Observing electron motion in solids
We describe an experimental technique that allows for the direct determination of the motion (i.e., the momentum) of electrons in atoms, molecules, and solids. This ({ital e},2{ital e}) technique centers on a fast electron`s ejecting a second electron from a target. Precise spectroscopy of both electrons` final energies and momenta provides very significant information on the second electron`s initial state. Decades of past ({ital e},2{ital e}) studies on single-molecule states have now progressed into studies of condensed matter. The interpretation of these experiments is mediated in this colloquium by analysis of intermediate models in the form of chainlike molecules.

title: Analytic distorted waves for intermediate-energy alpha particles

title: A high-resolution electron momentum spectroscopy and density functional theory study into the complete valence electronic structure of allene
abstract: A study of the electronic structure of the complete valence shell of allene (1,2-propadiene) is reported. New high-resolution binding-energy spectra were measured in the energy regime 6–34.5 eV over a range of different target electron momenta, so that momentum distributions (MDs) could be determined for each molecular orbital. These data supersede the low-resolution work of Braidwood et al. [ (1994) 2075–2087], and also clarify some ambiguities with the earlier results. Theoretical MDs were calculated using a plane wave impulse approximation (PWIA) model for the reaction mechanism and density functional theory (DFT) for the wave function. Three basis sets, at the local spin density (LSD) approximation level and, additionally, incorporating nonlocal corrections such as the generalized gradient approximation (GGA), were studied. A critical comparison between the experimental and theoretical MDs was made, and it allowed us to determine the “optimum” wave function for allene from the basis sets we considered. This wave function is then used to derive allene's chemically interesting molecular properties. A summary of some of these results and a comparison of them with those of other workers is also presented with the level of agreement typically being good.

title: Off-shell effects in the (p, 2p) reaction
abstract: It is shown that, within the limitations of the distorted-wave off-shell impulse approximation, future accurate (p, 2p) experiments near 150 MeV incident energy can be helpful in distinguishing between some of six phenomenological nuclear potentials that are examined. On-shell differences between the Reid soft-core and five different one-boson-exchange potentials are amplified in the (p, 2p) context in such a way that an accurately measurable feature, the peak height ratio for 1p knockout, is sensitive to them.

title: Theory of (p,2p) reactions at medium energies
abstract: A new and effective means of calculating matrix elements relevant to direct interactions is introduced and applied to a distorted-wave t matrix approximation analysis of the /sup 12/C(p,2p9/sup 11/B and /sup 16/O(p,2p)/sup 15/N reactions at 45-50 MeV incident energy. A realistic separable two-body t matrix has been employed and core polarization, whereby the final state is generated after excitation of giant resonance target states, has been included. The integrals involved in the matrix elements were calculated analytically by making a parametrization of the distorted scattering wave functions, the nucleon-nucleon interaction, and the bound state wave function, the parameters being chosen in accordance with elastic (p,p) and inelastic (p,p') data and realistic shell model wave functions. The results indicate the inadequacy of a distorted-wave t-matrix approximation analysis at these energies.

title: Time-Dependent Scattering Experiment
abstract: Theory is developed for a time-dependenit scatternng experiment that consists in following the time development of a photon wave packet scattered resonantly from the metastable state of an appropriate nucleus.

title: Modelling shock heating in cluster mergers – I. Moving beyond the spherical accretion model
abstract: The thermal history of the intracluster medium (ICM) is complex. Heat input from cluster mergers, from active galactic nuclei (AGN) and from winds in galaxies offsets and may even prevent the cooling of the ICM. Consequently, the processes that set the temperature and density structure of the ICM play a key role in determining how galaxies form. In this paper, we focus on the heating of the ICM during cluster mergers, with the eventual aim of incorporating this mechanism into semi-analytic models for galaxy formation. 
 
 
 
We generate and examine a suite of non-radiative hydrodynamic simulations of mergers in which the initial temperature and density structure of the systems are set using realistic scaling laws. Our collisions cover a range of mass ratios and impact parameters, and consider both systems composed entirely of gas (these reduce the physical processes involved), and systems comprising a realistic mixture of gas and dark matter. We find that the heating of the ICM can be understood relatively simply by considering evolution of the gas entropy during the mergers. The increase in this quantity in our simulations closely corresponds to that predicted from scaling relations based on the increase in cluster mass. 
 
 
 
We examine the physical processes that succeed in generating the entropy in order to understand why previous analytical approaches failed. We find the following. (i) The energy that is thermalized during the collision greatly exceeds the kinetic energy available when the systems first touch. The smaller system penetrates deep into the gravitational potential before it is disrupted. (ii) For systems with a large mass ratio, most of the energy is thermalized in the massive component. The heating of the smaller system is minor and its gas sinks to the centre of the final system. This contrasts with spherically symmetric analytical models in which accreted material is simply added to the outer radius of the system. (iii) The bulk of the entropy generation occurs in two distinct episodes. The first episode occurs following the collision of the cores, when a large shock wave is generated that propagates outwards from the centre. This causes the combined system to expand rapidly and overshoot hydrostatic equilibrium. The second entropy generation episode occurs as this material is shock heated as it recollapses. Both heating processes play an important role, contributing approximately equally to the final entropy. This revised model for entropy generation improves our physical understanding of cosmological gas simulations.

title: On the origin of cores in simulated galaxy clusters
abstract: The diffuse plasma that fills galaxy groups and clusters (the intracluster medium) is a by-product of galaxy formation. The present thermal state of this gas results from a competition between gas cooling and heating. The heating comes from two distinct sources: gravitational heating associated with the collapse of the dark matter halo and additional thermal input from the formation of galaxies and their black holes. A long-term goal of this research is to decode the observed temperature, density and entropy profiles of clusters and to understand the relative roles of these processes. However, a long-standing problem has been that cosmological simulations based on smoothed particle hydrodynamics (SPH) and Eulerian mesh-based codes predict different results even when cooling and galaxy/black hole heating are switched off. Clusters formed in SPH simulations show near power-law entropy profiles, while those formed in Eulerian simulations develop a core and do not allow gas to reach such low entropies. Since the cooling rate is closely connected to the minimum entropy of the gas distribution, the differences are of potentially key importance. 
 
