Explicitly covariant light-front dynamics and relativistic few-body systems

The wave function of a composite system is defined in relativity on a space–time surface. In the explicitly covariant light-front dynamics, reviewed in the present article, the wave functions are defined on the plane ω·x=0, where ω is an arbitrary four-vector with ω²=0. The standard non-covariant approach is recovered as a particular case for ω=(1, 0, 0,−1). Using the light-front plane is of crucial importance, while the explicit covariance gives strong advantages emphasized through all the review.The properties of the relativistic few-body wave functions are discussed in detail and are illustrated by examples in a solvable model. The three-dimensional graph technique for the calculation of amplitudes in the covariant light-front perturbation theory is presented.The structure of the electromagnetic amplitudes is studied. We investigate the ambiguities which arise in any approximate light-front calculations, and which lead to a non-physical dependence of the electromagnetic amplitude on the orientation of the light-front plane. The elastic and transition form factors free from these ambiguities are found for spin 0, and 1 systems.The formalism is applied to the calculation of the relativistic wave functions of two-nucleon systems (deuteron and scattering state), with particular attention to the role of their new components in the deuteron elastic and electrodisintegration form factors and to their connection with meson exchange currents. Straightforward applications to the pion and nucleon form factors and the ρ−π transition are also made.     

Accurate solutions of quasipotential equations with orbital momentum ℓ=1

It is shown that the integral quasipotential Logunov-Tavkhelidze and Kadyshevskii equations with local —in Lobachevskii momentum space — quasipotentials, the transforms of which are even rational functions of r in relativistic configurational space, may be reduced to a Sturm-Liouville problem in the case of unit orbital momentum. In the critical limit, when the bound-state mass is zero, accurate wave functions are obtained.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 5, pp. 56–60, May, 1990.     

Second approximation of the generalized WKBJ method VI. Application to the potential scattering of relativistic electrons

The generalized WKBJ method is used to study the phase shifts of the wave functions of relativistic electrons scattered by a static central field. Equations corresponding to the second approximation of the generalized WKBJ method are used to calculate the relativistic scattering phases.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 1, pp. 72–81, January, 1971.The author thanks L. A. Kronrod for carrying out the computer calculations.     

The relativistic interquark potential

A method for the calculation of interaction potentials in a momentum space is proposed which is based on exact calculations of the Lorentz structures of the corresponding interaction amplitudes. With this method the kernel of the QCD-motivated potential of a quark-antiquark relativistic system is obtained for different masses and an arbitrary angular momentum J. The calculation is performed taking into account the anomalous chromodynamic moments of the quarks. The case of the singlet state of a relativistic quark system is considered. __________ Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 87–94, November, 2006.     

A relativistic study of the nucleon helicity amplitudes

Abstact: We perform a calculation of the relativistic transition form factors for the electromagnetic excitation of the nucleon resonances. We use as input the 3-quark wave functions obtained in a Constituent Quark Model with three-body forces in the hypercentral approach. With respect to the non relativistic calculations a significant contribution is obtained up to Q ²≃ 2 (GeV/c)². However, the low Q ²-behaviour exhibits a lack of strength, which may be connected with the need of taking into account explicitly further degrees of freedom beyond the three constituent quark ones. Received: 16 April 1998     

Electron shake probabilities of heavy elements as a result of M‐shell vacancy production

The electron shakeup‐plus‐shakeoff probabilities accompanying M‐shell vacancy creation have been calculated for elements between Z = 72 and 92. The calculations were performed relativistically in the sudden approximation by the use of the Dirac–Fock–Slater wave functions. The relativistic effects are demonstrated in comparison with the nonrelativistic calculations, and the validity of the approximation method based on the difference in the effective nuclear charge is discussed. The dependence of different initial M‐subshell vacancies on the shake probability is studied. Copyright © 2014 John Wiley & Sons, Ltd.     

Analog of the frobenius method for solving homogeneous integral equations of the quasi-potential approach in a relativistic configurational representation

A method is suggested for constructing a solution of the homogeneous integral equation of a three-dimensional, covariant, simultaneous theory of bound states formulated in a relativistic configurational representation. The method is based on representing the unknown solutions in the form of a combination of functions that includes hyperbolic functions and polynomials (degenerate power series). Using this method and the REDUCE system of analytical calculations, the exact conditions determining the mass spectrum and the exact wave functions for a two-particle relativistic system with a quasi-potential [tanh(πr/2)]/r are found. F. Skorina State University, Gomel’. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 7, pp. 53–61, July, 1997.     

