Electric and magnetic form factors of strange baryons

Predictions for the electromagnetic form factors of the , and hyperons are presented. The numerical calculations are performed within the framework of the fully relativistic constituent-quark model developed by the Bonn group. The computed magnetic moments compare favorably with the experimentally known values. Most magnetic form factors G_M (Q²) can be parameterized in terms of a dipole with cutoff masses ranging from 0.79 to 1.14 GeV.Received: 2 October 2003, Published online: 20 April 2004PACS: 11.10.St Bound and unstable states; Bethe-Salpeter equations - 12.39.Ki Relativistic quark model - 13.40.Gp Electromagnetic form factors     

Stability of semiclassical bound states of nonlinear Schrödinger equations with potentials

In this paper, we study the Lyapunov stabilities of some semiclassical bound states of the (nonhomogeneous) nonlinear Schrödinger equation, We prove that among those bound states, those which are concentrated near local minima (respectively maxima) of the potentialV are stable (respectively unstable). We also prove that those bound states are positive if is sufficiently small.     

Quantization for brachistochrone problem

The brachistochrone curve corresponds to the minimization of the time functional. In this paper we discuss the dynamics of a massive particle, which moves classically on the brachistochrone curve under the potential V=-mgy. We derive the Lagrangian and the Hamiltonian of the particle and show that this problem corresponds to the particle in an infinite wall with a harmonic oscillator potential and the solutions of Schrödingers equation are confluent hypergeometric functions. We also discuss the periodic potential problem for the brachistochrones and obtain the band structure of Kronig-Penney model for the particle with positive energy in a certain limit.Received: 29 January 2003, Published online: 30 July 2003PACS: 03.65.-w Quantum mechanics - 03.65.Ge Solutions of wave equations: bound states - 71.15.Ap Basis sets (LCAO, plane-wave, APW, etc.) and related methodology (scattering methods, ASA, linearized methods, etc.)     

n-Dimensional representations of the unified field tensor* g λν

For the first time Hlavatý represented the tensor^*g^v, defined by (15a), in terms of the unified field tensorg in the space-timeX ₄. Recently, the representations of^* g ^v in terms ofg in two- and three-dimensional generalized Riemannian space were obtained by Chung. The purpose of the present paper is to obtain the generalized representations of^* g ^v in terms ofg in a generalizedn-dimensional Riemannian spaceX _n.     

Relativistic Schrödinger Theory and the Hartree–Fock Approach

Within the framework of Relativistic Schrödinger Theory (RST), the scalar two-particle systems with electromagnetic interactions are treated on the basis of a non-Abelian gauge group U(2) which is broken down to the Abelian subgroup U(1)×U(1). In order that the RST dynamics be consistent with the (non-Abelian) Maxwell equations, there arises a compatibility condition which yields cross relationships for the links between the field strengths and currents of both particles such that self-interactions are eliminated. In the non-relativistic limit, the RST dynamics becomes identical to the well-known Hartree–Fock equations (for spinless particles). Consequently the original RST field equations may be considered as the relativistic generalization of the Hartree–Fock equations, and the exchange interactions of the conventional theory (induced by the anti-symmetrization postulate) do reappear here as ordinary gauge interactions due to a broken symmetry.     

Ionization of the hydrogen atom: from weak to strong static electric fields

A quantum dynamical treatment of the S-G effect, to the leading order in for the electron, where is the fine-structure constant, and for spin 1/2 charged particles (e.g., the proton), in general, leads to a unitary expression for the probability density on the observation screen, where the magnetic field has a controllable longitudinal uniform component along the initial average direction of propagation of the particle, in addition to a non-uniform, almost longitudinal, magnetic field lying in the plane defined by the quantization axis, in question, of the spin and the initial average direction of propagation.Received: 3 April 2003, Published online: 22 July 2003PACS: 03.65.-w Quantum mechanics - 03.65.Nk Scattering theory - 24.70.+s Polarization phenomena in reactions     

Vector Measures on the Logic of <Emphasis Type="Italic">J</Emphasis>-projections of a Krein Space

Let be a Hilbert space with an inner product . In Jajte, R., and Paszkiewicz, A. (1978, Vector measure on the closed subspaces of a Hilbert space, Studia Mathematica 63, 229–251), the -measure on the logic of all orthogonal projections on H was studied. We examine the -measure on the hyperbolic logic of all J-projections on a Krein space. PACS: 03.65.Ta, 03.65.Db, 03.65.Ca.     

