Oscillator strengths and lifetimes for the P XII

Semi-empirical weighted oscillator strengths (gf) and lifetimes presented in this work for all experimentally known electric dipole P XII spectral lines and energy levels were computed within a multiconfiguration Hartree-Fock relativistic approach. In this calculation, the electrostatic parameters were optimized by a leastsquares procedure in order to improve the adjustment to experimental energy levels. The method produces lifetime and gf values that are in agreement with intensity observations used for the interpretation of spectrograms of solar and laboratory plasmas.     

Rigid Body Motion in Special Relativity

We study the acceleration and collisions of rigid bodies in special relativity. After a brief historical review, we give a physical definition of the term ‘rigid body’ in relativistic straight line motion. We show that the definition of ‘rigid body’ in relativity differs from the usual classical definition, so there is no difficulty in dealing with rigid bodies in relativistic motion. We then describe

1. The motion of a rigid body undergoing constant acceleration to a given velocity.
2. The acceleration of a rigid body due to an applied impulse.
3. Collisions between rigid bodies.

     

Oscillator strengths and lifetimes for the S V spectrum

The semi-empirical weighted oscillator strengths (gf) and the lifetimes presented in this work for all experimentally known electric dipole S V spectral lines and energy levels were carried out in a multiconfiguration Hartree–Fock relativistic (HFR) approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure, in order to improve the adjustment to experimental energy levels. This method produces lifetime values and gf values that are in agreement with intensity observations used for the interpretation of spectrograms of solar and laboratory plasmas.     

Electric dipole transitions for highly excited states in helium-like sulphur

We have calculated relativistic energies, weighted oscillator strengths and transition probabilities for electric dipole (E1) transitions among the terms belonging to 1snl (n?9, l?3) configurations in helium-like sulphur. The calculations are based upon the multiconfiguration Hartree-Fock method within the framework of Breit-Pauli relativistic corrections. Our calculated values are also compared with other experimental and theoretical results.     

Relativistic versus nonrelativistic solution of the N-fermion problem in a hyperradius-confining potential

We investigate the quantum system of N identical fermions in the relativistic limit. In this article the considered potential is a combination of Coulombic, linear confining and harmonic oscillator terms. By using Jacobi coordinates and introducing the hyperradius quantity we obtain the wave functions of the system as well as the corresponding energy eigenvalues. Assuming that all particles are confined within a hypersphere we calculate the corresponding x _bag . In particular we consider the case N = 3 which corresponds to baryonic systems. By using the experimental values of the charge radius of each baryon we calculate the potential coefficients. Within our treatment the results of the MIT bag model are recovered for N = 1. Finally we compare the results obtained by the Dirac equation with the corresponding results of the Schrödinger equation and we find that the energy spectra obtained by the former are much closer to experimental values.     

W-symmetry and the rigid particle

We prove that W₃ is the gauge symmetry of the scale-invariant rigid particle, whose action is given by the integrated extrinsic curvature of its world line. This is achieved by showing that its equations of motion can be written in terms of the Boussinesq operator. The W₃ generators T and W then appear respectively as functions of the induced world line metric and the extrinsic curvature. We also show how the equations of motion for the standard relativistic particle arise from those of the rigid particle whenever it is consistent to impose the “zero-curvature gauge”, and how to rewrite them in terms of the KdV operator. The relation between particle models and integrable systems is further pursued in the case of the spinning particle, whose equations of motion are closely related to the SKdV operator. We also partially extend our analysis in the supersymmetric domain to the scale-invariant rigid particle by explicitly constructing a supercovariant version of its action.     

Twin Paradox and the Logical Foundation of Relativity Theory

We study the foundation of space-time theory in the framework of first-order logic (FOL). Since the foundation of mathematics has been successfully carried through (via set theory) in FOL, it is not entirely impossible to do the same for space-time theory (or relativity). First we recall a simple and streamlined FOL-axiomatization Specrel of special relativity from the literature. Specrel is complete with respect to questions about inertial motion. Then we ask ourselves whether we can prove the usual relativistic properties of accelerated motion (e.g., clocks in acceleration) in Specrel. As it turns out, this is practically equivalent to asking whether Specrel is strong enough to “handle” (or treat) accelerated observers. We show that there is a mathematical principle called induction (IND) coming from real analysis which needs to be added to Specrel in order to handle situations involving relativistic acceleration. We present an extended version AccRel of Specrel which is strong enough to handle accelerated motion, in particular, accelerated observers. Among others, we show that~the Twin Paradox becomes provable in AccRel, but it is not provable without IND.     