Consequences of relativity for the hyperfine interactions — with applications to transition metals

The strong influence of relativity on the hyperfine interaction is demonstrated by non-, scalar andfully relativistic calculations for solid transition metal systems. By calculations of hyperfine fields andof the nuclear spin lattice relaxation rate of Ag in Ag _x Pt_1–x it is shown that scalar relativistic calculations, which neglect the influence of spin-orbit coupling, seem to be sufficient to account for relativistic effects in many cases. To account properly for the symmetry-breaking caused by spin-orbit coupling, which is reflected by many hyperfine interaction properties, a fully relativistic approach is demanded. The corresponding formalism in the framework of the KKR-GF (Korringa-Kohn-Rostoker-Green's function) method of band structure calculation for magnetic solids is outlined. As applications results for the hyperfine fields of pure transition metals andalloys are presented.     

Calculation of the cross section of helium ionization by an electron impact with the formation of a helium ion in an excited state

The total cross sections of He and He⁺ ionization by an electron impact are calculated in the first Born approximation. Calculations of the matrix elements are carried out by the Fock-Dirac multiconfiguration relativistic method using an intermediate type of coupling with orthogonal functions of the initial and final states. A single-electron wave function of the continuous spectrum for an Auger electron is obtained using the Fock-Dirac single-configuration method. The results of the calculations performed with orthogonal and nonorthogonal wave functions of the initial and final states are compared. The ionization cross sections are calculated for cases in which a knock-on electron of the continuous spectrum is described by both the orthogonal and nonorthogonal wave functions with respect to the wave functions of the core electrons.     

Systematic generation of relativistic gaussian basis sets

A method for the Gaussian basis set generation for molecular relativistic Dirac-Fock calculations is proposed. The basis set exponents are obtained in the process of stochastic optimization (a hybrid of simplex and simulated annealing optimization techniques has been employed) of a functional defined as the sum of squares of differences between the numerical relativistic atomic wave functions and the wave functions obtained using the Gaussian function expansion. After this pre-optimization step the exponents are refined by ordinary gradient energy-functional based procedure. The present method seems to be very effective and robust. As an example the optimized basis sets of atoms from H (Z=1) to Ar (Z=18) are presented. Results of the Dirac-Fock calculations for all atoms under study are presented and compared with the numerical Dirac-Fock results and results obtained using the Gaussian basis sets according to Okada et al.: J. Chem. Phys.93 (1990) 5013. Slovak Grant Agency has funded the work reported in this paper, project No. 1/4205/98.     

Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ¹⁶O and ²⁰⁸Pb, the deformed nucleus ²⁰Ne. Good agreement is obtained.     

Calculation by plane wave Born approximations of electron-impact ionization of silver and copper

The plane wave Born approximation is used to calculate total electron impact ionization cross section of silver and copper. Wavefunctions of the target and residual ions were modeled by non orthogonal Hartree-Fock and Dirac-Fock orbitals. The wave functions of the atom and residual ion are calculated with allowance for relaxation effects. The one-electron wavefunction of the continuous spectrum for the ejected electron is obtained using single-configuration Hartree-Fock and Dirac-Fock method. The orthogonalization of the ejected electron wave functions to all occupied orbitals of the target atom is performed. Results of calculations are compared to available experimental measurements and theoretical calculations performed by non relativistic one-electron PWBA, where the ejected electrons is modeled by the hydrogenic Coulomb wave function.     

Analytic properties of scattering amplitudes in two variables in general quantum field theory

It is shown that scattering amplitudes have analytic properties as functions of momentum transfer not only for physical, but also for complex energies. This follows from local relativistic field theory for all reactions for which an ordinary dispersion relation can be proved.It is further shown that such amplitudes are boundary values of analytic functions of the two variables energy and momentum transfer. A domain of holomorphy — which is however not best possible — is given explicitly. It follows then that partial waves can be analytically continued to complex energies.     

Study of relativistic bound state wave functions in quasielastic (e,e′ p) reactions

The unpolarized response functions of the quasielastic ¹⁶O(e,e′ p)¹⁵N reaction are calculated for three different types of relativistic bound-state wave functions. The wave functions are obtained from relativistic Hartree, relativistic Hartree-Fock and density-dependent relativistic Hartree calculations that reproduce the experimental rms charge radius of ¹⁶O. The sensitivity of the unpolarized response functions to the single-particle structure of the different models is investigated in the relativistic plane-wave impulse approximation. Redistributions of the momentum dependence in the longitudinal and transverse response function can be related to the binding energy of the single-particle states. The interference responses R_LT and R_TT reveal a strong sensitivity to the small component of the relativistic bound-state wave function.     

