Quantum impact-parameter method

When colliding particles are heavy and their interactions are long range, the impact parameter method conveniently describes the problem (9, 10, 32, 57). This method is based on the concept that the motion of nucleus is described classically and that of electrons is described quantum mechanically. If the angular momentum of colliding system is larger than K, the trajectory of an incident or a scattered particle can be defined. The impact parameter method will be useful where the total scattering is determined mainly by these processes. 

To obtain the reaction attributes for a particular set of vibrational, rotational and translational energies, many trajectories were simulated at given values of N2 vibrational and rotational quantum numbers and N2-O relative translational energy. The N2 molecular orientation, vibrational phase and impact parameter were chosen randomly for each trajectory. The reaction attributes were then determined by averaging the outcomes of all collisions. The information obtained is state-specific, so for example, the energy distributions of the reactant and product molecules can be determined. The method used to calculate the vibrational and rotational state of the product molecule is outlined in Ref. 67. With the QCT approach, reaction cross sections were determined solely from the precollision state. The method knows nothing of the fluid flow environment and so... 

Coupled channel methods for colllnear quantum reactive calculations are sufficiently well developed that calculations can be performed routinely. Unfortunately, colllnear calculations cannot provide any Insight Into the angular distribution of reaction products, because the Impact parameter dependence of reaction probabilities Is undefined. On the other hand, the best approximate 3D methods for atom-molecule reactions are computationally very Intensive, and for this reason. It Is Impractical to use most 3D approximate methods to make a systematic study of the effects of potential surfaces on resonances, and therefore the effects of surfaces on reactive angular distributions. For this reason, we have become Interested In an approximate model of reaction dynamics which was proposed many years ago by Child (24), Connor and Child (25), and Wyatt (26). They proposed the Rotating Linear Model (RLM), which Is In some sense a 3D theory of reactions, because the line upon which reaction occurs Is allowed to tumble freely In space. A full three-dimensional theory would treat motion of the six coordinates (In the center of mass) associated with the two... 

From a very general point of view every ion-atom collision system has to be treated as a correlated many-body time-dependent quantum system. To solve this from an ab initio point of view is still impossible. So, one has to rely on various approximations. Nowadays the best method which can be applied to realistic collision systems (which we discuss here) is on the level of the non-selfconsistent time-dependent Hartree-Fock-Slater or, in the relativistic case, the Dirac-Fock-Slater method. Up-to-now no correlation beyond this approximation can be taken into account in the case of 3 or more electrons. (This is in accordance with the definition of correlation given by Lowdin [1] in 1956) In addition no QED contributions, i.e. no correction to the 1/r Coulomb interaction between the electrons, ever have been taken into account, although in very heavy collision systems this effect may become important. This will be discussed in section 5. A short survey of the theory used is followed by our results on impact parameter dependent electron transfer and excitation calculations of ion-atom and ion-solid collisions as well as first results of an ab initio calculation of MO X-rays in such complicated many particle scattering systems. 

The paper [8] includes results of investigating electron mechanisms of the impact of active particles, radicals, hydrated electrons artificially generated by plasma on the behavior of cyanide complexes of zinc in water solutions. The above investigation was conducted using quantum chemistry methods. Quantum-chemical calculation of electron structure of the complexes Zn(CN)42 4EP-20H- with complete optimization of all geometric parameters [9] was performed. 

A very important contribution to the knowledge of the sensitivity of explosives to impact has been given by Delpuech and Cherville [45]. They came to the conclusion that the basic criterion of sensitivity of explosives lies in the distribution of electrons in their ground state and the comparison with that in the excited state. With the advent of quantum mechanical methods, and particularly (hat of l.N.D.O. [46] they were able to calculate the distribution of electrons in explosives, thus introducing a new and original criterion of sensitivity of explosives. For quantitative estimation they introduced a parameter AC //,... 

Density functional theory (DFT) is today a very powerful tool in the study of electronic structures of molecules. Advancements in DFT, in particular the development of Becke s 3-parameter functional (B3LYP), together with the nearly exponential growth of computer power, have made it possible to treat ever larger systems at a reasonable level of accuracy. Using the B3LYP with a medium-sized basis set, one can routinely handle systems containing more than 100 atoms today, a development that has opened the door for many applications. One of the fields that quantum chemical methods have had very positive impacts on in recent years is the study of enzymatic reaction mechanisms. 

While new applications of the electron-photon coincidence method, such as zero field quantum beats, will continue the full analysis of the experimental results is complex. The determination of parameters, such as the spin orbit phase parameters e and A, which allow specific dynamical features of theoretical models to be tested will take on a greater significance. For heavy atoms this is of particular significance since there is only limited theoretical results available and effects, such as spin orbit interaction, must be taken into account. Perhaps also the "ultimate" electron impact experiments are starting where polarised electrons are used as the projectile in coincidence experiments. 

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