The role of singletons in S7S^7 compactifications

We derive the isometry irrep content of squashed seven-sphere compactifications of eleven-dimensional supergravity, i.e., the left-squashed ($LS^7$) with ${\mathcal N}=1$ and right-squashed ($RS^7$) with ${\mathcal N}=0$ supersymmetry, in a manner completely independent of the round sphere. Then we compare this result with the spectrum obtained by Higgsing the round sphere spectrum. This way we discover features of the spectra which makes it possible to argue that the only way the round spectrum can be related by a Higgs mechanism to the one of $LS^7$ is if the singletons are included in the round sphere spectrum. For this to work also in the $RS^7$ case it seems that the gravitino of the $LS^7$ spectrum must be replaced by a fermionic singleton present in the $RS^7$ spectrum.Comment: 24 pages including appendix with 12 figure, v2 minor typos correcte

The Low-level Spectrum of the W3W_3 String

We investigate the spectrum of physical states in the $W_3$ string theory, up to level 2 for a multi-scalar string, and up to level 4 for the two-scalar string. The (open) $W_3$ string has a photon as its only massless state. By using screening charges to study the null physical states in the two-scalar $W_3$ string, we are able to learn about the gauge symmetries of the states in the multi-scalar $W_3$ string.Comment: 31 pages, Plain Tex, CTP TAMU-70/92, Goteborg ITP 92-43, Imperial/TP/91-92/22, KCL-TH-92-

Spatially self-similar spherically symmetric perfect-fluid models

Einstein's field equations for spatially self-similar spherically symmetric perfect-fluid models are investigated. The field equations are rewritten as a first-order system of autonomous differential equations. Dimensionless variables are chosen in such a way that the number of equations in the coupled system is reduced as far as possible and so that the reduced phase space becomes compact and regular. The system is subsequently analysed qualitatively with the theory of dynamical systems.Comment: 21 pages, 6 eps-figure

The state space and physical interpretation of self-similar spherically symmetric perfect-fluid models

The purpose of this paper is to further investigate the solution space of self-similar spherically symmetric perfect-fluid models and gain deeper understanding of the physical aspects of these solutions. We achieve this by combining the state space description of the homothetic approach with the use of the physically interesting quantities arising in the comoving approach. We focus on three types of models. First, we consider models that are natural inhomogeneous generalizations of the Friedmann Universe; such models are asymptotically Friedmann in their past and evolve fluctuations in the energy density at later times. Second, we consider so-called quasi-static models. This class includes models that undergo self-similar gravitational collapse and is important for studying the formation of naked singularities. If naked singularities do form, they have profound implications for the predictability of general relativity as a theory. Third, we consider a new class of asymptotically Minkowski self-similar spacetimes, emphasizing that some of them are associated with the self-similar solutions associated with the critical behaviour observed in recent gravitational collapse calculations.Comment: 24 pages, 12 figure

An almost isotropic cosmic microwave temperature does not imply an almost isotropic universe

In this letter we will show that, contrary to what is widely believed, an almost isotropic cosmic microwave background (CMB) temperature does not imply that the universe is ``close to a Friedmann-Lemaitre universe''. There are two important manifestations of anisotropy in the geometry of the universe, (i) the anisotropy in the overall expansion, and (ii) the intrinsic anisotropy of the gravitational field, described by the Weyl curvature tensor, although the former usually receives more attention than the latter in the astrophysical literature. Here we consider a class of spatially homogeneous models for which the anisotropy of the CMB temperature is within the current observational limits but whose Weyl curvature is not negligible, i.e. these models are not close to isotropy even though the CMB temperature is almost isotropic.Comment: 5 pages (AASTeX, aaspp4.sty), submitted to Astrophysical Journal Letter

The effects of deformation and pairing correlations on nuclear charge form factor

A set of moderately deformed $s-d$ shell nuclei is employed for testing the reliability of the nuclear ground state wave functions which are obtained in the context of a BCS approach and offer a simultaneous consideration of deformation and pairing correlations effects. In this method, the mean field is assumed to be an axially symmetric Woods-Saxon potential and the effective two-body interaction is a monopole pairing force. As quantities of main interest we have chosen the nuclear form factors, the occupancies of the active (surface) orbits and the Fermi sea depletion, which provide quite good tests for microscopic descriptions of nuclei within many body theories. For our comparisons with results emerging from other similar methods, an axially deformed harmonic oscillator field is also utilized.Comment: 20 pages, 12 figures, 2 table

Experimental f-value and isotopic structure for the Ni I line blended with [OI] at 6300A

We have measured the oscillator strength of the Ni I line at 6300.34 \AA, which is known to be blended with the forbidden [O I] $\lambda$6300 line, used for determination of the oxygen abundance in cool stars. We give also wavelengths of the two isotopic line components of $^{58}$Ni and $^{60}$Ni derived from the asymmetric laboratory line profile. These two line components of Ni I have to be considered when calculating a line profile of the 6300 \AA\ feature observed in stellar and solar spectra. We also discuss the labelling of the energy levels involved in the Ni I line, as level mixing makes the theoretical predictions uncertain.Comment: Accepted for publication in ApJLetter

Localization and clustering in the nuclear Fermi liquid

Using the framework of nuclear energy density functionals we examine the conditions for single-nucleon localization and formation of cluster structures in finite nuclei. We propose to characterize localization by the ratio of the dispersion of single-nucleon wave functions to the average inter-nucleon distance. This parameter generally increases with mass and describes the gradual transition from a hybrid phase in light nuclei, characterized by the spatial localization of individual nucleon states that leads to the formation of cluster structures, toward the Fermi liquid phase in heavier nuclei. Values of the localization parameter that correspond to a crystal phase cannot occur in finite nuclei. Typical length and energy scales in nuclei allow the formation of liquid drops, clusters, and halo structures.Comment: 6 pages, 3 figure