Cosmological gravitomagnetism and Mach's principle

The spin axes of gyroscopes experimentally define local non-rotating frames. But what physical cause governs the time-evolution of gyroscope axes? We consider linear perturbations of Friedmann-Robertson-Walker cosmologies with k=0. We ask: Will cosmological vorticity perturbations exactly drag the spin axes of gyroscopes relative to the directions of geodesics to quasars in the asymptotic unperturbed FRW space? Using Cartan's formalism with local orthonormal bases we cast the laws of linear cosmological gravitomagnetism into a form showing the close correspondence with the laws of ordinary magnetism. Our results, valid for any equation of state for cosmological matter, are: 1) The dragging of a gyroscope axis by rotational perturbations of matter beyond the Hubble-dot radius from the gyroscope is exponentially suppressed, where dot is the derivative with respect to cosmic time. 2) If the perturbation of matter is a homogeneous rotation inside some radius around a gyroscope, then exact dragging of the gyroscope axis by the rotational perturbation is reached exponentially fast as the rotation radius grows beyond the H-dot radius. 3) For the most general linear cosmological perturbations the time-evolution of all gyroscope spin axes exactly follow a weighted average of the energy currents of cosmological matter. The weight function is the same as in Ampere's law except that the inverse square law is replaced by the Yukawa force with the Hubble-dot cutoff. Our results demonstrate (in first order perturbation theory for FRW cosmologies with k = 0) the validity of Mach's hypothesis that axes of local non-rotating frames precisely follow an average of the motion of cosmic matter.Comment: 18 pages, 1 figure. Comments and references adde

Enhanced time response of 1-in. LaBr3(Ce) crystals by leading edge and constant fraction techniques

We have characterized in depth the time response of three detectors equipped with cylindrical LaBr$_{3}$ (Ce) crystals with dimensions of 1-in. in height and 1-in. in diameter, and having nominal Ce doping concentration of 5%, 8% and 10%. Measurements were performed at $^{60}$Co and $^{22}$Na {\gamma}-ray energies against a fast BaF$_{2}$ reference detector. The time resolution was optimized by the choice of the photomultiplier bias voltage and the fine tuning of the parameters of the constant fraction discriminator, namely the zero-crossing and the external delay. We report here on the optimal time resolution of the three crystals. It is observed that timing properties are influenced by the amount of Ce doping and the crystal homogeneity. For the crystal with 8% of Ce doping the use of the ORTEC 935 CFD at very shorts delays in addition to the Hamamatsu R9779 PMT has made it possible to improve the LaBr$_{3}$(Ce) time resolution from the best literature value at 60Co photon energies to below 100 ps.Comment: Article submitted to Nuclear Instruments and Methods in Physics Research Section A: Accelerators, Spectrometers, Detectors and Associated Equipmen

Search for octupole correlations in 147^{147}Nd

Properties of excited states in $^{147}$Nd have been studied with multispectra and $\gamma \gamma$ coincidence measurements. Twenty-four new $\gamma$-lines and three new levels have been introduced into the level scheme of $^{147}$Nd. Lifetimes of eight excited levels in $^{147}$Nd, populated in the $\beta$ decay of $^{147}$Pr, have been measured using the advanced time-delayed $\beta\gamma\gamma$(t) method. Reduced transition probabilities have been determined for 30 $\gamma$-transitions in $^{147}$Nd. Potential energy surfaces on the ($\beta_{2}$,$\beta_{3}$) plane calculated for $^{147}$Nd using the Strutinsky method predict two single quasiparticle configurations with nonzero octupole deformation, with K=1/2 and K=5/2. We do not observe parity doublet bands with K=5/2. For pair of opposite parity bands that could form the K=1/2 parity doublet we were able only to determine lower limit of the dipole moment, $|D_0|\geq$0.02 e$\cdot fm$.Comment: Submitted to PR

