Relativistic algebraic spinors and quantum motions in phase space

Following suggestions of Schönberg and Bohm, we study the tensorial phase space representation of the Dirac and Feynman-Gell-Mann equations in terms of the complex Dirac algebra C₄, a Jordan-Wigner algebra G₄, and Wigner transformations. To do this we solve the problem of the conditions under which elements in C₄ generate minimal ideals, and extend this to G₄. This yields the linear theory of Dirac spin spaces and tensor representations of Dirac spinors, and the spin-1/2 wave equations are represented through fermionic state vectors in a higher space as a set of interconnected tensor relations.     

Relativistic theory of nuclear forces

A theory of nuclear forces is proposed which results in a nonlinear relativistic equation for their potential. This equation is used to explain nuclear saturation.     

Relativistic effects in ternary fission

Relativistic effects can explain the energy shift of - 6 keV reported by Ramayya et al. for the -ray de-exciting the first 2 ⁺ state, at 3368.03 keV, of the ¹⁰Be cluster emitted together with the fragments ¹⁴⁶Ba and ⁹⁶Sr in the ternary fission of ²⁵²Cf; the calculated shift is equal to -6.14 (0.16) keV. An explanation is presented for the apparent absence of Doppler broadening. For the configurations ¹³⁸Xe-¹⁰⁴Zr-¹⁰Be and ¹³⁶Te-¹⁰⁶Mo-¹⁰Be, recently reported by Hamilton et al. , observable shifts of the 3367.43 keV -line are predicted.Received: 2 June 2003, Revised: 14 January 2004, Published online: 10 August 2004PACS: 03.30. + p Special relativity - 23.20.-g Electromagnetic transitions - 25.85.-w Fission reactions     

Relativistic hartree-fock description of high-density nuclear matter

Relativistic Hartree-Fock equations are solved for an infinite system of nucleons and mesons. At high densities there exists a phase transition from a Fermi “sphere” to a Fermi “shell”, characterized by a discontinuity in the heat capacity. The precise value of the critical density is sensitive to the approximations.     

Relativistic effects in one-dimensional hydrogen atom

The dependence of stationary levels of a Dirac particle in the regularized Coulomb potential V _??(z) = ?q/(|z| + ??) on the cutoff parameter ?? is studied. It is shown that, in 1 + 1 D, the energy spectrum of a Dirac particle in such a potential reveals some specific features which nonanalytically depend on the coupling constant q and are essentially relativistic in nature. These properties turn out to be most important for ?? ? 1, explicitly demonstrating the existence of a physically reasonable energy spectrum for an arbitrarily small ?? > 0 and, at the same time, the absence of regular limit ?? ?? 0 (hence, the absence of a well-defined spectral problem for the Dirac equation without regularization for arbitrary q in 1 + 1 D).     

Relativistic effects in the variable-screening model

The variable-screening model devised for a quantitative treatment of screening effects in slow (quasimolecular) ion-atom collisions is extended to include relativistic effects. Relativistic correction terms corresponding to a relative energy correction of second order in the electron velocity are incorporated into the effective molecular single-electron Hamiltonian. The model is applied to the calculation of relativistic molecular-orbital correlation diagrams for the quasimolecular systems Br+Br, Xe+Xe, and I+Au. A detailed comparison of our results with the results of relativistic calculations for (unscreened) one-electron systems and calculations based on self-consistent field methods is performed. The agreement with Dirac-Fock-Slater results is fairly good, and could be improved further by read-justing the values of the parameters in the atomic potentials used to construct the effective molecular potential.     

Relativistic effects in the variable-screening model

The variable-screening model devised for a quantitative treatment of screening effects in slow (quasimolecular) ion-atom collisions is extended to include relativistic effects. Relativistic correction terms corresponding to a relative energy correction of second order in the electron velocity are incorporated into the effective molecular single-electron Hamiltonian. The model is applied to the calculation of relativistic molecular-orbital correlation diagrams for the quasimolecular systems Br+Br, Xe+Xe, and I+Au. A detailed comparison of our results with the results of relativistic calculations for (unscreened) one-electron systems and calculations based on self-consistent field methods is performed. The agreement with Dirac-Fock-Slater results is fairly good, and could be improved further by read-justing the values of the parameters in the atomic potentials used to construct the effective molecular potential.     

Relativistic effects in bound two-particle systems

The predictions of relativistic Schrödinger theory (RST) for the relativistic effects in helium-like ions with high nuclear charge ( -80) are elaborated in the electrostatic approximation (i.e. neglection of the magnetic interactions). The corresponding RST results are found to meet with the experimental data and with the predictions of other theoretical approaches, provided an estimate of the (neglected) magnetic effects is taken into account. This suggests to carry through high-precision calculations (including the magnetic forces) in order to further test the physical significance of RST.Received: 28 August 2003, Published online: 20 April 2004PACS: 03.65.Pm Relativistic wave equations - 03.65.Ge Solutions of wave equations: bound states - 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.)     

Relativistic mean-field parametrization of effective interaction in nuclear matter

The results of the modern relativistic Dirac-Brueckner calculations of nuclear matter are parametrized in terms of the relativistic- mean-field theory with scalar and vector nonlinear selfinteractions. It is shown that the inclusion of the isoscalar vector-meson quartic selfinteraction is essential for obtaining a proper density dependence of the vector potential in the mean-field model. The obtained mean-field parameters represent a simple parametrization of effective interaction in nuclear matter. This interaction may be used in the mean-field studies of the structure of finite nuclei without the introduction of additional free parameters.This work was supported in part by the Grant Agency of the Slovak Academy of Sciences under Grant No. GA SAV-517/1991.     

Relativistic repulsive effects in nonrelativistic systems

A ladder approximation to the Weinberg equation constitutes a basis for a study of relativistic effects in a model two-nucleon system. The essential changes in the low energy phase shifts and in the ground state binding energy are recovered when passing from a nonrelativistic to the relativistic treatment. Signs of the relativistic corrections are such as if the interaction were becoming more repulsive.     

Relativistic nuclear and neutron matter at finite temperatures

Nuclear matter as well as neutron matter is studied in the framework of a relativistic nuclear field theory at finite temperature. A spectral representation for the two-point Green's function at finite temperature and finite density is constructed. The bulk properties of the interacting system are calculated in the Hartree and Hartree-Fock approach. In additionσ ³- andσ ⁴-self-interactions have been taken into account. We present and discuss the results of hot and dense matter for temperaturesT≦ 50 MeV and densitiesθ≦6θ ₀ (ρ ₀≈0.17 fm^?3) using six different model parameter sets.