Covariant Calculation of General Relativistic Effects in an Orbiting Gyroscope Experiment

We carry out a covariant calculation of the measurable relativistic effects in an orbiting gyroscope experiment. The experiment, currently known as Gravity Probe B, compares the spin directions of an array of spinning gyroscopes with the optical axis of a telescope, all housed in a spacecraft that rolls about the optical axis. The spacecraft is steered so that the telescope always points toward a known guide star. We calculate the variation in the spin directions relative to readout loops rigidly fixed in the spacecraft, and express the variations in terms of quantities that can be measured, to sufficient accuracy, using an Earth-centered coordinate system. The measurable effects include the aberration of starlight, the geodetic precession caused by space curvature, the frame-dragging effect caused by the rotation of the Earth and the deflection of light by the Sun.Comment: 7 pages, 1 figure, to be submitted to Phys. Rev.

Wave Mechanics of Two Hard Core Quantum Particles in 1-D Box

The wave mechanics of two impenetrable hard core particles in 1-D box is analyzed. Each particle in the box behaves like an independent entity represented by a {\it macro-orbital} (a kind of pair waveform). While the expectation value of their interaction, $$, vanishes for every state of two particles, the expectation value of their relative separation,$$, satisfies $\ge \lambda/2$ (or $q \ge \pi/d$, with $2d = L$ being the size of the box). The particles in their ground state define a close-packed arrangement of their wave packets (with $= \lambda/2$, phase position separation $\Delta\phi = 2\pi$ and momentum $|q_o| = \pi/d$) and experience a mutual repulsive force ({\it zero point repulsion}) $f_o = h^2/2md^3$ which also tries to expand the box. While the relative dynamics of two particles in their excited states represents usual collisional motion, the same in their ground state becomes collisionless. These results have great significance in determining the correct microscopic understanding of widely different many body systems.Comment: 12 pages, no figur

Geodetic precession and frame dragging observed far from massive objects and close to a gyroscope

Total precession (geodetic precession and frame dragging) depends on the velocity of each source of gravitation, which means that it depends on the choice of the coordinate system. We consider the latter as an anomaly specifically in the Gravity Probe B experiment, we investigated it and solved this anomaly. Thus, we proved that if our present expression for the geodetic precession is correct, then the frame dragging should be 25% less than its predicted value.Comment: 11 page

The nuclear Schiff moment and time invariance violation in atoms

Parity and time invariance violating (P,T-odd) nuclear forces produce P,T-odd nuclear moments. In turn, these moments can induce electric dipole moments (EDMs) in atoms through the mixing of electron wavefunctions of opposite parity. The nuclear EDM is screened by atomic electrons. The EDM of an atom with closed electron subshells is induced by the nuclear Schiff moment. Previously the interaction with the Schiff moment has been defined for a point-like nucleus. No problems arise with the calculation of the electron matrix element of this interaction as long as the electrons are considered to be non-relativistic. However, a more realistic model obviously involves a nucleus of finite-size and relativistic electrons. In this work we have calculated the finite nuclear-size and relativistic corrections to the Schiff moment. The relativistic corrections originate from the electron wavefunctions and are incorporated into a ``nuclear'' moment, which we term the local dipole moment. For mercury these corrections amount to about 25%. We have found that the natural generalization of the electrostatic potential of the Schiff moment for a finite-size nucleus corresponds to an electric field distribution which, inside the nucleus, is well approximated as constant and directed along the nuclear spin, and outside the nucleus is zero. Also in this work the plutonium atomic EDM is estimated.Comment: 16 pages, 1 figure, minor misprints correcte

Quantum mechanical virial theorem in systems with translational and rotational symmetry

Generalized virial theorem for quantum mechanical nonrelativistic and relativistic systems with translational and rotational symmetry is derived in the form of the commutator between the generator of dilations G and the Hamiltonian H. If the conditions of translational and rotational symmetry together with the additional conditions of the theorem are satisfied, the matrix elements of the commutator [G, H] are equal to zero on the subspace of the Hilbert space. Normalized simultaneous eigenvectors of the particular set of commuting operators which contains H, J^{2}, J_{z} and additional operators form an orthonormal basis in this subspace. It is expected that the theorem is relevant for a large number of quantum mechanical N-particle systems with translational and rotational symmetry.Comment: 24 pages, accepted for publication in International Journal of Theoretical Physic

