Heavy ion beam lifetimes at relativistic and ultrarelativistic colliders

The effects of higher order corrections in ultra-relativistic nuclear collisions are considered. It is found that higher order contributions are small at low energy, large at intermediate energy and small again at very high energy. An explanation for this effect is given. This means that the Weizsacker-Williams formula is a good approximation to use in calculating cross sections and beam lifetimes at energies relevant to RHIC and LHC.Comment: 10 pages, 2 tables, 4 figure

The Nystrom plus Correction Method for Solving Bound State Equations in Momentum Space

A new method is presented for solving the momentum-space Schrodinger equation with a linear potential. The Lande-subtracted momentum space integral equation can be transformed into a matrix equation by the Nystrom method. The method produces only approximate eigenvalues in the cases of singular potentials such as the linear potential. The eigenvalues generated by the Nystrom method can be improved by calculating the numerical errors and adding the appropriate corrections. The end results are more accurate eigenvalues than those generated by the basis function method. The method is also shown to work for a relativistic equation such as the Thompson equation.Comment: Revtex, 21 pages, 4 tables, to be published in Physical Review

A Quantum-Mechanical Equivalent-Photon Spectrum for Heavy-Ion Physics

In a previous paper, we calculated the fully quantum-mechanical cross section for electromagnetic excitation during peripheral heavy-ion collisions. Here, we examine the sensitivity of that cross section to the detailed structure of the projectile and target nuclei. At the transition energies relevant to nuclear physics, we find the cross section to be weakly dependent on the projectile charge radius, and to be sensitive to only the leading momentum-transfer dependence of the target transition form factors. We exploit these facts to derive a quantum-mechanical ``equivalent-photon spectrum'' valid in the long-wavelength limit. This improved spectrum includes the effects of projectile size, the finite longitudinal momentum transfer required by kinematics, and the response of the target nucleus to the off-shell photon.Comment: 19 pages, 5 figure

CLASS B2108+213: A new wide separation gravitational lens system

We present observations of CLASS B2108+213, the widest separation gravitational lens system discovered by the Cosmic Lens All-Sky Survey. Radio imaging using the VLA at 8.46 GHz and MERLIN at 5 GHz shows two compact components separated by 4.56 arcsec with a faint third component in between which we believe is emission from a lensing galaxy. 5-GHz VLBA observations reveal milliarcsecond-scale structure in the two lensed images that is consistent with gravitational lensing. Optical emission from the two lensed images and two lensing galaxies within the Einstein radius is detected in Hubble Space Telescope imaging. Furthermore, an optical gravitational arc, associated with the strongest lensed component, has been detected. Surrounding the system are a number of faint galaxies which may help explain the wide image separation. A plausible mass distribution model for CLASS B2108+213 is also presented.Comment: 9 pages, 8 figures, accepted for publication in MNRA

Another exact inflationary solution

A new closed-form inflationary solution is given for a hyperbolic interaction potential. The method used to arrive at this solution is outlined as it appears possible to generate additional sets of equations which satisfy the model. In addition a new form of decaying cosmological constant is presented.Comment: 10 pages, 0 figure

The new two-image gravitational lens system CLASS B2319+051

We report the discovery of a new two-image gravitational lens system from the Cosmic Lens All-Sky Survey, CLASS B2319+051. Radio imaging with the Very Large Array (VLA) and Multi-Element Radio-Linked Interferometer Network (MERLIN) shows two compact components with a flux density ratio of 5:1, separated by 1.36 arcsec. Observations with the Very Long Baseline Array (VLBA) resolve each of the radio components into a pair of parity-reversed subcomponents. Hubble Space Telescope (HST) observations with the Near-Infrared Camera and Multi-Object Spectrometer (NICMOS) show a bright elliptical galaxy (G1) coincident with the radio position, and a second irregular galaxy (G2) 3.4 arcsec to the northwest. Previous spectroscopic studies have indicated that these galaxies are at different redshifts: z(G1) = 0.624, z(G2) = 0.588. Infrared counterparts to the lensed radio components are not detected in the NICMOS image, and the source redshift has not yet been determined. Preliminary mass modeling based on the VLBA subcomponent data indicates that the lensing potential includes a strong external shear contribution. A VLA monitoring program is currently being undertaken to measure the differential time delay.Comment: 16 pages, 7 figs, several typos corrected, AJ in press (August 2001

