An exactly solvable four transition point model

Heavy particle collisions, in particular low-energy ion-atom collisions, are amenable to semiclassical JWKB phase integral analysis in the complex plane of the internuclear separation. Analytic continuation in this plane requires due attention to the Stokes phenomenon which parametrizes the physical mechanisms of curve crossing, non-crossing, the hybrid Nikitin model, rotational coupling and predissociation. Complex transition points represent adiabatic degeneracies. In the case of two or more such points, the Stokes constants may only be completely determined by resort to the so-called comparison- equation method involving, in particular, parabolic cylinder functions or Whittaker functions and their strong-coupling asymptotics. In particular, the Nikitin model is a two transition-point one-double-pole problem in each half-plane corresponding to either ingoing or outgoing waves. When the four transition points are closely clustered, new techniques are required to determine Stokes constants. However, such investigations remain incomplete, A model problem is therefore solved exactly for scattering along a one-dimensional z-axis. The energy eigenvalue is b(2)-a(2) and the potential comprises -z(2)/2 (parabolic) and -a(2) + b(2)/2z(2) (centrifugal/centripetal) components. The square of the wavenumber has in the complex z-plane, four zeros each a transition point at z = +/-a +/- ib and has a double pole at z = 0. In cases (a) and (b), a and b are real and unitarity obtains. In case (a) the reflection and transition coefficients are parametrized by exponentials when a(2) + b(2) > 1/2. In case (b) they are parametrized by trigonometrics when a(2) + b(2) <1/2 and total reflection is achievable. In case (c) a and b are complex and in general unitarity is not achieved due to loss of flux to a continuum (O'Rourke and Crothers, 1992 Proc. R. Sec. 438 1). Nevertheless, case (c) coefficients reduce to (a) or (b) under appropriate limiting conditions. Setting z = ht, with h a real constant, an attempt is made to model a two-state collision problem modelled by a pair of coupled first-order impact parameter equations and an appropriate (T) over tilde-tau relation, where (T) over tilde is the Stueckelberg variable and tau is the reduced or scaled time. The attempt fails because (T) over tilde is an odd function of tau, which is unphysical in a real collision problem. However, it is pointed out that by applying the Kummer exponential model to each half-plane (O'Rourke and Crothers 1994 J. Phys. B: At. Mel. Opt. Phys. 27 2497) the current model is in effect extended to a collision problem with four transition points and a double pole in each half-plane. Moreover, the attempt in itself is not a complete failure since it is shown that the result is a perfect diabatic inelastic collision for a traceless Hamiltonian matrix, or at least when both diagonal elements are odd and the off-diagonal elements equal and even.

Magnetomechanical interplay in spin-polarized point contacts

We investigate the interplay between magnetic and structural dynamics in ferromagnetic atomic point contacts. In particular, we look at the effect of the atomic relaxation on the energy barrier for magnetic domain wall migration and, reversely, at the effect of the magnetic state on the mechanical forces and structural relaxation. We observe changes of the barrier height due to the atomic relaxation up to 200%, suggesting a very strong coupling between the structural and the magnetic degrees of freedom. The reverse interplay is weak; i.e., the magnetic state has little effect on the structural relaxation at equilibrium or under nonequilibrium, current-carrying conditions.

Neutral and Charged 1-Butyl-3-methylimidazolium Triflate Clusters: Equilibrium Concentration in the Vapor Phase and Thermal Properties of Nanometric Droplets

Ground state energy, structure, and harmonic vibrational modes of 1-butyl-3-methylimidazolium triflate ([bmim][Tf]) clusters have been computed using an all-atom empirical potential model. Neutral and charged species have been considered up to a size (30 [bmim][Tf] pairs) well into the nanometric range. Free energy computations and thermodynamic modeling have been used to predict the equilibrium composition of the vapor phase as a function of temperature and density. The results point to a nonnegligible concentration of very small charged species at pressures (P ~ 0.01 Pa) and temperatures (T 600 K) at the boundary of the stability range of [bmim][Tf]. Thermal properties of nanometric neutral droplets have been investigated in the 0 T 700 K range. A near-continuous transition between a liquidlike phase at high T and a solidlike phase at low T takes place at T ~ 190 K in close correspondence with the bulk glass point Tg ~ 200 K. Solidification is accompanied by a transition in the dielectric properties of the droplet, giving rise to a small permanent dipole embedded into the solid cluster. The simulation results highlight the molecular precursors of several macroscopic properties and phenomena and point to the close competition of Coulomb and dispersion forces as their common origin.

