Secondary threshold laws for multiple ionization of atoms

We propose a physical mechanism that leads to the emergence of secondary threshold laws in processes of multiple ionization of atoms. We argue that the removal of n electrons (n>2) from a many-electron atom may proceed via intermediate resonant states of the corresponding doubly charged ion. For atoms such as rare gases, the density of such resonances in the vicinity of subsequent ionization thresholds is high. As a result, the appearance energies for multiply charged ions are close to these thresholds, while the effective power indices mu in the near-threshold energy dependence of the cross section, sigmaproportional toE(mu), are lower compared to those from the Wannier theory. This provides a possible explanation of the recent experimental results of B. Gstir [Nucl. Instrum. Methods Phys. Res. B 205, 413 (2003)].

Laser-driven proton scaling laws and new paths towards energy increase

The past few years have seen remarkable progress in the development of laser-based particle accelerators. The ability to produce ultrabright beams of multi-megaelectronvolt protons routinely has many potential uses from engineering to medicine, but for this potential to be realized substantial improvements in the performances of these devices must be made. Here we show that in the laser-driven accelerator that has been demonstrated experimentally to produce the highest energy protons, scaling laws derived from fluid models and supported by numerical simulations can be used to accurately describe the acceleration of proton beams for a large range of laser and target parameters. This enables us to evaluate the laser parameters needed to produce high-energy and high-quality proton beams of interest for radiography of dense objects or proton therapy of deep-seated tumours.

A simple model of atomic interactions in noble metals based explicitly on electronic structure

A total energy tight-binding model with a basis of just one s state per atom is introduced. It is argued that this simplest of all tight-binding models provides a surprisingly good description of the structural stability and elastic constants of noble metals. By assuming inverse power scaling laws for the hopping integrals and the repulsive pair potential, it is shown that the density matrix in a perfect primitive crystal is independent of volume, and structural energy differences and equations of state are then derived analytically. The model is most likely to be of use when one wishes to consider explicitly and self-consistently the electronic and atomic structures of a generic metallic system, with the minium of computation expense. The relationship to the free-electron jellium model is described. The applicability of the model to other metals is also considered briefly.

Single-ionization of helium at Ti:sapphire wavelengths: rates and scaling laws

We present a numerical and theoretical study of intense-field single-electron ionization of helium at 390 nm and 780 nm. Accurate ionization rates (over an intensity range of (0.175-34) X10^14 W/ cm^2 at 390 nm, and (0.275 - 14.4) X 10^14 W /cm^2 at 780 nm) are obtained from full-dimensionality integrations of the time-dependent helium-laser Schroedinger equation. We show that the power law of lowest order perturbation theory, modified with a ponderomotive-shifted ionization potential, is capable of modelling the ionization rates over an intensity range that extends up to two orders of magnitude higher than that applicable to perturbation theory alone. Writing the modified perturbation theory in terms of scaled wavelength and intensity variables, we obtain to first approximation a single ionization law for both the 390 nm and 780 nm cases. To model the data in the high intensity limit as well as in the low, a new function is introduced for the rate. This function has, in part, a resemblance to that derived from tunnelling theory but, importantly, retains the correct frequency-dependence and scaling behaviour derived from the perturbative-like models at lower intensities. Comparison with the predictions of classical ADK tunnelling theory confirms that ADK performs poorly in the frequency and intensity domain treated here.

Placing political economy: organising opposition to free trade before the abolition of the Corn Laws

The unfurling of global capitalism – and its attendant effects – has long been fertile intellectual terrain for geographers. But whilst studies of the processes and mechanisms of globalisation undoubtedly assume a talismanic importance in the discipline, geographers, with few exceptions, have left examinations of early economic liberalism to historians. One such critically important episode in the evolution of the liberal economic project was the repeal of the so-called 'Corn Laws' in 1846. Whilst the precise impact of the Manchester-based Anti-Corn Law League (ACLL) continues to be a matter of conjecture, Eric Sheppard has asserted that their particular take on political economy managed to assume a 'truth-like status' and worldwide universality. But the ACLL's campaign represents only one, albeit decisive, stage in the long intellectual and practical struggle between 'protectionists' and the disciples of free trade. Studies of the non-'Manchester' components have tended to focus squarely upon national politics. This paper examines a pivotal attempt in 1838 by Lord Melbourne's Government to experiment with the effective elimination of import duties on fresh fruit. Unlike most agricultural commodities, table fruit was produced in a tightly defined area, thus allowing the Government's experiment to play out, in theory, without national political fallout. Whilst the Government's clandestine actions left little time for a concerted opposition to develop, Kentish fruit growers soon organised. A formidable lobby was forged that drew wide local support yet also evolved beyond the original 'epistemic community'. Whilst the coalition failed in their efforts to reintroduce protective duties, their actions allow us to see how protectionist ideologies and policies were vivified through practices at many different spatial scales and to better understand the complex spatiality of protectionist takes on political economy. Their campaign also changed – at least in the short term – the course of British mercantile policy.