B0850+054: a new gravitational lens system from CLASS

We report the discovery of a new gravitational lens system from the CLASS survey. Radio observations with the VLA, the WSRT and MERLIN show that the radio source B0850+054 is comprised of two compact components with identical spectra, a separation of 0.7 arcsec and a flux density ratio of 6:1. VLBA observations at 5 GHz reveal structures that are consistent with the gravitational lens hypothesis. The brighter of the two images is resolved into a linear string of at least six sub-components whilst the weaker image is radially stretched towards the lens galaxy. UKIRT K-band imaging detects an 18.7 mag extended object, but the resolution of the observations is not sufficient to resolve the lensed images and the lens galaxy. Mass modelling has not been possible with the present data and the acquisition of high-resolution optical data is a priority for this system.Comment: 5 pages, 4 figures, accepted for publication in MNRA

A New Quadruple Gravitational Lens System: CLASS B0128+437

High resolution MERLIN observations of a newly-discovered four-image gravitational lens system, B0128+437, are presented. The system was found after a careful re-analysis of the entire CLASS dataset. The MERLIN observations resolve four components in a characteristic quadruple-image configuration; the maximum image separation is 542 mas and the total flux density is 48 mJy at 5 GHz. A best-fit lens model with a singular isothermal ellipsoid results in large errors in the image positions. A significantly improved fit is obtained after the addition of a shear component, suggesting that the lensing system is more complex and may consist of multiple deflectors. The integrated radio spectrum of the background source indicates that it is a GigaHertz-Peaked Spectrum (GPS) source. It may therefore be possible to resolve structure within the radio images with deep VLBI observations and thus better constrain the lensing mass distribution.Comment: Accepted for publication in MNRAS. 4 pages, 3 included PostScript figure

Desingularization of vortices for the Euler equation

We study the existence of stationary classical solutions of the incompressible Euler equation in the plane that approximate singular stationnary solutions of this equation. The construction is performed by studying the asymptotics of equation -\eps^2 \Delta u^\eps=(u^\eps-q-\frac{\kappa}{2\pi} \log \frac{1}{\eps})_+^p with Dirichlet boundary conditions and $q$ a given function. We also study the desingularization of pairs of vortices by minimal energy nodal solutions and the desingularization of rotating vortices.Comment: 40 page

Disentangling Baryons and Dark Matter in the Spiral Gravitational Lens B1933+503

Measuring the relative mass contributions of luminous and dark matter in spiral galaxies is important for understanding their formation and evolution. The combination of a galaxy rotation curve and strong lensing is a powerful way to break the disk-halo degeneracy that is inherent in each of the methods individually. We present an analysis of the 10-image radio spiral lens B1933+503 at z_l=0.755, incorporating (1) new global VLBI observations, (2) new adaptive-optics assisted K-band imaging, (3) new spectroscopic observations for the lens galaxy rotation curve and the source redshift. We construct a three-dimensionally axisymmetric mass distribution with 3 components: an exponential profile for the disk, a point mass for the bulge, and an NFW profile for the halo. The mass model is simultaneously fitted to the kinematics and the lensing data. The NFW halo needs to be oblate with a flattening of a/c=0.33^{+0.07}_{-0.05} to be consistent with the radio data. This suggests that baryons are effective at making the halos oblate near the center. The lensing and kinematics analysis probe the inner ~10 kpc of the galaxy, and we obtain a lower limit on the halo scale radius of 16 kpc (95% CI). The dark matter mass fraction inside a sphere with a radius of 2.2 disk scale lengths is f_{DM,2.2}=0.43^{+0.10}_{-0.09}. The contribution of the disk to the total circular velocity at 2.2 disk scale lengths is 0.76^{+0.05}_{-0.06}, suggesting that the disk is marginally submaximal. The stellar mass of the disk from our modeling is log_{10}(M_{*}/M_{sun}) = 11.06^{+0.09}_{-0.11} assuming that the cold gas contributes ~20% to the total disk mass. In comparison to the stellar masses estimated from stellar population synthesis models, the stellar initial mass function of Chabrier is preferred to that of Salpeter by a probability factor of 7.2.Comment: 16 pages, 13 figures, minor revisions based on referee's comments, accepted for publication in Ap