Interaction quasipotential for spinor and scalar particles

The two-time Green functions and corresponding quasipotentials for the system of two relativistic particles with spins 0 and 1/2, interacting through exchange of a massless vector boson and a massive scalar boson, are calculated. The calculations are performed using the covariant single-time method of Logunov and Tavkhelidze in the second order of perturbation theory. The dependence of these quantities on the total energy of the system is given. It is shown that, despite a nonlocal form of the quasipotentials, the three-dimensional equations for the wavefunctions can be reduced to the one-dimensional equations using the partial wave decomposition.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 57–61, February, 1989.In conclusion, the authors express their gratitude to A. A. Afonin, E. A. Dei, V. I. Savrin, and N. B. Skachkov for helpful discussions.     

High precision analysis of finlines on semiconductor substrate

In this study, the effect of the metallization thickness in finlines on semiconcuctor substrate is researched. The propagation parameters are computed to measure the inluence of the metallization. The theory and numerical results are presented to the propagation constant and characteristic impedance of the bilateral and unilateral finlines. The full wave analysis of the transverse transmission line — TTL method is used to determine the electromagnetic fields of the structure in Fourier transform domain — FTD. Applying the suitable boundary conditions, the moment method and expanding the fields in a set of suitable bases functions, a homogeneous matrix system is obtained and the propagation constant is computed. The characteristic impedance is obtained using the relation of the voltage in the slot and the transmitted power by the structure.Computational programs are developed to obtain numerical results to the propagation parameters composed by the propagation constant and characteristic impedance.This work received financial support by CAPES and CNPq.     

Electronic charge distribution of the polarizable O2− ion in MgO and CaO in contrast to the F− ion in NaF

The electronic charge densities of NaF, MgO, and CaO are obtained by self-consistent band structure calculations using the augmented plane wave (APW) method. The fact that F^– is stable, whilst O^2– is unstable as a free ion affects the radial charge density of fluorides and ionic oxides significantly. The Watson sphere model can simulate the stabilizing crystalline environment of an O^2– ion and provides an ionic density which, when superposed with the cation density, leads to a radial charge density in excellent agreement with the one obtained by our APW calculations. It is therefore meaningful to speak of an O^2– ion, although the corresponding wave functions are more extended for O^2– than for F^–. Furthermore, the Watson sphere model can account for the main differences of the oxygen radial density between MgO and CaO and demonstrates that the polarizable O^2– ion is strongly affected by its environment.     

The scalar relativistic approximation

A new method has recently been proposed for the approximate calculation of relativistic effects in atoms and solids. In this method, which is called the scalar relativistic approximation (SRA), the spin-orbit coupling term appearing in Dirac's equation is dropped; occasionally the minority component of the wave function is also neglected in defining the charge density. We propose here another derivation of the SRA that clarifies the approximations. A simple analytical treatment of the SRA for the hydrogen atom is given, and, as an example of the application of the SRA to the calculation of atomic states, results of self-consistent, local-density calculations for the ytterbium atom are given. The results show that, except for the spin-orbit splitting, relativistic effects (due to the Darwin and mass-velocity terms) are taken into account by the SRA very well.     

Application of the method of asymptotic projection to the calculation of vertical ionization potentials

An alternative method is proposed for the calculation of ionized states corresponding to the excitation of both valence and core electrons. Unlike the well-known approaches, in which such states are constructed by removing an electron from the corresponding spin orbital, the method proposed employs the requirement that all the spin orbitals of the ionized system are orthogonal to the spin orbitals of the neutral system. The proper spin symmetry and the orthogonality of the wave functions of these states to the wave function of the neutral molecule are ensured by a simple-to-use method of taking into account the orthogonality that was proposed by us earlier. The adequacy of the proposed scheme is demonstrated by the calculation of 15 ionization potentials of diatomic and triatomic molecules at different levels of the theory. The results of the calculations, performed in optimized basis sets including three to five Gaussian s functions per electron, are in good agreement with experimental data and state-of-the-art results obtained by other methods in extended basis sets.