Self-similar analytical solutions for blast waves in inhomogeneous atmospheres with frozen-in-magnetic field

In the present paper, we have made an attempt to study the effects of the presence of a magnetic field on the cavity formation inside a blast wave propagating into a perfectly conducting gas with density varying as some power of distance from the plane or line of explosion. In order to obtain the closed form solutions for the flow variables inside the blast wave and to solve the problem of cavity formation analytically, a relation is taken between the ordinary pressure and the total pressure. It i s found that if the value of the inhomogeneity index is greater than a critical value (a function of M_A - Alfven Mach Number, - adiabatic index and i - wave geometry index), a contact discontinuity appears at some point inside the blast wave and the cavity formation occurs. The effect of the presence of magnetic field is found to increase the tendency of cavity formation.Received: 21 February 2003, Published online: 4 August 2003PACS: 47.40.-x Compressible flows; shock and detonation phenomena - 47.65.+a Magnetohydrodynamics and electrohydrodynamics     

Accurate asymptotic ground state potential curves of Cs$\mathsf{_2}$ from two-colour photoassociation

Over 100 high lying level energies of the lowest electronic states and in Cs₂ are determined in a -like scheme two-colour photoassociation spectroscopy. The results are analyzed with a coupled channel model using an asymptotic approach, based on nodal lines. From this analysis we determine the long range dispersion coefficient C₆ to 6846.2 15.6 a.u. We also obtain the first experimental determination of the amplitude of the asymptotic exchange term.Received: 4 November 2003, Published online: 20 January 2004PACS: 34.20.-b Interatomic and intermolecular potentials and forces, potential energy surfaces for collisions - 32.80.Pj Optical cooling of atoms; trapping - 03.65.Ge Solutions of wave equations: bound states     

Black hole memory

We discuss the formation of black holes during the very early stages of a universe in which the gravitational constant evolves with time. We argue that black holes will retain memory of the value of the gravitational constant,G, at the time of their formation. Their horizon size and their thermal characteristics are determined by the value ofG when they form, not by the value we measure in the external universe today. The observational effects of primordial black hole explosions are therefore radically altered.This essay received the fourth award from the Gravity Research Foundation, 1993—Ed.     

Are quantum wave packets observable? Sokolov effect: puzzling generation of 2p states in the 2s hydrogen beam passing trough a wide metal slit

The observation of excitation of 2p states in a collimated 2s hydrogen beam passing through a wide metal slit with no direct contacts or electric field applied (Sokolov effect) up to now has had no reasonable explanation. A solution presented in this paper is formulated within the standard quantum-mechanical framework with a consecutive wave packet treatment of the atomic center-of-mass wave function. It is found that a very weak interaction of the beam diffraction halo with the slit, though negligible for center-of-mass motion, coherently affects the intrinsic state of an atom in the beam and efficiently induces transitions. High sensitivity of this interference phenomena may be used to measure transverse coherence length of the beam.Received: 25 March 2003, Published online: 15 July 2003PACS: 03.65.-w Quantum mechanics     

Energy level displacement of the excited $n\ell$ state of pionic hydrogen

The energy level displacements of the excited states of pionic hydrogen and the contribution of the transitions and the transitions of the pair, coupled by the attractive Coulomb field in the S-wave state with a continuous energy spectrum, to the shift of the energy level of the ground state of pionic hydrogen, caused by strong low-energy interactions, are calculated within a quantum field theoretic, relativistic covariant and model-independent approach.Received: 19 November 2003, Revised: 25 November 2003, Published online: 5 February 2004PACS: 13.75.Gx Pion-baryon interactions - 11.10.St Bound and unstable states; Bethe-Salpeter equations - 21.30.Fe Forces in hadronic systems and effective interactions - 31.15.Ar Ab initio calculationsPermanent address A.N. Ivanov: State Polytechnical University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation;Permanent address N.I. Troitskaya: State Polytechnical University, Department of Nuclear Physics, 195251 St. Petersburg, Russian Federation.     

Two-quasiparticle and collective excitations in transitional 108,110 Pd nuclei

High-spin states in ^108,110Pd isotopes are studied by -ray spectroscopy of heavy-ion-induced fission. The Pd isotopes are produced in the fission channel of the ³¹P + ¹⁷⁶Yb reaction at beam energy 152 MeV. The prompt -rays are detected with the EUROBALL4 multidetector array. The yrast states of ^108,110Pd have been observed above the region of the first backbend. The level scheme of ¹⁰⁸Pd was extended with a new negative-parity band. The yrast sequence in ¹¹⁰Pd is observed up to spin I = 14 ⁺ and negative-parity bands have also been identified. The backbending in these even-mass Pd isotopes is associated with the alignment of the neutron (h _11/2)² pair. The negative-parity states arise from two neutron configurations and and they are interpreted in the frame of two-quasiparticle + rotor model as semidecoupled bands. The observed experimental staggering in the -bands of ^108,110Pd supports the theoretical predictions for -instability of their shapes.Received: 22 April 2003, Revised: 27 June 2003, Published online: 2 December 2003PACS: 21.60.-n Nuclear structure models and methods - 23.20.Lv transitions and level energies - 25.70.Jj Fusion and fusion-fission reactions - 27.60. + j      

