The transformation of irreducible tensor operators under spherical functions

The irreducible tensor operators and their tensor products employing Racah algebra are studied. Transformation procedure of the coordinate system operators act on are introduced. The rotation matrices and their parametrization by the spherical coordinates of vector in the fixed and rotated coordinate systems are determined. A new way of calculation of the irreducible coupled tensor product matrix elements is suggested. As an example, the proposed technique is applied for the matrix element construction for two electrons in a field of a fixed nucleus.Comment: To appear in Int. J. Theor. Phy

Calculation of Effective Coulomb Interaction for Pr3+Pr^{3+}, U4+U^{4+}, and UPt3UPt_3

In this paper, the Slater integrals for a screened Coulomb interaction of the the Yukawa form are calculated and by fitting the Thomas-Fermi wavevector, good agreement is obtained with experiment for the multiplet spectra of $Pr^{3+}$ and $U^{4+}$ ions. Moreover, a predicted multiplet spectrum for the heavy fermion superconductor $UPt_3$ is shown with a calculated Coulomb U of 1.6 eV. These effective Coulomb interactions, which are quite simple to calculate, should be useful inputs to further many-body calculations in correlated electron metals.Comment: 8 pages, revtex, 3 uuencoded postscript figure

Relativistic nuclear recoil corrections to the energy levels of hydrogen-like and high ZZ lithium like atoms in all orders in αZ\alpha Z

The relativistic nuclear recoil corrections to the energy levels of low-laying states of hydrogen-like and high $Z$ lithium-like atoms in all orders in $\alpha Z$ are calculated. The calculations are carried out using the B-spline method for the Dirac equation. For low $Z$ the results of the calculation are in good agreement with the $\alpha Z$ -expansion results. It is found that the nuclear recoil contribution, additional to the Salpeter's one, to the Lamb shift ($n=2$) of hydrogen is $-1.32(6)\,kHz$. The total nuclear recoil correction to the energy of the $(1s)^{2}2p_{\frac{1}{2}}-(1s)^{2}2s$ transition in lithium-like uranium constitutes $-0.07\,eV$ and is largely made up of QED contributions.Comment: 19 pages, latex, accepted for publication in Phys. Rev.

Relativistic transition wavelenghts and probabilities for spectral lines of Ne II

Transition wavelengths and probabilities for several 2p4 3p - 2p4 3s and 2p4 3d - 2p4 3p lines in fuorine-like neon ion (NeII) have been calculated within the multiconfiguration Dirac-Fock (MCDF) method with quantum electrodynamics (QED) corrections. The results are compared with all existing experimental and theoretical data

Early carboniferous brachiopod faunas from the Baoshan block, west Yunnan, southwest China

38 brachiopod species in 27 genera and subgenera are described from the Yudong Formation in the Shidian-Baoshan area, west Yunnan, southwest China. New taxa include two new subgenera: Unispirifer (Septimispirifer) and Brachythyrina (Longathyrina), and seven new species: Eomarginifera yunnanensis, Marginatia cylindrica, Unispirifer (Unispirifer) xiangshanensis, Unispirifer (Septimispirifer) wafangjieensis, Brachythyrina (Brachythyrina) transversa, Brachythyrina (Longathyrina) baoshanensis, and Girtyella wafangjieensis. Based on the described material and constraints from associated coral and conodont faunas, the age of the brachiopod fauna from the Yudon Formation is considered late Tournaisian (Early Carboniferous), with a possibility extending into earlyViseacutean.<br /

The impact of ‘exile’ on thought: Plotinus, Derrida and Gnosticism

This article examines the impact of ‘exile’ – as an individual or collective experience – on how human experience is theorized. The relationship between ‘exile’ and thought is initially approached historically by looking at the period that Eric Dodds famously called the ‘age of anxiety’ in late antiquity, i.e. the period between the emperors Aurelius and Constantine. A particular interest is in the dynamics of ‘empire’ and the concomitant religious ferment as a context in which ‘exile’, both experientially and symbolically, appears to assume an overbearing significance. Plotinus’ narrative of emanation and epistrophe as well as a group of narratives often classified as ‘Gnosticism’ are juxtaposed as two radical examples of a wider spiritual trend at the time according to which ‘exile’ could be considered constitutive of human experience. By way of an historical analogy, the insights gained from this study of late antiquity are then used to guide an analysis of the current, ‘restless’ epoch, in which experiences of displacement and exile on a mass scale undermine traditional notions of belonging, thus reviving the gnostic vision of cosmic reality as an alien, exilic environment. The article concludes with a discussion of Jacques Derrida’s work as an example of contemporary gnosticism, in which a ‘metaphysics of exile’ is presented in the disguise of an ‘exile from metaphysics’