On the stability of self-gravitating accreting flows

Analytic methods show stability of the stationary accretion of test fluids but they are inconclusive in the case of self-gravitating stationary flows. We investigate numerically stability of those stationary flows onto compact objects that are transonic and rich in gas. In all studied examples solutions appear stable. Numerical investigation suggests also that the analogy between sonic and event horizons holds for small perturbations of compact support but fails in the case of finite perturbations.Comment: 10 pages, accepted for publication in PR

A Quasi-Spherical Gravitational Wave Solution in Kaluza-Klein Theory

An exact solution of the source-free Kaluza-Klein field equations is presented. It is a 5D generalization of the Robinson-Trautman quasi-spherical gravitational wave with a cosmological constant. The properties of the 5D solution are briefly described.Comment: 10 pages Latex, Revtex, submitted to GR

Mach's principle: Exact frame-dragging via gravitomagnetism in perturbed Friedmann-Robertson-Walker universes with K=(±1,0)K = (\pm 1, 0)

We show that the dragging of the axis directions of local inertial frames by a weighted average of the energy currents in the universe is exact for all linear perturbations of any Friedmann-Robertson-Walker (FRW) universe with K = (+1, -1, 0) and of Einstein's static closed universe. This includes FRW universes which are arbitrarily close to the Milne Universe, which is empty, and to the de Sitter universe. Hence the postulate formulated by E. Mach about the physical cause for the time-evolution of the axis directions of inertial frames is shown to hold in cosmological General Relativity for linear perturbations. The time-evolution of axis directions of local inertial frames (relative to given local fiducial axes) is given experimentally by the precession angular velocity of gyroscopes, which in turn is given by the operational definition of the gravitomagnetic field. The gravitomagnetic field is caused by cosmological energy currents via the momentum constraint. This equation for cosmological gravitomagnetism is analogous to Ampere's law, but it holds also for time-dependent situtations. In the solution for an open universe the 1/r^2-force of Ampere is replaced by a Yukawa force which is of identical form for FRW backgrounds with $K = (-1, 0).$ The scale of the exponential cutoff is the H-dot radius, where H is the Hubble rate, and dot is the derivative with respect to cosmic time. Analogous results hold for energy currents in a closed FRW universe, K = +1, and in Einstein's closed static universe.Comment: 23 pages, no figures. Final published version. Additional material in Secs. I.A, I.J, III, V.H. Additional reference

Multi-variable translation equation which arises from homothety

In many regular cases, there exists a (properly defined) limit of iterations of a function in several real variables, and this limit satisfies the functional equation (1-z)f(x)=f(f(xz)(1-z)/z); here z is a scalar and x is a vector. This is a special case of a well-known translation equation. In this paper we present a complete solution to this functional equation in case f is a continuous function on a single point compactification of a 2-dimensional real vector space. It appears that, up to conjugation by a homogeneous continuous function, there are exactly four solutions. Further, in a 1-dimensional case we present a solution with no regularity assumptions on f.Comment: 15 page

On the difference between proton and neutron spin-orbit splittings in nuclei

The latest experimental data on nuclei at $^{132}$Sn permit us for the first time to determine the spin-orbit splittings of neutrons and protons in identical orbits in this neutron-rich doubly-magic region and compare the case to that of $^{208}$Pb. Using the new results, which are now consistent for the two neutron-rich doubly magic regions, a theoretical analysis defines the isotopic dependence of the mean field spin-orbit potential and leads to a simple explicit expression for the difference between the spin-orbit splittings of neutrons and protons. The isotopic dependence is explained in the framework of different theoretical approaches.Comment: 8 pages, revte

Nuclear structure of Ac-231

The low-energy structure of 231Ac has been investigated by means of gamma ray spectroscopy following the beta-decay of 231Ra. Multipolarities of 28 transitions have been established by measuring conversion electrons with a mini-orange electron spectrometer. The decay scheme of 231Ra --> 231Ac has been constructed for the first time. The Advanced Time Delayed beta-gamma-gamma(t) method has been used to measure the half-lives of five levels. The moderately fast B(E1) transition rates derived suggest that the octupole effects, albeit weak, are still present in this exotic nucleus