Modular construction of special mixed quantum states

For a homogeneous quantum network of N subsystems with n levels each we consider separable generalized Werner states. A generalized Werner state is defined as a mixture of the totally mixed state and an arbitrary pure state : with a mixture coefficient . For this density operator to be separable, will have an upper bound . Below this bound one should alternatively be able to reproduce by a mixture of entirely separable input-states. For this purpose we introduce a set of modules, each contributing elementary coherence properties with respect to a generalized coherence vector. Based on these there exists a general step-by-step mixing process for any . For being a cat-state it is possible to define an optimal process, which produces states right up to the separability boundary ( ).Received: 3 December 2002, Published online: 29 July 2003PACS: 03.65.Ud Entanglement and quantum nonlocality (e.g. EPR paradox, Bells inequalities, GHZ states, etc.) - 03.67.-a Quantum information - 03.65.-w Quantum mechanics     

Multi-quasiparticle states in 184 W via multi-nucleon transfer

A multi-nucleon transfer reaction using an 850 MeV ¹³⁶Xe beam incident on a ¹⁹⁸Pt target was used to populate high-spin states in ¹⁸⁴W, 14 nucleons from the target. A 4-quasiparticle isomer with ns has been observed for the first time and its de-excitation through collective and intrinsic structures studied. The results are compared with predictions of blocked BCS Nilsson calculations. Observation of this metastable state completes the tungsten 4-quasiparticle isomer systematics from A = 176 to 186. Mapping out the most yrast 4-quasiparticle isomers in these even-even tungsten isotopes suggests the existence of a highly favoured state in ¹⁸⁸W, within reach of current experimental set-ups.Received: 14 October 2003, Revised: 14 November 2003, Published online: 18 May 2004PACS: 21.10.Tg Lifetimes - 23.20.Lv transitions and level energies - 27.70. + q      

Quantum mechanics based on position

The only observational quantity which quantum mechanics needs to address islocation. The typical primitive observation on a microsystem (e.g., photon) isdetection at alocation (e.g., by a photomultiplier looking at a grating). To analyze an experiment, (a) form a conceptual ensemble of replicas of it, (b) assign a wave function (in position representation) to its initial condition, (c) evolve the wave function by the Schrödinger equation (known, once and for all, as a function of the system's composition), (d) compute the probability for particle detection at various times and places. The initial wave function is chosen on the basis of experience with such treatments. Key experiments are thus treated: (i) time-of-flight, (ii) Stern-Gerlach, (iii) Franck-Hertz, (iv) photon recoil, (v) photoionization. Quantum states, dynamical variables, and measurements, and the usual postulates about them, are superfluous. The explicit treatments are nonrelativistic; the existence of relativistic generalizations is left open.     

Bianchi identities,electromagnetic waves,and charge conservation in theP(4) theory of gravitation and electromagnetism

The Bianchi identities for theP(4)=O(1, 3) ^4* theory of gravitation and electromagnetism are decomposed into the standardO(1, 3) Riemannian Bianchi identity plus an additional ^4* component. When combined with the Einstein-Maxwell affine field equations the ^4* components of theP(4) Bianchi identities imply conservation of magnetic charge and the wave equation for the Maxwell field strength tensor. These results are analyzed in light of the special geometrical postulates of theP(4) theory. We show that our development is the analog of the manner in which the Riemannian Bianchi identities, when combined with Einstein's field equations, imply conservation of stress-energy-momentum and the wave equation for the LanczosH-tensor.     

Vector bosons in the expanding universe

We exactly solve the relativistic wave equation for vector bosons in the expanding universe and show that the current of the vector bosons in this background is rapidly oscillating in early time. Additionally, we derive the solutions of the Proca equation from the solutions of the Duffin-Kemmer-Petiau (DKP) equations in the same background and obtain the massless-particle, photon, solutions by taking the limit of these solutions. PACS. 03.65.Pm, 04.60.-m, 98.80.Cq Received: 20 May 2005, Published online: 30 August 2005     

Quasi-stationary states of hydrogen

We consider the hydrogen atom within the context of a theory of relativistic quantum mechanics that allows for a probabilistic interpretation of the wave function. We find the radial equation that determines the energy levels of bound states, represented by quasi-stationary states. We compute the order of magnitude of the shifts from the usual spectrum obtained from the Dirac equation, and we find that the leading terms for these corrections are of the order of ⁶ log fors-states and ⁶ for other states. They are small compared to the Lamb shift, which is of the order of ⁵ log .     

Existence of solutions for Schrödinger evolution equations

We study the existence, uniqueness and regularity of the solution of the initial value problem for the time dependent Schrödinger equationiu/t=(–1/2)u+V(t,x)u,u(0)=u ₀. We provide sufficient conditions onV(t,x) such that the equation generates a unique unitary propagatorU(t,s) and such thatU(t,s)u ₀C ¹(,L ²) C ⁰(H ²( ⁿ )) foru ₀H ²( ⁿ ). The conditions are general enough to accommodate moving singularities of type x^–2+(n4) or x^–n/2+(n3).