Conformations, vibrational frequencies and Raman intensities of short-chain fatty acid methyl esters using DFT with 6-31G(d) and Sadlej pVTZ basis sets

Density functional calculations, using B3LPY/6-31G(d) methods, have been used to investigate the conformations and vibrational (Raman) spectra of three short-chain fatty acid methyl esters (FAMEs) with the formula CnH2nO2 (n = 3-5). In all three FAMEs, the lowest energy conformer has a simple 'all-trans' structure but there are other conformers, with different torsions about the backbone, which lie reasonably close in energy to the global minimum. One result of this is that the solid samples we studied do not appear to consist entirely of the lowest energy conformer. Indeed, to account for the 'extra' bands that were observed in the Raman data but were not predicted for the all-trans conformer, it was necessary to add-in contributions from other conformers before a complete set of vibrational assignments could be made. Provided this was done, the agreement between experimental Raman frequencies and 6-31G(d) values (after scaling) was excellent, RSD = 12.6 cm(-1). However, the agreement between predicted and observed intensities was much less satisfactory. To confirm the validity of the approach followed by the 6-3 1 G(d) basis set, we used a larger basis set, Sadlej pVTZ, and found that these calculations gave accurate Raman intensities and simulated spectra (summed from two different conformers) that were in quantitative agreement with experiment. In addition, the unscaled Sadlej pVTZ, and the scaled 6-3 1 G(d) calculations gave the same vibrational mode assignments for all bands in the experimental data. This work provides the foundation for calculations on longer-chain FAMEs (which are closer to those found as triglycerides in edible fats and oils) because it shows that scaled 6-3 1 G(d) calculations give equally accurate frequency predictions, and the same vibrational mode assignments, as the much more CPU-expensive Sadlej pVTZ basis set calculations.

Variability in thermal and UV-B energy fluxes through time and their influence on plant diversity and speciation

Throughout Earth's history there have been temporal and spatial variations in the amount of visible and ultraviolet radiation received by ecosystems. This paper examines if temporal changes in these forms of energy receipt could have influenced the tempo and mode of plant diversity and speciation, focusing in particular upon Cenozoic time-scales. Evidence for changing patterns of plant diversity and speciation apparent in various fossil records and molecular phylogenies are considered alongside calculated changes in thermal and solar ultraviolet energy (specifically UV-B) over the past 50 Myr. We suggest that changes in thermal energy influx (amount and variability) affected the tempo of evolution through its influence upon community dynamics (e.g. population size, diversity, turnover, extinctions). It was not only the amount of thermal energy but also variability in its flux that may have influenced these processes, and ultimately the rate of diversification. We suggest that variations in UV-B would have influenced the mode and tempo of speciation through changes to genome stability during intervals of elevated UV-B. We argue, therefore, that although variability in thermal energy and UV-B fluxes through time may lead to the same end-point (changing the rate of diversification), the processes responsible are very different and both need to be considered when linking evolutionary processes to energy flux.

Low-energy electron attachment to chloroform (CHCl3) molecules: A joint experimental and theoretical study

Results from a joint experimental and theoretical study of electron attachment to chloroform (CHCl3) molecules in the gas phase are reported. In an electron swarm study involving a pulsed Townsend technique with equal gas and electron temperatures, accurate attachment rate coefficients were determined over the temperature range 295-373 K; they show an Arrhenius-type rise with increasing temperature, corresponding to an activation energy of 0.11 (1) eV. In a high resolution electron beam experiment involving two versions of the laser photoelectron attachment method, the relative cross section for Cl- formation from CHCl3 over the energy range 0.001-1.25 eV at the gas temperature T-G = 300 K was measured. It exhibits clear downward cusp structure at the threshold for excitation of one quantum of the vibrational symmetric deformation mode nu(3), indicating that this mode is active in the primary attachment process. With reference to our thermal attachment rate coefficient k(T = 300 K) = 3.9(2) x 10(-9) cm(3) s(-1), a new highly resolved absolute attachment cross section for T-G = 300 K was determined. This cross section is extended to higher energies by measurements, carried out with a pulsed electron beam apparatus which also provided new data for the distinctly weaker fragment anions HCl2- and CCl2-. The resulting total absolute cross section for anion formation is used to calculate the dependence of the attachment rate coefficient k(T-e;T-G) on electron temperature T-e over the range 50-15000 K at the fixed gas temperature T-G = 300 K. In addition, we report the dependence of the relative cross section for Cl- formation on gas temperature T-G = 310-435 K). For comparison with the experimental data, R-matrix calculations have been carried out for the dominant anion channel Cl-. The results recover the main experimental observations and predict the dependence of the DEA cross section on the initial vibrational level nu(3) and on the vibrational temperature. Our results are compared with those of previous electron beam and electron swarm experiments.

