Closed-form expressions for correlated density matrices: application to dispersive interactions and example of (He)2

Empirically correlated density matrices of N-electron systems are investigated. Exact closed-form expressions are derived for the one- and two-electron reduced density matrices from a general pairwise correlated wave function. Approximate expressions are proposed which reflect dispersive interactions between closed-shell centro-symmetric subsystems. Said expressions clearly illustrate the consequences of second-order correlation effects on the reduced density matrices. Application is made to a simple example: the (He)2 system. Reduced density matrices are explicitly calculated, correct to second order in correlation, and compared with approximations of independent electrons and independent electron pairs. The models proposed allow for variational calculations of interaction energies and equilibrium distance as well as a clear interpretation of dispersive effects on electron distributions. Both exchange and second order correlation effects are shown to play a critical role on the quality of the results.Comment: 22 page

Pathways to double ionization of atoms in strong fields

We discuss the final stages of double ionization of atoms in a strong linearly polarized laser field within a classical model. We propose that all trajectories leading to non-sequential double ionization pass close to a saddle in phase space which we identify and characterize. The saddle lies in a two degree of freedom subspace of symmetrically escaping electrons. The distribution of longitudinal momenta of ions as calculated within the subspace shows the double hump structure observed in experiments. Including a symmetric bending mode of the electrons allows us to reproduce the transverse ion momenta. We discuss also a path to sequential ionization and show that it does not lead to the observed momentum distributions.Comment: 10 pages, 10 figures; fig.6 and 7 exchanged in the final version accepted for publication in Phys. Rev.

The L_X--M relation of Clusters of Galaxies

We present a new measurement of the scaling relation between X-ray luminosity and total mass for 17,000 galaxy clusters in the maxBCG cluster sample. Stacking sub-samples within fixed ranges of optical richness, N_200, we measure the mean 0.1-2.4 keV X-ray luminosity, , from the ROSAT All-Sky Survey. The mean mass, , is measured from weak gravitational lensing of SDSS background galaxies (Johnston et al. 2007). For 9 <= N_200 < 200, the data are well fit by a power-law, /10^42 h^-2 erg/s = (12.6+1.4-1.3 (stat) +/- 1.6 (sys)) (/10^14 h^-1 M_sun)^1.65+/-0.13. The slope agrees to within 10% with previous estimates based on X-ray selected catalogs, implying that the covariance in L_X and N_200 at fixed halo mass is not large. The luminosity intercent is 30%, or 2\sigma, lower than determined from the X-ray flux-limited sample of Reiprich & Bohringer (2002), assuming hydrostatic equilibrium. This difference could arise from a combination of Malmquist bias and/or systematic error in hydrostatic mass estimates, both of which are expected. The intercept agrees with that derived by Stanek et al. (2006) using a model for the statistical correspondence between clusters and halos in a WMAP3 cosmology with power spectrum normalization sigma_8 = 0.85. Similar exercises applied to future data sets will allow constraints on the covariance among optical and hot gas properties of clusters at fixed mass.Comment: 5 pages, 1 figure, MNRAS accepte

Non-sequential triple ionization in strong fields

We consider the final stage of triple ionization of atoms in a strong linearly polarized laser field. We propose that for intensities below the saturation value for triple ionization the process is dominated by the simultaneous escape of three electrons from a highly excited intermediate complex. We identify within a classical model two pathways to triple ionization, one with a triangular configuration of electrons and one with a more linear one. Both are saddles in phase space. A stability analysis indicates that the triangular configuration has the larger cross sections and should be the dominant one. Trajectory simulations within the dominant symmetry subspace reproduce the experimentally observed distribution of ion momenta parallel to the polarization axis.Comment: 9 pages, 8 figures, accepted for publication in Phys. Rev.

Thermal X-rays from Millisecond Pulsars: Constraining the Fundamental Properties of Neutron Stars

Abridged) We model the X-ray properties of millisecond pulsars (MSPs) by considering hot spot emission from a weakly magnetized rotating neutron star (NS) covered by an optically-thick hydrogen atmosphere. We investigate the limitations of using the thermal X-ray pulse profiles of MSPs to constrain the mass-to-radius ($M/R$) ratio of the underlying NS. The accuracy is strongly dependent on the viewing angle and magnetic inclination. For certain systems, the accuracy is ultimately limited only by photon statistics implying that future X-ray observatories could, in principle, achieve constraints on $M/R$ and hence the NS equation of state to better than $\sim$5%. We demonstrate that valuable information regarding the basic properties of the NS can be extracted even from X-ray data of fairly limited photon statistics through modeling of archival spectroscopic and timing observations of the nearby isolated PSRs J0030+0451 and J2124--3358. The X-ray emission from these pulsars is consistent with the presence of a hydrogen atmosphere and a dipolar magnetic field configuration, in agreement with previous findings for PSR J0437--4715. For both MSPs, the favorable geometry allows us to place interesting limits on the allowed $M/R$ of NSs. Assuming 1.4 M$_{\odot}$, the stellar radius is constrained to be $R > 9.4$ km and $R > 7.8$ km (68% confidence) for PSRs J0030+0451 and J2124--3358, respectively. We explore the prospects of using future observatories such as \textit{Constellation-X} and \textit{XEUS} to conduct blind X-ray timing searches for MSPs not detectable at radio wavelengths due to unfavorable viewing geometry. Using the observational constraints on the pulsar obliquities we are also able to place strong constraints on the magnetic field evolution model proposed by Ruderman.Comment: 9 pages, 7 figures, published in the Astrophysical Journal (Volume 689, Issue 1, pp. 407-415

