Analytical relationship for the cranking inertia

The wave function of a spheroidal harmonic oscillator without spin-orbit interaction is expressed in terms of associated Laguerre and Hermite polynomials. The pairing gap and Fermi energy are found by solving the BCS system of two equations. Analytical relationships for the matrix elements of inertia are obtained function of the main quantum numbers and potential derivative. They may be used to test complex computer codes one should develop in a realistic approach of the fission dynamics. The results given for the $^{240}$Pu nucleus are compared with a hydrodynamical model. The importance of taking into account the correction term due to the variation of the occupation number is stressed.Comment: 12 pages, 4 figure

Detection and Interpretation Of Long-Lived X-Ray Quasi-Periodic Pulsations in the X-Class Solar Flare On 2013 May 14

Quasi-periodic pulsations (QPP) seen in the time derivative of the GOES soft X-ray light curves are analyzed for the near-limb X3.2 event on 14 May 2013. The pulsations are apparent for a total of at least two hours from the impulsive phase to well into the decay phase, with a total of 163 distinct pulses evident to the naked eye. A wavelet analysis shows that the characteristic time scale of these pulsations increases systematically from $\sim$25 s at 01:10 UT, the time of the GOES peak, to $\sim$100 s at 02:00 UT. A second ridge in the wavelet power spectrum, most likely associated with flaring emission from a different active region, shows an increase from $\sim$40 s at 01:40 UT to $\sim$100 s at 03:10 UT. We assume that the QPP that produced the first ridge result from vertical kink-mode oscillations of the newly formed loops following magnetic reconnection in the coronal current sheet. This allows us to estimate the magnetic field strength as a function of altitude given the density, loop length, and QPP time scale as functions of time determined from the GOES light curves and RHESSI images. The calculated magnetic field strength of the newly formed loops ranges from about $\sim$500 G at an altitude of 24 Mm to a low value of $\sim$10 G at 60 Mm, in general agreement with the expected values at these altitudes. Fast sausage mode oscillations are also discussed and cannot be ruled out as an alternate mechanism for producing the QPP

The Electron Scattering Region in Seyfert Nuclei

The electron scattering region (ESR) is one of important ingredients in Seyfert nuclei because it makes possible to observe the hidden broad line region (hereafter HBLR) in some type 2 Seyfert nuclei (hereafter S2s). However, little is known about its physical and geometrical properties. Using the number ratio of S2s with and without HBLR, we investigate statistically where the ESR is in Seyfert nuclei. Our analysis suggests that the ESR is located at radius between $\sim$ 0.01 pc and $\sim$ 0.1 pc from the central engine. We also discuss a possible origin of the ESR briefly.Comment: 5 pages and 1 figure. The Astrophysical Journal (Letters), in pres

Spatially Resolved Far-Ultraviolet Spectroscopy of the Nuclear Region of NGC 1068

We carry out high-resolution FUSE spectroscopy of the nuclear region of NGC 1068. The first set of spectra was obtained with a 30" square aperture that collects all emission from the narrow-line region. The data reveal a strong broad OVI component of FWHM ~3500 kms-1 and two narrow OVI 1031/1037 components of ~350 kms-1. The CIII 977 and NIII 991 emission lines in this spectrum can be fitted with a narrow component of FWHM ~1000 kms-1 and a broad one of ~2500 kms-1. Another set of seven spatially resolved spectra were made using a long slit of 1.25" X 20", at steps of ~1" along the axis of the emission-line cone. We find that (1) Major emission lines in the FUSE wavelength range consist of a broad and a narrow component; (2) There is a gradient in the velocity field for the narrow OVI component of ~200 kms-1 from ~2" southwest of the nucleus to ~4" northeast. A similar pattern is also observed with the broad OVI component, with a gradient of ~3000 kms-1. These are consistent with the HST/STIS findings and suggest a biconical structure in which the velocity field is mainly radial outflow; (3) A major portion of the CIII and NIII line flux is produced in the compact core. They are therefore not effective temperature diagnostics for the conical region; and (4) The best-fitted UV continuum suggests virtually no reddening, and the HeII 1085/1640 ratio suggests a consistently low extinction factor across the cone.Comment: To appear in the Astrophysical Journal. 37 pages with 12 figure

Generalized Involution Models for Wreath Products

We prove that if a finite group $H$ has a generalized involution model, as defined by Bump and Ginzburg, then the wreath product $H \wr S_n$ also has a generalized involution model. This extends the work of Baddeley concerning involution models for wreath products. As an application, we construct a Gelfand model for wreath products of the form $A \wr S_n$ with $A$ abelian, and give an alternate proof of a recent result due to Adin, Postnikov, and Roichman describing a particularly elegant Gelfand model for the wreath product \ZZ_r \wr S_n. We conclude by discussing some notable properties of this representation and its decomposition into irreducible constituents, proving a conjecture of Adin, Roichman, and Postnikov's.Comment: 29 page

ASCA observations of type-2 Seyfert Galaxies. III. Orientation and X-ray Absorption

We discuss the spectral properties of a sample of type-2 Seyfert galaxies based upon the analysis of \asca data. In this paper we consider the sources for which the X-ray spectra appear to be dominated by the nuclear continuum, transmitted through a large column of absorbing material. We find that both Seyfert-2 galaxies and NELGs show iron K$\alpha$ line profiles indicative of reprocessing of nuclear X-rays in a face-on accretion disk. Such line profiles are also observed in Seyfert-1 galaxies. This result is contrary to unification models, which would predict the inner regions of Seyfert-2 galaxies to be observed edge-on. This raises some questions as to the orientation of the circumnuclear absorber. If the observed differences between Seyfert type-1 and type-2 galaxies, and NELGs are not due to differences in the orientation of the absorbing material, then we suggest that differences in dust composition and grain size, and in the density of the circumnuclear gas could be of primary importance.Comment: 28 pages, 3 figures. LaTeX with encapsulated postscript. To appear in the Astrophysical Journa

Effects of crack tip geometry on dislocation emission and cleavage: A possible path to enhanced ductility

We present a systematic study of the effect of crack blunting on subsequent crack propagation and dislocation emission. We show that the stress intensity factor required to propagate the crack is increased as the crack is blunted by up to thirteen atomic layers, but only by a relatively modest amount for a crack with a sharp 60$^\circ$ corner. The effect of the blunting is far less than would be expected from a smoothly blunted crack; the sharp corners preserve the stress concentration, reducing the effect of the blunting. However, for some material parameters blunting changes the preferred deformation mode from brittle cleavage to dislocation emission. In such materials, the absorption of preexisting dislocations by the crack tip can cause the crack tip to be locally arrested, causing a significant increase in the microscopic toughness of the crack tip. Continuum plasticity models have shown that even a moderate increase in the microscopic toughness can lead to an increase in the macroscopic fracture toughness of the material by several orders of magnitude. We thus propose an atomic-scale mechanism at the crack tip, that ultimately may lead to a high fracture toughness in some materials where a sharp crack would seem to be able to propagate in a brittle manner. Results for blunt cracks loaded in mode II are also presented.Comment: 12 pages, REVTeX using epsfig.sty. 13 PostScript figures. Final version to appear in Phys. Rev. B. Main changes: Discussion slightly shortened, one figure remove