Fully differential cross section

Recently Schulz et aland Fischer et al have had some difficulty in applying the CDW-EIS theory successfully for fully differential cross sections in fast ion-atom collisions at large perturbations. These ionization cross sections are expected to be sensitive to the quality of the target wave function and therefore accurate wave functions are needed to calculate these cross sections. Thus one purpose of this paper is to address this problem theoretically by re-examining the CDW-EIS model and the assumptions on which it is based. We will explore this by employing different potentials to represent the interaction between the ionized electron, projectile ion and residual target ion. For other recent work carried out on fully differential cross sections see and references therein. This discussion is presented in section 4. 

Fully Differential cross sections for highly charged ions... 

The fully differential cross section (FDCS) is given by... 

To conclude we have examined the applicability of the continuum-distorted-wave theory to experiments carried out using the reaction microscopy technique for both doubly differential cross sections for longitudinal electron velocities and fully differential cross sections applied to the single ionization of 3.6 MeV amu on neutral target atoms. For the case of the... 

Figure 19(a) shows the QM simulation of the differential cross-section (DCS) in the HF + D channel, over the same extended energy range as in Fig. 5. The agreement with experiment is seen to be qualitatively reasonable. The forward-backward peaking and direct reaction swathe observed in the experiment also occur in the QM calculation, although the relative magnitudes are not consistent. Thus fully quantitative agreement between QM calculations and experiment in all of the reaction attributes must await further refinements of the PES, and/or a more rigorous treatment of the open-shell character of the F(2P) atom.90...

It is clear that the unmistakable resonance fingerprint provided by a narrow Lorentzian peak in the integral cross section (ICS) will be rare for reactive resonances in a collision experiment. However, a fully resolved scattering experiment provides a wealth of data concerning the reaction dynamics. We expect that the state-to-state differential cross sections (DCS) as functions of energy can be analyzed, using various methods, to reveal the presence of reactive resonances. In the following subsections, we discuss how various collision observables are influenced by existence of a complex intermediate. Many of the resonance detection schemes that have been proposed, such as the use of collision time delay, are purely theoretical in that the observations required are not currently feasible in the laboratory. Nevertheless, these ideas are also discussed since it is useful to have method available... 

The reaction-microscope technique is capable of measuring a fully (sixfold) differential cross section, by detecting the three-dimensional momenta of two particles of opposite charge, viz. the ion and one electron. Such a fully differential measurement was recently accomplished [7]. However, the very first experiments were content with recording the NSDI yield as a function of two momentum components of the ion, one parallel (P ) and one transverse (P ) to the linearly polarized laser field, while the second transverse component (P ,2) was integrated over. In terms of the amplitude (4.1), this corresponds to the momentum distribution... 

More recently we described the calculation of differential cross sections (DCSs) for the CI+H2 reaction.[35] These were used in the interpretation of ongoing crossed molecular beam studies. The rationale for this investigation is that DCSs offer, in principle, a far more detailed probe of the dynamics than the integral cross sections (ICSs). This paper [35] marked the first ever fully quantum mechanical determination of reactive DCSs for a set of coupled ab initio PESs. Because of space constraints, no details of the determination of the DCSs were reported.[35] The goal of the present article is to present, for future reference, these details. 

More information on excitation processes can be gained from measurements of the differential cross section of the elastically or inelastically scattered particles. The phenomena expected in the differential cross sections will be the same as found in the corresponding ion-atom scattering experiments. They have been demonstrated most beautifully in the standard case He+ + Ne which has been studied thoroughly both experimentally and theoretically.97-99100101 102 A fully developed theory exists for the interpretation of differential cross sections in cases where excited states play an important role.10 96 9798... 

Before such measurements were fully developed, the measurements of the angular distribution alone were carried out by Turner et al. [97] in a crossed beam experiment. They studied the differential cross-sections of the reaction + D2 N2D" + D over the laboratory energy range... 

The development of the experimental techniques for the production of slow molecular beams described in Chapter 14 offers the unique possibility of studying state and angle-resolved differential scattering of molecules in the presence of external electromagnetic fields. Molecular beam experiments with Stark decelerated and guided molecular beams can be designed to probe fully state-resolved differential cross-sections (DCSs), which contain detailed information about the collision process. This... 

The reactions H + H2 and F + H2 (and their isotopic variants) have been the benchmark systems in the field of chemical reaction dynamics. For them, fully converged three-dimensional (3D) quantum scattering calculations of state-to-state differential cross sections (DCS) have been performed and accurate comparisons with very detailed experimental observables carried out [3-9]. To date, only for one other neutral three-atom system have the exact (i.e., fully converged) 3D quantum scattering calculations of state-to-state DCS on a reliable ab initio potential energy surface (PES) been carried out, namely, for the prototypical reaction Cl + H2 [10], a system chemical kineticists have been interested in since the time of Max Bodenstein (for a historical overview, see the paper by Truhlar in this volume). However, in contrast to H + H2 and F + H2, no experimental dynamical information is available on Cl + H2. Here we highlight the results of the first dynamical investigation of the Cl + H2 and Cl + D2 reactions by the crossed molecular beam... 

Figure 1 Coherent differential cross section vs. momentom transfer for fully deuterated 1,4-polybutadiene. Squares T = 200 K circles 280 K. Lines are guides to the eyes. The data were taken from Narros, A. ...

Kohguchi H, Suzuki T, Alexander M. (2001) Fully state-resolved differential cross sections for the inelastic scattering of the open-shell NO molecule by Ar. Science 294 832-834. 

The fully rigorous quantum mechanical elastic differential cross section is given by [64]... 

Let us consider how the skin is structured to better understand how this tissue performs some of its vital functions. Consider the cross section of the skin sketched in Fig. 1. This illustration shows the readily distinguishable layers of the skin, from the outside of the skin inwards the 10 pm thin, fully differentiated, devitalized outer epidermal layer called the stratum corneum the 100 pm thin live, cellular epidermis and the 1000 pm thin (1 mm thin) dermis. Note that all the thicknesses specified here are representative only, for the actual thickness of each stratum varies severalfold from place to place on the body. Dispersed... 

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