The Mean and Scatter of the Velocity Dispersion-Optical Richness Relation for maxBCG Galaxy Clusters

The distribution of galaxies in position and velocity around the centers of galaxy clusters encodes important information about cluster mass and structure. Using the maxBCG galaxy cluster catalog identified from imaging data obtained in the Sloan Digital Sky Survey, we study the BCG-galaxy velocity correlation function. By modeling its non-Gaussianity, we measure the mean and scatter in velocity dispersion at fixed richness. The mean velocity dispersion increases from 202+/-10 km/s for small groups to more than 854+/-102 km/s for large clusters. We show the scatter to be at most 40.5+/-3.5%, declining to 14.9+/-9.4% in the richest bins. We test our methods in the C4 cluster catalog, a spectroscopic cluster catalog produced from the Sloan Digital Sky Survey DR2 spectroscopic sample, and in mock galaxy catalogs constructed from N-body simulations. Our methods are robust, measuring the scatter to well within one-sigma of the true value, and the mean to within 10%, in the mock catalogs. By convolving the scatter in velocity dispersion at fixed richness with the observed richness space density function, we measure the velocity dispersion function of the maxBCG galaxy clusters. Although velocity dispersion and richness do not form a true mass-observable relation, the relationship between velocity dispersion and mass is theoretically well characterized and has low scatter. Thus our results provide a key link between theory and observations up to the velocity bias between dark matter and galaxies.Comment: 25 pages, 15 figures, 2 tables, published in Ap

Is pulsar B0656+14 a very nearby RRAT source?

The recently discovered RRAT sources are characterized by very bright radio bursts which, while being periodically related, occur infrequently. We find bursts with the same characteristics for the known pulsar B0656+14. These bursts represent pulses from the bright end of an extended smooth pulse-energy distribution and are shown to be unlike giant pulses, giant micropulses or the pulses of normal pulsars. The extreme peak-fluxes of the brightest of these pulses indicates that PSR B0656+14, were it not so near, could only have been discovered as an RRAT source. Longer observations of the RRATs may reveal that they, like PSR B0656+14, emit weaker emission in addition to the bursts.Comment: 4 pages, 4 figures, accepted by ApJ

Low-temperature ordered phases of the spin-12\frac{1}{2} XXZ chain system Cs2_2CoCl4_4

In this study the magnetic order of the spin-1/2 XXZ chain system Cs$_2$CoCl$_4$ in a temperature range from 50 mK to 0.5 K and in applied magnetic fields up to 3.5 T is investigated by high-resolution measurements of the thermal expansion and the specific heat. Applying magnetic fields along a or c suppresses $T_\textrm{N}$ completely at about 2.1 T. In addition, we find an adjacent intermediate phase before the magnetization saturates close to 2.5 T. For magnetic fields applied along b, a surprisingly rich phase diagram arises. Two additional transitions are observed at critical fields $\mu_0 H_{SF1}\simeq 0.25$ T and $\mu_0 H_{SF2}\simeq 0.7$ T, which we propose to arise from a two-stage spin-flop transition.Comment: 10 pages, 10 figure

Direct measurement of the 14N(p,g)15O S-factor

We have measured the 14N(p,g)15O excitation function for energies in the range E_p = 155--524 keV. Fits of these data using R-matrix theory yield a value for the S-factor at zero energy of 1.64(17) keV b, which is significantly smaller than the result of a previous direct measurement. The corresponding reduction in the stellar reaction rate for 14N(p,g)15O has a number of interesting consequences, including an impact on estimates for the age of the Galaxy derived from globular clusters.Comment: 5 pages, 3 figures, submitted to Phys. Rev. Let

Three-Dimensional Supergravity and the Cosmological Constant

Witten has argued that in $2+1$ dimensions local supersymmetry can ensure the vanishing of the cosmological constant without requiring the equality of bose and fermi masses. We find that this mechanism is implemented in a novel fashion in the (2+1)-dimensional supersymmetric abelian Higgs model coupled to supergravity. The vortex solitons are annihilated by half of the supersymmetry transformations. The covariantly constant spinors required to define these supersymmetries exist by virtue of a surprising cancellation between the Aharonov-Bohm phase and the phase associated with the holonomy of the spin connection. However the other half of the supersymmetry transformations, whose actions ordinarily generate the soliton supermultiplet, are not well-defined and bose-fermi degeneracy is consequently absent in the soliton spectrum.Comment: 12 pages, phyzz