Higgs algebraic symmetry of screened system in a spherical geometry

The orbits and the dynamical symmetries for the screened Coulomb potentials and isotropic harmonic oscillators have been studied by Wu and Zeng [Z. B. Wu and J. Y. Zeng, Phys. Rev. A 62,032509 (2000)]. We find the similar properties in the responding systems in a spherical space, whose dynamical symmetries are described by Higgs Algebra. There exists a conserved aphelion and perihelion vector, which, together with angular momentum, constitute the generators of the geometrical symmetry group at the aphelia and perihelia points $(\dot{r}=0)$.Comment: 8 pages, 1 fi

What information can we obtain from the yield ratio π−/π+\pi^-/\pi^+ in heavy-ion collisions ?

The recently reported data on the yield ratio $\pi^-/\pi^+$ in central rapidity region of heavy-ion collisions are analyzed by theoretical formula which accounts for Coulomb interaction between central charged fragment (CCF) consisting of nearly stopped nucleons with effective charge Z_{\mbox{\scriptsize eff}} and charged pions produced in the same region of the phase space. The Coulomb wave function method is used instead of the usual Gamow factor in order to account for the finite production range of pions, $\beta$. For Gaussian shape of the pion production sources it results in a quasi-scaling in $\beta$ and Z_{\mbox{\scriptsize eff}} which makes determination of parameters $\beta$ and Z_{\mbox{\scriptsize eff}} from the existing experimental data difficult. Only sufficiently accurate data taken in the extreme small $m_{\scriptscriptstyle T}$-$m_{\pi}$ region, where this quasi-scaling is broken, could be used for this purpose.Comment: 7 pages, Latex type, 8 figure

Soft-photon corrections in multi-body meson decays

The effects due to soft-photon emission (and the related virtual corrections) in multi-body decays of B, D, and K mesons are analysed. We present analytic expressions for the universal O(alpha) correction factors which can be applied to all multi-body decay modes where a tight soft-photon energy cut in the decaying-particle rest-frame is applied. All-order resummations valid in the limit of small and large velocities of the final-state particles are also discussed. The phenomenological implications of these correction factors in the distortion of Dalitz-plot distributions of K -> 3 pi decays are briefly analysed.Comment: 8 pages, 2 figures (v2: minor modifications - published version

Bound states of neutral particles in external electric fields

Neutral fermions of spin $\frac 12$ with magnetic moment can interact with electromagnetic fields through nonminimal coupling. The Dirac--Pauli equation for such a fermion coupled to a spherically symmetric or central electric field can be reduced to two simultaneous ordinary differential equations by separation of variables in spherical coordinates. For a wide variety of central electric fields, bound-state solutions of critical energy values can be found analytically. The degeneracy of these energy levels turns out to be numerably infinite. This reveals the possibility of condensing infinitely many fermions into a single energy level. For radially constant and radially linear electric fields, the system of ordinary differential equations can be completely solved, and all bound-state solutions are obtained in closed forms. The radially constant field supports scattering solutions as well. For radially linear fields, more energy levels (in addition to the critical one) are infinitely degenerate. The simultaneous presence of central magnetic and electric fields is discussed.Comment: REVTeX, 14 pages, no figur

Searches for violation of fundamental time reversal and space reflection symmetries in solid state experiments

The electric dipole moment (EDM) of a particle violates both time reversal (T) and space reflection (P) symmetries. There have been recent suggestions for searches of the electron EDM using solid state experiments [1,2]. These experiments could improve the sensitivity compared to present atomic and molecular experiments by several orders of magnitude. In the present paper we calculate the expected effect. We also suggest that this kind of experiment is sensitive to T,P-violation in nuclear forces and calculate effects caused by the nuclear Schiff moment. The compounds under consideration contain magnetic Gd$^{3+}$ ions and oxygen O$^{2-}$ ions. We demonstrate that the main mechanism for the T,P-odd effects is related to the penetration of the Oxygen 2p-electrons to the Gd core. All the effects are related to the deformation of the crystal lattice.Comment: 13 pages, 6 figure