sum rules

We describe a procedure to take into account the spatial dispersion of the optical excitations in the susceptibility sum rules. We show that this implies that relativistic corrections of the same order must be considered. The final result is a decrease of the total oscillator strength equal to the ratio of the average electron kinetic energy with mc². We propose experiments with synchrotron radiation sources on crystals of heavy elements to observe the described effect. Received 5 June 2001     

Double S- and P-wave charmonium production in e+e? annihilation

On the basis of perturbative QCD and the relativistic quark model we calculate relativistic and bound state corrections in the production processes of a pair of S-wave and P-wave charmonium states. Relativistic factors in the production amplitude connected with the relative motion of heavy quarks and the transformation law of the bound state wave function to the reference frame of the moving S- and Pwave mesons are taken into account. For the gluon and quark propagators entering the production vertex function we use a truncated expansion in the ratio of the relative quark momenta to the center-of-mass energy $ \sqrt s $ \sqrt s up to the second order. Relativistic corrections to the quark bound state wave functions in the rest frame are considered by means of the Breit-like potential. It turns out that the examined effects change essentially the nonrelativistic results of the cross section for the considered reactions at the center-of-mass energy $ \sqrt s $ \sqrt s = 10.6 GeV.     

Determination of the mass spectrum of the bound state in the framework of the relativistic hamiltonian approach

We propose one a variant of calculation of the energy spectrum of bound state systems with relativistic corrections. In the framework of quantum field theory, an expression that takes into account relativistic corrections to the mass of the bound state with a known nonrelativistic pair interaction potential is proposed on the basis of calculating the asymptotic behavior of correlation functions of the corresponding field currents with the necessary quantum numbers. Excluding the time variables allows one to determine nonperturbative corrections to the interaction potential. The following results have been obtained in the framework of this approach. The nonperturbative corrections arising due to the relativistic nature of a system to the interaction Hamiltonian are determined. The dependence of the constituent mass of bound-state forming particles on the free state mass and on the orbital and radial quantum numbers is analytically derived. The energy level shift of muonic hydrogen taking into account relativistic corrections is calculated. The energy spectrum of a wide class of potentials that describe the Coulomb bound state is analytically derived with relativistic corrections. The mass spectrum of the glueballs and the constituent masses of the gluons are analytically calculated taking into account spin-orbit, spin—spin, and tensor interactions. Our numerical results have shown very good agreement with the lattice data. Taking into account nonperturbative and nonlocality characters of interactions, the mass spectrum of the mesons consisting of light-light and light-heavy quarks with orbital and radial excitations is determined. Our results show that good agreement with the experimental data for the slope and the intercept of the Regge trajectory can be obtained only taking into account the nonperturbative and the nonlocal characters of interactions. The dependences of the constituent masses of constituent particles on the masses of a free state are certain. When quarks are light, then the difference between current and valent masses of quarks is greater than valent masses of quarks, and when quarks are heavy, then the difference between these masses is insignificant. One of the alternative variants of taking nonlocality into account has been suggested for the definition of properties of hadrons at large distances. The dependence of the constituent masses of constituent particles on the radius of confinement is determined.     

Inclusive Electron Scattering Response Functions of 3He

Theoretical longitudinal and transverse electron scattering response functions are discussed in the quasi-elastic region for momentum transfers q ?? 500 MeV/c. The response functions are calculated nonrelativistically, however, relativistic corrections to the nucleon one-body charge and current operators are taken into account. The frame dependence of the results is illustrated and it is shown that the so-called active nucleon Breit frame is the most suitable reference frame. In addition we review the results of a two-fragment model, which takes into account the correct relativistic energy of the final hadronic state assuming that a nucleon is knocked out quasi-elastically. New results for the transverse response function are presented at 700?MeV/c ?? q ?? 1 GeV/c.     

Centrifugal acceleration surprises

A gedanken experiment of bead motion along a rotating pipe with relativistic velocities is discussed. It is shown that when v ₀>c/2,the centrifugal acceleration changes its sign and braking has begun. It is pointed out that in investigating pulsar magnetospheres, we must take into account the effect of rotating relativistic stream braking.Published from Izvestiya Vysshikh Uchebnykh Zavedenii, Radiofizika, Vol. 39, No. 1, pp. 39–45, January, 1996.G.Z. Machabeli's research was supported, in part, by INTAS No 1010 ct 930015.     

