Exact Solutions of Model Hamiltonian Problems with Effective Interactions

We demonstrate with soluble models how to employ the effective Hamiltonian approach of Lee and Suzuki to obtain all the exact eigenvalues of the full Hamiltonian. We propose a new iteration scheme to obtain the effective Hamiltonian and demonstrate its convergence properties.Comment: 12 pages and 1 figur

Global Properties of fp-Shell Interactions in Many-nucleon Systems

Spectral distribution theory, which can be used to compare microscopic interactions over a broad range of nuclei, is applied in an analysis of two modern effective interactions based on the realistic CD-Bonn potential for $0\hbar\Omega$ no-core shell model calculations in the fp shell, as well as in a comparison of these with the realistic shell-model GXPF1 interaction. In particular, we explore the ability of these interaction to account for the development of isovector pairing correlations and collective rotational motion in the fp shell. Our findings expose the similarities of these two-body interactions, especially as this relates to their pairing and rotational characteristics. Further, the GXPF1 interaction is used to determine the strength parameter of a quadrupole term that can be used to augment an isovector-pairing model interaction with Sp(4) dynamical symmetry, which in turn is shown to yield reasonable agreement with the low-lying energy spectra of $^{58}$Ni and $^{58}$Cu.Comment: 21 pages, 3 figures, accepted in Nuclear Physics

Large-space shell-model calculations for light nuclei

An effective two-body interaction is constructed from a new Reid-like $NN$ potential for a large no-core space consisting of six major shells and is used to generate the shell-model properties for light nuclei from $A$=2 to 6. (For practical reasons, the model space is partially truncated for $A$=6.) Binding energies and other physical observables are calculated and compare favorably with experiment.Comment: prepared using LaTex, 21 manuscript pages, no figure

Gravitational radiation from gamma-ray bursts as observational opportunities for LIGO and VIRGO

Gamma-ray bursts are believed to originate in core-collapse of massive stars. This produces an active nucleus containing a rapidly rotating Kerr black hole surrounded by a uniformly magnetized torus represented by two counter-oriented current rings. We quantify black hole spin-interactions with the torus and charged particles along open magnetic flux-tubes subtended by the event horizon. A major output of Egw=4e53 erg is radiated in gravitational waves of frequency fgw=500 Hz by a quadrupole mass-moment in the torus. Consistent with GRB-SNe, we find (i) Ts=90s (tens of s, Kouveliotou et al. 1993), (ii) aspherical SNe of kinetic energy Esn=2e51 erg (2e51 erg in SN1998bw, Hoeflich et al. 1999) and (iii) GRB-energies Egamma=2e50 erg (3e50erg in Frail et al. 2001). GRB-SNe occur perhaps about once a year within D=100Mpc. Correlating LIGO/Virgo detectors enables searches for nearby events and their spectral closure density 6e-9 around 250Hz in the stochastic background radiation in gravitational waves. At current sensitivity, LIGO-Hanford may place an upper bound around 150MSolar in GRB030329. Detection of Egw thus provides a method for identifying Kerr black holes by calorimetry.Comment: to appear in PRD, 49

A First Search for coincident Gravitational Waves and High Energy Neutrinos using LIGO, Virgo and ANTARES data from 2007

We present the results of the first search for gravitational wave bursts associated with high energy neutrinos. Together, these messengers could reveal new, hidden sources that are not observed by conventional photon astronomy, particularly at high energy. Our search uses neutrinos detected by the underwater neutrino telescope ANTARES in its 5 line configuration during the period January - September 2007, which coincided with the fifth and first science runs of LIGO and Virgo, respectively. The LIGO-Virgo data were analysed for candidate gravitational-wave signals coincident in time and direction with the neutrino events. No significant coincident events were observed. We place limits on the density of joint high energy neutrino - gravitational wave emission events in the local universe, and compare them with densities of merger and core-collapse events.Comment: 19 pages, 8 figures, science summary page at http://www.ligo.org/science/Publication-S5LV_ANTARES/index.php. Public access area to figures, tables at https://dcc.ligo.org/cgi-bin/DocDB/ShowDocument?docid=p120000

Statistical mechanics of two-dimensional vortices and stellar systems

The formation of large-scale vortices is an intriguing phenomenon in two-dimensional turbulence. Such organization is observed in large-scale oceanic or atmospheric flows, and can be reproduced in laboratory experiments and numerical simulations. A general explanation of this organization was first proposed by Onsager (1949) by considering the statistical mechanics for a set of point vortices in two-dimensional hydrodynamics. Similarly, the structure and the organization of stellar systems (globular clusters, elliptical galaxies,...) in astrophysics can be understood by developing a statistical mechanics for a system of particles in gravitational interaction as initiated by Chandrasekhar (1942). These statistical mechanics turn out to be relatively similar and present the same difficulties due to the unshielded long-range nature of the interaction. This analogy concerns not only the equilibrium states, i.e. the formation of large-scale structures, but also the relaxation towards equilibrium and the statistics of fluctuations. We will discuss these analogies in detail and also point out the specificities of each system.Comment: Chapter of the forthcoming "Lecture Notes in Physics" volume: ``Dynamics and Thermodynamics of Systems with Long Range Interactions'', T. Dauxois, S. Ruffo, E. Arimondo, M. Wilkens Eds., Lecture Notes in Physics Vol. 602, Springer (2002