Resting energy expenditure in non-ventilated, non-sedated patients recovering from serious traumatic brain injury: Comparison of prediction equations with indirect calorimetry values

Background & aims: Little is known about energy requirements in brain injured (TBI) patients, despite evidence suggesting adequate nutritional support can improve clinical outcomes. The study aim was to compare predicted energy requirements with measured resting energy expenditure (REE) values, in patients recovering from TBI.

Methods: Indirect calorimetry (IC) was used to measure REE in 45 patients with TBI. Predicted energy requirements were determined using FAO/WHO/UNU and Harris–Benedict (HB) equations. Bland– Altman and regression analysis were used for analysis.

Results: One-hundred and sixty-seven successful measurements were recorded in patients with TBI. At an individual level, both equations predicted REE poorly. The mean of the differences of standardised areas of measured REE and FAO/WHO/UNU was near zero (9 kcal) but the variation in both directions was substantial (range 591 to þ573 kcal). Similarly, the differences of areas of measured REE and HB demonstrated a mean of 1.9 kcal and range 568 to þ571 kcal. Glasgow coma score, patient status, weight and body temperature were signi?cant predictors of measured REE (p < 0.001; R²⁼ 0.47).

Conclusions: Clinical equations are poor predictors of measured REE in patients with TBI. The variability in REE is substantial. Clinicians should be aware of the limitations of prediction equations when estimating energy requirements in TBI patients.

Lowest energy potentials of Li2 + F accessible at ultracold temperatures

Ab initio calculations for the strongly exoergic Li2+F harpoon reaction are presented using density-functional theory, complete active space self-consistent field, and multireference configuration interaction methods to argue that this reaction would be an ideal candidate for investigation with ultracold molecules. The lowest six states are calculated with the aug-correlation-consistent polarized valence triple-zeta basis set and at least two can be accessed by a ground rovibronic Li2 molecule with zero collision energy at all reaction geometries. The large reactive cross section (characteristic of harpoon reactions) and chemiluminescent products are additional attractive features of these reactions.

Track displacement and energy loss in a railway embankment

The mainline railway track between Dublin and Belfast was constructed during the 1850s, with substantial lengths of railway embankment constructed over soft, peaty soils. In recent years Northern Ireland Railways (NIR) has noticed that the sections of the railway track constructed on these peaty soils have been deteriorating at an increasing rate. Train speeds have been reduced in response to concerns that cyclic track displacements appear to be increasing over time in response to train loading. Track maintenance has also increased significantly. The research described in this paper was undertaken to quantify the response to cyclic train loading of two portions of this track founded on peaty soils. Track displacements were recorded using a sensor system specifically created for this project. The sensor consisted of a photosensitive array, mounted on the sleepers, and a laser, which was targeted onto the photosensitive array from a location outside the area of influence of train loading. Track deflections from 5 to 20 mm were measured under train speeds from near zero to over 120 km/h. The temporal variation in track displacement was used to calibrate an analytical (Winkler) model. This analysis suggests that the deformation of the embankment under train loading was not due to dynamic excitation but rather to static deformation of the poor-quality fill and soft foundation materials. As a consequence, the analytical model highlighted that train speed has limited effect on the magnitude of the deflection of the embankment within NIR operating speeds, but has the potential to significantly reduce the power lost to the damping within the embankment and subgrade.

Positron annihilation in large polyatomic molecules. The role of vibrational Feshbach resonances and binding

We analyse the process of rapid positron annihilation in large polyatomic molecules due to positron capture into vibrational Feshbach resonances. Resonant annihilation occurs in molecules which can bind positrons, and we analyse positron binding to alkanes using zero-range potentials. Related questions of spectra of annihilation gamma quanta and molecular fragmentation following annihilation, are discussed briefly.