In this paper, we investigate the origin of this discrepancy. By comparing simulations run using the GADGET-2 SPH code and the FLASH adaptive Eulerian mesh code, we show that the discrepancy arises during the idealized merger of two clusters and that the differences are not the result of the lower effective resolution of Eulerian cosmological simulations. The difference is not sensitive to the minimum mesh size (in Eulerian codes) or the number of particles used (in SPH codes). We investigate whether the difference is the result of the different gravity solvers, the Galilean non-invariance of the mesh code or an effect of unsuitable artificial viscosity in the SPH code. Instead, we find that the difference is inherent to the treatment of vortices in the two codes. Particles in the SPH simulations retain a close connection to their initial entropy, while this connection is much weaker in the mesh simulations. The origin of this difference lies in the treatment of eddies and fluid instabilities. These are suppressed in the SPH simulations, while the cluster mergers generate strong vortices in the Eulerian simulations that very efficiently mix the fluid and erase the low-entropy gas. We discuss the potentially profound implications of these results.

title: Entropy Generation in Merging Galaxy Clusters
abstract: In McCarthy et al. (2007, astro-) we present an analysis of entropy generation during cluster mergers, using SPH simulations. This conference proceeding contribution summarizes some of the most important findings of that paper, without all the technical details. Our main result is that during cluster mergers, entropy is generated in two major shock episodes, that heat the gas from the inside-out, in a way that distributes most of the energy within the more massive clump. This is different from the "onion-skin" model adopted in many simple analytic models of cluster formation.

title: Ram pressure stripping the hot gaseous haloes of galaxies in groups and clusters
abstract: We use a large suite of carefully controlled full hydrodynamic simulations to study the ram pressure stripping of the hot gaseous haloes of galaxies as they fall into massive groups and clusters. The sensitivity of the results to the orbit, total galaxy mass, and galaxy structural properties is explored. For typical structural and orbital parameters, we find that ∼30 per cent of the initial hot galactic halo gas can remain in place after 10 Gyr. We propose a physically simple analytic model that describes the stripping seen in the simulations remarkably well. The model is analogous to the original formulation of Gunn & Gott, except that it is appropriate for the case of a spherical (hot) gas distribution (as opposed to a face-on cold disc) and takes into account that stripping is not instantaneous but occurs on a characteristic time-scale. The model reproduces the results of the simulations to within ≈10 per cent at almost all times for all the orbits, mass ratios, and galaxy structural properties we have explored. The one exception involves unlikely systems where the orbit of the galaxy is highly non-radial and its mass exceeds about 10 per cent of the group or cluster into which it is falling (in which case the model underpredicts the stripping following pericentric passage). The proposed model has several interesting applications, including modelling the ram pressure stripping of both observed and cosmologically simulated galaxies and as a way to improve present semi-analytic models of galaxy formation. One immediate consequence is that the colours and morphologies of satellite galaxies in groups and clusters will differ significantly from those predicted with the standard assumption of complete stripping of the hot coronae.

title: The impact of mergers on relaxed X-ray clusters – I. Dynamical evolution and emergent transient structures
abstract: We report on the analysis of a suite of smoothed particle hydrodynamics simulations (incorporating cooling and star formation) of mergers involving idealized X-ray clusters whose initial conditions resemble relaxed clusters with cool compact cores observed by Chandra and XMM. The simulations sample the most-interesting, theoretically plausible, range of impact parameters and progenitor mass ratios. We find that all mergers evolve via a common progression. We illustrate this progression in the projected gas density, X-ray surface brightness, Sunyaev-Zel'dovich, temperature, and gas-entropy maps. Several different classes of transient 'cold front' like features can arise over the course of a merger. Each class is distinguished by a distinct morphological signature and physical cause. We find that all these classes are present in Chandra and XMM observations of merging systems and propose a naming scheme for these features: 'comet-like' tails, bridges, plumes, streams and edges. In none of the cases considered do the initial cool compact cores of the primary and the secondary get destroyed during the course of the mergers. Instead, the two remnant cores eventually combine to form a new core that, depending on the final mass of the remnant, can have a greater cooling efficiency than either of its progenitors. We quantify the evolving morphology of our mergers using centroid variance, power ratios and offset between the X-ray and the projected mass maps. We find that the centroid variance best captures the dynamical state of the cluster. It also provides an excellent indicator of how far the system is from virial and hydrostatic equilibrium. Placing the system at z = 0.1, we find that all easily identified observable traces of the secondary disappear from a simulated 50-ks Chandra image following the second pericentric passage. The system, however, takes an additional ∼2 Gyr to relax and virialize. Observationally, the only reliable indicator of a system in this state is the smoothness of its X-ray surface brightness isophotes, not temperature fluctuations. Temperature fluctuations at the level of AT/T ∼20 per cent, can persist in the final systems well past the point of virialization, suggesting that the existence of temperature fluctuations, in and of themselves, does not necessarily indicate a disturbed or unrelaxed system.