Born Reciprocity and the Granularity of Spacetime

The Schrödinger-Robertson inequality for relativistic position and momentum operators X ^μ, P _ν, μ, ν = 0, 1, 2, 3, is interpreted in terms of Born reciprocity and ‘non-commutative’ relativistic position-momentum space geometry. For states which saturate the Schrödinger-Robertson inequality, a typology of semiclassical limits is pointed out, characterised by the orbit structure within its unitary irreducible representations, of the full invariance group of Born reciprocity, the so-called ‘quaplectic’ group U(3, 1) #x2297;_s H(3, 1) (the semi-direct product of the unitary relativistic dynamical symmetry U(3, 1) with the Weyl-Heisenberg group H(3, 1)). The example of the ‘scalar’ case, namely the relativistic oscillator, and associated multimode squeezed states, is treated in detail. In this case, it is suggested that the semiclassical limit corresponds to the separate emergence of spacetime and matter, in the form of the stress-energy tensor, and the quadrupole tensor, which are in general reciprocally equivalent.     

Weighted oscillator strengths and lifetimes for the S IX and S X spectra

The weighted oscillator strengths (gf) and the lifetimes presented in this work were carried out in a multi configuration Hartree-Fock relativistic (HFR) approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure, in order to improve the adjustment to experimental energy levels. This method produces gf-values that are in better agreement with intensity observations and lifetime values that are closer to the experimental ones. In this work, we presented all the experimentally known electric dipole S IX and S X spectral lines.     

Weighted oscillator strengths and lifetimes for the Si XII and Si XIII spectra

The weighted oscillator strengths (gf) and the lifetimes for Si XII and Si XIII presented in this work were carried out in a multiconfiguration Hartree-Fock relativistic (HFR) approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure, in order to improve the adjustment to experimental energy levels. This method produces gf-values that are in better agreement with intensity observations and lifetime values that are closer to the experimental ones. In this work we present all the experimentally known electric dipole Si XII and Si XIII spectral lines.     

Equation of State of Tantalum and Plutonium in a Spherical Cell Approximation and at Extremely High Pressures

We first present the equation of state (EOS) of a relativistic homogeneous electron gas in the exchange only approximation. We then go on to use this result to determine approximately the EOS of the heavy metals Pu and Ta. An essential ingredient is the electron density at the boundary of the Wigner-Seitz polyhedron and we determine this density using relativistic Thomas-Fermi theory.     

Weighted oscillator strengths and lifetimes for the Si I spectrum

The weighted oscillator strengths (gf) and the lifetimes for Si I presented in this work were carried out in a multiconfiguration Hartree-Fock relativistic approach. In this calculation, the electrostatic parameters were optimized by a least-squares procedure, in order to improve the adjustment to experimental energy levels. This method produces gf-values that are in better agreement with intensity observations and lifetime values that are closer to the experimental ones. In this work we present all the experimentally known electric dipole Si I spectral lines.     

Fine-structure effects in relativistic calculations of the static polarizability of the helium atom

We use the relativistic configuration-interaction method and the model potential method to calculate the scalar and tensor components of the dipole polarizabilities for the excited states 1s3p ³ P ₀ and 1s3p ³ P ₂ of the helium atom. The calculations of the reduced matrix elements for the resonant terms in the spectral expansion of the polarizabilities are derived using two-electron basis functions of the relativistic Hamiltonian of the atom, a Hamiltonian that incorporates the Coulomb and Breit electron-electron interactions. We formulate a new approach to determining the parameters of the Fuss model potential. Finally, we show that the polarizability values are sensitive to the choice of the wave functions used in the calculations. Zh. éksp. Teor. Fiz. 115, 494–504 (February 1999)     

Signature and unitary in the multi-Regge model

In a previous paper it was shown how factorisation and signature properties for production processes arose from a well-defined set of singularities in complex angular momentum and helicity. These arose for Feynman diagrams without crossed channel singularities. In this paper we show how the general case gives rise to a sum of terms of this form. We also show how these precise singularities are crucial to prevent the occurence of terms in inclusive pionisation cross sections which are much greater than the canonical pomeron terms.     

An Analytic Approach to Torus Bifurcation in a Quasiperiodically Forced Duffing Oscillator

Abstract

A weakly nonlinear quasiconservative Duffing oscillator under quasiperiodic forcing is studied with the help of an analytic expression for the complex Poincare mapping. This mapping is then used to analyze the quasiperiodic response of the oscillator and the different zones of various periodicity. This map plays the same significant role as the averages equations in the theory of a periodically forced Duffing oscillator.     

Fermi field and Dirac oscillator in a Som–Raychaudhuri space-time

We investigate the relativistic dynamics of a Dirac field in the Som–Raychaudhuri space-time, which is described by a Gödel-type metric and a stationary cylindrical symmetric solution of Einstein field equations for a charged dust distribution in rigid rotation. In order to analyze the effect of various physical parameters of this space-time, we solve the Dirac equation in the Som–Raychaudhuri space-time and obtain the energy levels and eigenfunctions of the Dirac operator by using the Nikiforov–Uvarov method. We also examine the behaviour of the Dirac oscillator in the Som–Raychaudhuri space-time, in particular, the effect of its frequency and the vorticity parameter.     