Low-energy positron interactions with atoms and molecules

This paper is a review of low-energy positron interactions with atoms and molecules. Processes of interest include elastic scattering, electronic and vibrational excitation, ionization, positronium formation and annihilation. An overview is presented of the currently available theoretical and experimental techniques to study these phenomena, including the use of trap-based positron beam sources to study collision processes with improved energy resolution. State-resolved measurements of electronic and vibrational excitation cross sections and measurement of annihilation rates in atoms and molecules as a function of incident positron energy are discussed. Where data are available, comparisons are made with analogous electron scattering cross sections. Resonance phenomena, common in electron scattering, appear to be less common in positron scattering. Possible exceptions include the sharp onsets of positron-impact electronic and vibrational excitation of selected molecules. Recent energy-resolved studies of positron annihilation in hydrocarbons containing more than a few carbon atoms provide direct evidence that vibrational Feshbach resonances underpin the anomalously large annihilation rates observed for many polyatomic species. We discuss open questions regarding this process in larger molecules, as well as positron annihilation in smaller molecules where the theoretical picture is less clear.

Application of the zero-range potential model to positron annihilation on molecules

In this paper we use a zero-range potential (ZRP) method to model positron interaction with molecules. This allows us to investigate the e?ect of molecular vibrations on positron–molecule annihilation using the van der Waals dimer Kr2 as an example. We also use the ZRP to explore positron binding to polyatomics and examine the dependence of the binding energy on the size of the molecule for alkanes. We ?nd that a second bound state appears for a molecule with ten carbons, similar to recent experimental evidence for such a state emerging in alkanes with twelve carbons.

Comparison of positron-impact vibrational excitation cross sections with the Born-dipole model

The development of cold trap-based positron beams and new scattering techniques has recently enabled the ?rst measurements of state-resolved positron-impact vibrational excitation cross sections. These measurements revealed a number of features worth further consideration, such as relatively sharp increases near threshold. This paper describes a comparison of the magnitudes and shapes of these cross sections with the predictions of the Born-dipole model. Agreement of the magnitudes of the cross sections varies widely, ranging from reasonable to excellent agreement for CO2 and CF4 to poor agreement for CO and CH4. In contrast, the energy dependence of these cross sections in all these cases is close to that predicted by the Born model.

The role of vibrational doorway states in positron annihilation with large molecules

Positron annihilation rates in many polyatomic molecular gases are anomalously high. Qualitatively, this can be explained by positron capture in vibrational Feshbach resonances, which can occur for molecules with positive positron a?nities [Gribakin, Phys. Rev. A 61 (2000) 022720]. To verify this idea quantitatively, we examine the densities of vibrational excitation spectra of alkanes. To understand the energy dependence of the annihilation rates for alkanes, we propose that positron capture is mediated by vibrational doorway states, in which positron binding is accompanied by the excitation of fundamentals.

Low-Energy Electron Attachment to the Dichlorodifluoromethane (CCl2F2) Molecule

Results from a joint experimental study of electron attachment to dichlorodifluoromethane (CCl2F2) molecules in the gas phase are reported. In a high resolution electron beam experiment involving two versions of the laser photoelectron attachment method, the relative cross section for formation of the dominant anion Cl- wits measured over the energy range 0.001-1.8 eV at the gas temperature T-G = 300 K. It exhibits cusp structure at thresholds for vibrational excitation of the v(3)(a(1)) mode due to interaction with the attachment channels. With reference to the thermal attachment rate coefficient k(T-e;T-G = 300 K) = 2.2(8) x 10(-9) cm(-3) s(-1) (fitted average from several data), a new highly resolved absolute attachment cross section for TG = 300 K was determined. Partial cross sections for formation of the anions Cl-, Cl-2(-), F-, ClF-, and CCl2F- were measured over the range 0-12 eV, using three different electron beam experiments of medium energy resolution. The dependence of the attachment rate coefficient k(T-e;T-G = 300 K) on electron temperature T-e wits calculated over the range 50-15 000 K, based on a newly constructed total cross section for anion formation at T-G = 300 K. R-matrix Calculations for Cl- production have been carried out for comparison with the experimental data. The R-matrix results are in line with the main experimental observations and predict the dependence of the DEA cross section on the initial vibrational level v(3) and on the vibrational temperature. Furthermore, the cross section for I Vibrational excitation of the v(3) mode hits been computed.