Ground state of antiferromagnetic ordering in fullerene C60C_{60} molecule

Theoretical study of mutual orientation of fullerene $C_{60}$ molecule atom spins is presented in this work. Spin-spin interaction was described by Habbard's model. Existence of antiferromagnetic sturcture of spin sub-system in ground state is found

A Possible Origin of Dark Matter, Dark Energy, and Particle-Antiparticle Asymmetry

In this paper we present a possible origin of dark matter and dark energy from a solution of the Einstein's equation to a primordial universe, which was presented in a previous paper. We also analyze the Dirac's equation in this primordial universe and present the possible origin of the particle-antiparticle asymmetry. We also present ghost primordial particles as candidates to some quantum vacuum contituents.Comment: 19 pages,no figure

Effect of nuclear quadrupole moment on parity nonconservation in atoms

Nuclei with spin $I \ge 1$ have a weak quadrupole moment which leads to tensor contribution to the parity non-conserving interaction between nuclei and electrons. We calculate this contribution for Yb$^+$, Fr and Ra$^+$ and found it to be small. In contrast, in many lanthanides (e.g., Nd, Gd, Dy, Ho, Er, Pr, Sm) and Ra close levels of opposite parity lead to strong enhancement of the effect making it sufficiently large to be measured. Another possibility is to measure the PNC transitions between the hyperfine components of the ground state of Bi. Since nuclear weak charge is dominated by neutrons this opens a way of measuring quadrupole moments of neutron distribution in nuclei.Comment: 9 pages, 1 figur

Resonance Type Instabilities in the Gaseous Disks of the Flat Galaxies II. The stability of solitary vortex sheet

Linear stability analysis of the axisymmetric interface of velocity and density discontinuity in rotating gaseous disk has been performed numerically and analytically. Physical mechanisms leading to development of centrifugal and Kelvin-Helmholtz instability at the kink has been analysed in detail. In the incompressible limit it has been shown in the first time such areas in the parameter space that Kelvin-Helmholtz instability is stabilized by the density kink. This effect is caused by both specifical angular momentum conservation and buoyancy. The possibility of application of obtained results to the stability analysis of the gaseous disks of the real flat galaxies is discussed.Comment: Plain TeX, 10 pages, 6 postscript figures, uses epsf.te

Topics in Non-Riemannian Geometry

In this paper, we present some new results on non-Riemannian geometry, more specifically, asymmetric connections and Weyl's geometry. For asymmetric connections, we show that a projective change in the symmetric part generates a vector field that its not arbitrary, as usually presented, but rather, the gradient of a non-arbitrary scalar function. We use normal coordinates for the symmetric part of asymmetric connections as well as for the Weyl's geometry. This has a direct impact on asymmetric conections, although normal frames are usual in antisymmetic connections, unlike normal coordinates. In this symmetric part of asymmetric connections, the vector fields obeys a well-known partial differential equantion, whereas in Weyl's geometry, gauge vector fields obey an equation that we believe is presented for the first time in this paper. We deduce the exact solution of each of these vector fields as the gradient of a scalar function. For both asymmetric and Weyl's symmetric connections, the respective scalar functions obey respective scalar partial differential equations. As a consequence, Weyl's geometry is a conformal differential geometry and is associated with asymmetric geometry by a projective change. We also show that a metric tensor naturally appears in asymmetric geometry and is not introduced via a postulate, as is usually done. In Weyl's geometry, the eletromagnetic gauge is the gradient of a non-arbitrary scalar function and eletromagnetic fields are null. Despide the origin in Weyl's differential geometry, the use of the eletromagnetic gauge is correct in Lagrangean and Hamiltonian formulations of field theories.Comment: 11 pages, no figures, last versio

Effect of atomic electric quadrupole moment on positron binding

Effect of the electric quadrupole moment, $Q$, is studied for positron-atom bound systems. It is demonstrated that for $Q >50$ a.u. the electric quadrupole potential is sufficiently strong to bind positron (or electron) even in the absence of the dipole polarization potential. Such large values of $Q$ are not known for atomic ground states, however, they exist in molecules and excited atoms. In the state $2s2p~^3P^o_2$ of beryllium, the quadrupole contribution makes difference between stable bound state and decay to Be$^+$ ion and positronium. In a majority of atoms the quadrupole contribution is small and can be neglected.Comment: 5 pages, 1 figur

The motion of a charged particle in Kalusa-Klein manifolds

In this paper we use Jacobi fields to describe the motion of a charged particle in the classical gravitational, electromagnetic, and Yang-Mills fields.Comment: 8 pages, Mikte

Atoms which can bind positrons

Calculations of the positron binding energies to all atoms in the periodic table are presented and atoms where the positron-atom binding actually exists are identified. The results of these calculations and accurate calculations of other authors (which existed for several atoms only) are used to evaluate recommended values of the positron binding energies to the ground states of atoms. We also present the recommended energies of the positron excited bound levels and resonances (due to the binding of positron to excited states of atoms) which can not emit positronium and have relatively narrow widths. Such resonances in positron annihilation and scattering may be used to measure the positron binding energy.Comment: 19 pages, 10 tables, 2 figures, submitted to Phys. Rev. A. arXiv admin note: text overlap with arXiv:1204.6577,improved tex

Physical Principles Based on Geometric Properties

In this paper we present some results obtained in a previous paper about the Cartan's approach to Riemannian normal coordinates and our conformal transformations among pseudo-Riemannian manifolds. We also review the classical and the quantum angular momenta of a particle obtained as a consequence of geometry, without postulates. We present four classical principles, identifed as new results obtained from geometry. One of them has properties similar Heisemberg's uncertaintly principle and another has some properties similar to Bohr's principle. Our geometric result can be considered as a possible starting point toward a quantum theory without forces.Comment: 25 pages, no figure

Conformal Form of Pseudo-Riemannian Metrics by Normal Coordinate Transformations II

In this paper, we have reintroduced a new approach to conformal geometry developed and presented in two previous papers, in which we show that all n-dimensional pseudo-Riemannian metrics are conformal to a flat n-dimensional manifold as well as an n-dimensional manifold of constant curvature when Riemannian normal coordinates are well-behaved in the origin and in their neighborhood. This was based on an approach developed by French mathematician Elie Cartan. As a consequence of geometry, we have reintroduced the classical and quantum angular momenta of a particle and present new interpretations. We also show that all n-dimensional pseudo-Riemannian metrics can be embedded in a hyper-cone of a flat n+2-dimensional manifold.Comment: 33 pages,no figures. Paper of a talk given at the 14th International Conference on Geometry, Integrability and Quantization (Varna, Bulgaria, June 2012