Supersymmetry and duality in relativistic oscillator systems

A simple mapping is defined which takes the relativistic oscillator on a (1+1)-dimensional spacetime into a dual system consisting of a nonrelativistic oscillator confined to a circular space. The radius of the circle in the dual system measures the size of relativistic effects in the original system. It is shown that both of the dual oscillator systems have supersymmetric partners, and the exact wavefunctions and energy levels of all four of the intertwined systems are found.     

Pomeron factorisation and the reaction γN → φN

Because of the suitability of γN → φN for studying the Pomeron, we systematically investigate the tests for Pomeron factorisation possible in this rather clean reaction, particularly from the more feasible experiment which measures the φ-density-matrix, and also an experiment measuring the recoil nucleon polarisation; the complete set of initial polarisation configurations has been considered.For any two-body parity-conserving process, a simple consequence of factorisation is M-purity which asymptotically corresponds to purely natural or purely unnatural parity in the crossed channel. Factorisation tests, therefore, include M-purity tests, but M-purity does not necessarily imply factorisation.For the φ-decay density-matrix we give all the possible factorisation tests, and show that our tests are exhaustive. A separate measurement of the recoil nucleon polarisation is shown to complement adequately the information obtained from the φ-decay density-matrix in the factorising case.For the φ-density matrix, some of the M-purity tests refer to dominant amplitudes and persist even if s-channel meson-helicity-conservation (which is experimentally true approximately) holds exactly. These tests should be easy to perform. The tests which invoke factorisation more crucially than only M-purity do not persist in that manner; these refer to the helicity nonconserving amplitudes. However, factorisation for such small amplitudes could be advantageously tested here, because of their being masked by the large amplitudes elsewhere.The factorisation tests for the φ-density-matrix can be used to distinguish a pure Regge pole type Pomeron from (a) an M-pure “cut-pole mixture” type Pomeron or an M-impure (hence nonfactorising) “cut-pole mixture” type Pomeron and also (b) a factorising “cut-pole mixture” type Pomeron or a nonfactorising “cut-pole mixture” type Pomeron. Here we have taken departure from relative reality of all amplitudes as the defining criterion for a “cut-pole mixture.” Such tests would require polarised photons and/or targets.Present γN → φN data are not adequate enough to allow firm conclusions about Pomeron factorisation, though they do indicate M-purity for the Pomeron, corresponding to pure natural parity. This is consistent with Pomeron factorisation, but M-purity is only a necessary consequence of factorisation. Better and more γN → φN data are needed to get a more complete picture of Pomeron factorisation.     

Factorization method for Schrödinger equation in relativistic configuration space and q-deformations

Review paper is devoted to the relativistic configuration space (RCS) concept, a version of the relativistic Quantum Mechanics in RCS, the generalization of the Dirac-Infeld-Hall factorization method in the framework of the noncommutative differential calculus natural for RCS, different versions of the deformed oscillators, emerging as the generalization of the harmonic oscillator for RCS. In the formulation of the Newton-Wigner postulates for the relativistic localized states the hypothesis of commutativity of the position operator components is silently accepted as an evident fact. In the present work it is shown that commutativity is not necessary condition and the alternative (noncommutative) approach to the relativistic position operator and localization concept can be realized in a framework of the physically as well as mathematically comprehensive scheme. The different generalizations of the Dirac-Infeld-Hall factorization method for this case are constructed. This method enables us to find out all possible generalizations of the most important nonrelativistic integrable case—the harmonic oscillator. It is shown also that the relativistic oscillator = q—oscillator.     

Exclusive semileptonic decays of heavy mesons

Exclusive semileptonic decays of heavy mesons provide interesting information on systems consisting of quarks of unequal mass. We express the formfactors of the hadronic current in terms of relativistic bound state wave functions for which we take the solutions of a relativistic harmonic oscillator potential. The wave function overlap is determined by the quark mass dependent longitudinal momentum distribution and differs from results based on non relativistic wave functions. The semileptonic widths and lepton spectra are calculated using in addition nearest pole dominance for the momentum transfer dependence of the formfactors. We compare our results with recent experimental data. The formfactor calculation also allows an estimate of special nonleptonic transitions. From the CLEO results on \(\bar B^0 \to \pi ^ + \pi ^ -\) and \(\bar B^0 \to D^{* + } + \pi ^ -\) we find for the corresponding Kobayashi-Maskawa matrix element ratio the limit |V _ub /V _cb |?0.3.