Some exact analytical results and a semi-empirical formula for single electron ionization induced by ultrarelativistic heavy ions

The delta function gauge of the electromagnetic potential allows semiclassical formulas to be obtained for the probability of exciting a single electron out of the ground state in an ultrarelativistic heavy ion reaction. Exact formulas have been obtained in the limits of zero impact parameter and large, perturbative, impact parameter. The perturbative impact parameter result can be exploited to obtain a semi-empirical cross section formula of the form, sigma = A ln(gamma) + B, for single electron ionization. A and B can be evaluated for any combination of target and projectile, and the resulting simple formula is good at all ultrarelativistic energies. The analytical form of A and B elucidates a result previously found in numerical calculations: scaled ionization cross sections decrease with increasing charge of the nucleus being ionized. The cross section values obtained from the present formula are in good agreement with recent CERN SPS data from a Pb beam on various nuclear targets.Comment: 14 pages, latex, revtex source, no figure

Aspects of Coulomb Dissociation and Interference in Peripheral Nucleus-Nucleus Collisions

Coherent vector meson production in peripheral nucleus-nucleus collisions is discussed. These interactions may occur for impact parameters much larger than the sum of the nuclear radii. Since the vector meson production is always localized to one of the nuclei, the system acts as a two-source interferometer in the transverse plane. By tagging the outgoing nuclei for Coulomb dissociation it is possible to obtain a measure of the impact parameter and thus the source separation in the interferometer. This is of particular interest since the life-time of the vector mesons are generally much shorter than the impact parameters of the collisions.Comment: 10 pages, 4 figures, Presented at the Workshop on Electromagnetic Probes of Fundamental Physics, Erice, Italy, 16-21 October, 200

Two-Photon Interactions with Nuclear Breakup in Relativistic Heavy Ion Collisions

Highly charged relativistic heavy ions have high cross-sections for two-photon interactions. The photon flux is high enough that two-photon interactions may be accompanied by additional photonuclear interactions. Except for the shared impact parameter, these interactions are independent. Additional interactions like mutual Coulomb excitation are of experimental interest, since the neutrons from the nuclear dissociation provide a simple, relatively unbiased trigger. We calculate the cross sections, rapidity, mass and transverse momentum ($p_T)$ distributions for exclusive $\gamma\gamma$ production of mesons and lepton pairs, and for $\gamma\gamma$ reactions accompanied by mutual Coulomb dissociation. The cross-sections for $\gamma\gamma$ interactions accompanied by multiple neutron emission ($XnXn$) and single neutron emission ($1n1n$) are about 1/10 and 1/100 of that for the unaccompanied $\gamma\gamma$ interactions. We discuss the accuracy with which these cross-sections may be calculated. The typical $p_T$ of $\gamma\gamma$ final states is several times smaller than for comparable coherent photonuclear interactions, so $p_T$ may be an effective tool for separating the two classes of interactions.Comment: 17 pages, 12 figure

Coherent Vector Meson Photoproduction with Nuclear Breakup in Relativistic Heavy Ion Collisions

Relativistic heavy ions are copious sources of virtual photons. The large photon flux gives rise to a substantial photonuclear interaction probability at impact parameters where no hadronic interactions can occur. Multiple photonuclear interactions in a single collision are possible. In this letter, we use mutual Coulomb excitation of both nuclei as a tag for moderate impact parameter collisions. We calculate the cross section for coherent vector meson production accompanied by mutual excitation, and show that the median impact parameter is much smaller than for untagged production. The vector meson rapidity and transverse momentum distribution are very different from untagged exclusive vector meson production.Comment: 14 pages, including 4 figure

Microlensing Surveys of M31 in the Wide Field Imaging Era

The Andromeda Galaxy (M31) is the closest large galaxy to the Milky Way, thus it is an important laboratory for studying massive dark objects in galactic halos (MACHOs) by gravitational microlensing. Such studies strongly complement the studies of the Milky Way halo using the the Large and Small Magellanic Clouds. We consider the possibilities for microlensing surveys of M31 using the next generation of wide field imaging telescopes with fields of view in the square degree range. We consider proposals for such imagers both on the ground and in space. For concreteness, we specialize to the SNAP proposal for a space telescope and the LSST proposal for a ground based telescope. We find that a modest space-based survey of 50 visits of one hour each is considerably better than current ground based surveys covering 5 years. Crucially, systematic effects can be considerably better controlled with a space telescope because of both the infrared sensitivity and the angular resolution. To be competitive, 8 meter class wide-field ground based imagers must take exposures of several hundred seconds with several day cadence.Comment: 10 pages, 4 figures, 2 table

Exact Z2Z^2 scaling of pair production in the high-energy limit of heavy-ion collisions

The two-center Dirac equation for an electron in the external electromagnetic field of two colliding heavy ions in the limit in which the ions are moving at the speed of light is exactly solved and nonperturbative amplitudes for free electron-positron pair production are obtained. We find the condition for the applicability of this solution for large but finite collision energy, and use it to explain recent experimental results. The observed scaling of positron yields as the square of the projectile and target charges is a result of an exact cancellation of a nonperturbative charge dependence and holds as well for large coupling. Other observables would be sensitive to nonperturbative phases.Comment: 4 pages, Revtex, no figures, submitted to PR

Process 3 -> 3 and crossing symmetry violation

Using the Sudakov technique we sum the perturbation series for the process $3\to 3$ and obtain the compact analytical expression for the amplitude of this process, which takes into account all possible Coulomb interactions between colliding particles. Compare it with the amplitude of the lepton pair production in heavy ion collision i.e. in the process $2\to 4$, we show that crossing symmetry between this processes holds only if one neglects the interaction of produced pair with ions (i.e. in the approximation $Z_{1,2}\alpha \ll 1$).Comment: LaTeX2e, 10 pages, 5 eps figure

Luminosity Function of Faint Globular Clusters in M87

We present the luminosity function to very faint magnitudes for the globular clusters in M87, based on a 30 orbit \textit{Hubble Space Telescope (HST)} WFPC2 imaging program. The very deep images and corresponding improved false source rejection allow us to probe the mass function further beyond the turnover than has been done before. We compare our luminosity function to those that have been observed in the past, and confirm the similarity of the turnover luminosity between M87 and the Milky Way. We also find with high statistical significance that the M87 luminosity function is broader than that of the Milky Way. We discuss how determining the mass function of the cluster system to low masses can constrain theoretical models of the dynamical evolution of globular cluster systems. Our mass function is consistent with the dependence of mass loss on the initial cluster mass given by classical evaporation, and somewhat inconsistent with newer proposals that have a shallower mass dependence. In addition, the rate of mass loss is consistent with standard evaporation models, and not with the much higher rates proposed by some recent studies of very young cluster systems. We also find that the mass-size relation has very little slope, indicating that there is almost no increase in the size of a cluster with increasing mass.Comment: 22 pages, 5 figures, Accepted for publication in Ap