Search for gravitational-wave transients associated with magnetar bursts in advanced LIGO and advanced Virgo data from the third observing run

Gravitational waves are expected to be produced from neutron star oscillations associated with magnetar giant f lares and short bursts. We present the results of a search for short-duration (milliseconds to seconds) and longduration (∼100 s) transient gravitational waves from 13 magnetar short bursts observed during Advanced LIGO, Advanced Virgo, and KAGRA’s third observation run. These 13 bursts come from two magnetars, SGR1935 +2154 and SwiftJ1818.0−1607. We also include three other electromagnetic burst events detected by FermiGBM which were identified as likely coming from one or more magnetars, but they have no association with a known magnetar. No magnetar giant flares were detected during the analysis period. We find no evidence of gravitational waves associated with any of these 16 bursts. We place upper limits on the rms of the integrated incident gravitational-wave strain that reach 3.6 × 10−²³ Hz at 100 Hz for the short-duration search and 1.1 ×10−²² Hz at 450 Hz for the long-duration search. For a ringdown signal at 1590 Hz targeted by the short-duration search the limit is set to 2.3 × 10−²² Hz. Using the estimated distance to each magnetar, we derive upper limits upper limits on the emitted gravitational-wave energy of 1.5 × 1044 erg (1.0 × 1044 erg) for SGR 1935+2154 and 9.4 × 10^43 erg (1.3 × 1044 erg) for Swift J1818.0−1607, for the short-duration (long-duration) search. Assuming isotropic emission of electromagnetic radiation of the burst fluences, we constrain the ratio of gravitational-wave energy to electromagnetic energy for bursts from SGR 1935+2154 with the available fluence information. The lowest of these ratios is 4.5 × 103

A joint Fermi-GBM and Swift-BAT analysis of gravitational-wave candidates from the third gravitational-wave observing run

We present Fermi Gamma-ray Burst Monitor (Fermi-GBM) and Swift Burst Alert Telescope (Swift-BAT) searches for gamma-ray/X-ray counterparts to gravitational-wave (GW) candidate events identified during the third observing run of the Advanced LIGO and Advanced Virgo detectors. Using Fermi-GBM onboard triggers and subthreshold gamma-ray burst (GRB) candidates found in the Fermi-GBM ground analyses, the Targeted Search and the Untargeted Search, we investigate whether there are any coincident GRBs associated with the GWs. We also search the Swift-BAT rate data around the GW times to determine whether a GRB counterpart is present. No counterparts are found. Using both the Fermi-GBM Targeted Search and the Swift-BAT search, we calculate flux upper limits and present joint upper limits on the gamma-ray luminosity of each GW. Given these limits, we constrain theoretical models for the emission of gamma rays from binary black hole mergers

Constraints on the cosmic expansion history from GWTC–3

We use 47 gravitational wave sources from the Third LIGO–Virgo–Kamioka Gravitational Wave Detector Gravitational Wave Transient Catalog (GWTC–3) to estimate the Hubble parameter H(z), including its current value, the Hubble constant H0. Each gravitational wave (GW) signal provides the luminosity distance to the source, and we estimate the corresponding redshift using two methods: the redshifted masses and a galaxy catalog. Using the binary black hole (BBH) redshifted masses, we simultaneously infer the source mass distribution and H(z). The source mass distribution displays a peak around 34 M⊙, followed by a drop-off. Assuming this mass scale does not evolve with the redshift results in a H(z) measurement, yielding ${H}_{0}={68}_{-8}^{+12}\,\mathrm{km}\ \,\ {{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$ (68% credible interval) when combined with the H0 measurement from GW170817 and its electromagnetic counterpart. This represents an improvement of 17% with respect to the H0 estimate from GWTC–1. The second method associates each GW event with its probable host galaxy in the catalog GLADE+, statistically marginalizing over the redshifts of each event's potential hosts. Assuming a fixed BBH population, we estimate a value of ${H}_{0}={68}_{-6}^{+8}\,\mathrm{km}\ \,\ {{\rm{s}}}^{-1}\,{\mathrm{Mpc}}^{-1}$ with the galaxy catalog method, an improvement of 42% with respect to our GWTC–1 result and 20% with respect to recent H0 studies using GWTC–2 events. However, we show that this result is strongly impacted by assumptions about the BBH source mass distribution; the only event which is not strongly impacted by such assumptions (and is thus informative about H0) is the well-localized event GW190814