Relativistic configuration interaction calculations on Kα X-ray satellites of magnesium ions

In this work, the multi-configuration Dirac-Fock (MCDF) and relativistic configuration interaction (RCI) methods have been used to calculate the transition wavelengths, electric dipole transition probabilities, line strengths and absorption oscillator strengths for the Kα X-ray from Mg III to Mg XI. We also take the contributions from the Breit interaction, finite nuclear mass corrections and quantum electrodynamics corrections to the initial and final levels, into account. The present values for Mg X and Mg XI were in good agreement with the previous experimental and theoretical results. The new data in this work provide reference values for the level lifetimes, charge state distributions, and average charge of magnesium plasmas.     

Hadronization corrections to helicity components of the fragmentation function

In the hadronic decays of , gluon emission leads to the appearance of the longitudinal component of the fragmentation function, . Measurement of and the transverse component, , could thus provide insight into the gluon fragmentation function. However, hadronization corrections at low x can be significant. Here we present a method of accounting for such corrections, using the Jetset event generator as illustration. Received: 11 April 2001 / Revised version: 4 May 2001 / Published online: 29 June 2001     

Possible interpretation of the „anomalous“ behaviour of the proton spectrum at 0° from the deuteron fragmentation at 9 GeV/c

The momentum spectra of protons, produced at 0° as a result of fragmentation of relativistic deuterons on nuclei, are analyzed. Possible causes of the existing discrepancy of the data on the 0° proton spectrum from the¹ H(d,p)X reaction at 9.1 GeV/c with results of the impulse approximation calculations are considered. It is shown that taking into account the finite angular resolution of the experimental setup and the corresponding renormalization of the experimental data, on the one hand, and also the inclusion of the additional (to stripping) contribution of protons from the scattering of deuteron nucleons by target protons, on the other, make it possible to match these data with the results of calculations within the framework of the relativistic impulse approximation using the deuteron wave function for the Paris potential.     

Holomorphy of the scattering matrix with respect toc −2 for Dirac operators and an explicit treatment of relativistic corrections

We prove holomorphy of the scattering matrix at fixed energy with respect toc ^–2 for abstract Dirac operators. Relativistic corrections of orderc ^–2 to the nonrelativistic limit scattering matrix (associated with an abstract Pauli Hamiltonian) are explicitly determined. As applications of our abstract approach we discuss concrete realizations of the Dirac operator in one and three dimensions and explicitly compute relativistic corrections of orderc ^–2 of the reflection and transmission coefficients in one dimension and of the scattering matrix in three dimensions. Moreover, we give a comparison between our approach and the firstorder relativistic corrections according to Foldy-Wouthuysen scattering theory and show complete agreement of the two methods.Supported by Fonds zur Förderung der wissenschaftlichen Forschung in Österreich by an E. Schrödinger Fellowship and by Project No. P7425     

Ground state correlations and structure of odd spherical nuclei

It is well known that the Pauli principle plays a substantial role at low energies because the phonon operators are not ideal boson operators. Calculating the exact commutators between the quasiparticle and phonon operators, one can take into account the Pauli principle corrections. Besides, the ground state correlations due to the quasiparticle interaction in the ground state influence the single-particle fragmentation as well. In this paper, we generalize the basic equations of the quasiparticle-phonon nuclear model to account for both effects mentioned. As an illustration of our approach, calculations on the structure of the low-lying states in ¹³³Ba have been performed. The text was submitted by the authors in English.     

Dynamical relativistic corrections to the leptonic decay width of heavy quarkonia

We calculate the dynamical relativistic corrections, originating from radiative one-gluon exchange, to the leptonic decay width of heavy quarkonia in the framework of a covariant formulation of light-front dynamics. Comparison with the non-relativistic calculations of the leptonic decay width of J = 1 charmonium and bottomonium S-ground states shows that relativistic corrections are large. Most importantly, the calculation of these dynamical relativistic corrections legitimate a perturbative expansion in , even in the charmonium sector. This is in contrast with the ongoing belief based on calculations in the non-relativistic limit. Consequences for the ability of several phenomenological potentials to describe these decays are described. Received: 6 December 2001 / Published online: 5 April 2002     

Relativistic effects in neutrino (Antineutrino) disintegration of the deuteron

The cross section of neutrino disintegration of the deuteron with inclusion of relativistic corrections is calculated. The transition only to¹S₀-state is taken into account, so the results are valid for reactor and meson factory energies. Comparison with earlier works is given. It is shown, that accurate choice of bound state wave function is essential for the final results. The relativistic approach developed in this work should be used as a starting point for calculations of meson exchange current corrections.