1,582 research outputs found

    2020 USF Open Educational Resources Grant Report

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    Please find attached my final report from my $1000 2020 USF Open Educational Resources (OER) Grant. Although COVID-19 delayed the submission of this report, the global pandemic has also made open access materials even more essential to supporting student’s access at USF. I am appreciative of the funding to facilitate this project. Throughout this process, I was able to ensure that the materials/readings I was offering to students for free did not violate copyright laws and open my eyes to resources that I did not know were available. Based on the findings of my analysis, my course readings have been updated to maximize OER and ensure that student have equal education access

    Solutions of the Two-State Potential-Curve-Crossing Problem

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    A general theory of the two-state curve-crossing problem has been developed, with a complete solution of an accurate model for close crossings (including numerical computations for strong coupling). Results clarify the position of the Landau-Zener approximation and its improvements by Nikitin and others, provide a general way of extending these approximations into regions often treated incorrectly (including the high-energy limit), and can be readily adapted to simple, rapid calculations

    Diabatic and Adiabatic Representations for Atomic Collision Processes

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    ABSTRACT A consistent general definition of diabatic representations has not previously been given, even though many practical examples of such representations have been constructed for specific problems. Such a definition is provided in this paper. Beginning with a classical trajectory formulation, we describe the form and behavior of velocity‐dependent couplings in slow collisions, including the effects of electron‐translation factors (ETF’s). We compare the couplings arising from atomic representations and atomic ETF’s with those arising from molecular representations and ’’switching function’’ ETF’s. We show that a unique set of switching functions makes the two descriptions identical in their effects. We then show that an acceptable general definition of a diabatic representation is provided by the condition P+A=0, where P is the usual nonadiabatic coupling matrix and A represents corrections to it arising from electron translation factors (ETF’s). Two distinct types of diabatic representation result, depending on the definition taken for A. States that undergo no deformation are called F diabatic; those that have no velocity‐dependent couplings are called M diabatic. Finally, we discuss the properties of representations that are partially diabatic and partially adiabatic, and we give some rules for the construction of representations that should be nearly optimal for describing many types of collision processes

    Semiclassical Theory of Inelastic Collisions II. Momentum Space Formulation

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    The time-dependent equations of the classical picture of inelastic collisions (classical-trajectory equations) are derived using the momentum-space semiclassical approximation. Thereby it is shown that the classical-trajectory equations remain valid in the vicinity of classical turning points provided that (a) the momentum-space semiclassical approximation is valid, (b) the trajectories for elastic scattering in the various internal states differ only slightly, and (c) the slopes of the elastic scattering potentials have the same sign. A brief review of the existing derivations of the classical-trajectory equations is given, and the general conditions for their validity are discussed

    Theory of Near-Adiabatic Collisions. II. Scattering Coordinate Method

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    A rigorously correct and fully quantum-mechanical theory of slow atomic collisions is presented, which removes the formal defects and spurious nonadiabatic couplings of perturbed-stationary-states theory, and arrives at coupled equations for the heavy-particle motion which are the same as those obtained in the preceding paper by the electron translation factor formulation. Here, however, the theory is formulated in terms of suitably defined scattering coordinates, and electron translation factors do not appear. A unified physical interpretation of both approaches can thereby be made, and smaller terms in the coupled equations, describing corrections of order mΌ to electronic binding energies and to the collision kinetic energy, are placed on a firmer footing. Particular attention is paid to the critical test case of isotopic systems such as HD+ and it is shown how a correct theory of isotopic charge exchange can be formulated

    Studies of the Potential Curve Crossing Problem II. General Theory and a Model for Close Crossings

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    A unified formal treatment of the two-state potential-curve-crossing problem in atomic collision theory is presented, and the case of close crossings analyzed in detail. A complete solution for this case, including necessary computations, is given using a suitable generalization of the linear model originally suggested by Landau, Zener, and Stueckelberg. Our solution is based upon a hierarchy of approximations concerned with (i) choice of a discrete basis set for electronic coordinates, (ii) semiclassical treatment of the nuclear motion, (iii) an appropriate model for the two-state electronic Hamiltonian, and (iv) a complete solution to that model

    Theory of Near-Adiabatic Collisions. I. Electron-Translation-Factor Method

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    The theory of near-adiabatic collisions is formulated in a fully quantum-mechanical form, correctly taking into account the role of electron translation factors (ETF\u27s). A general form for the ETF, using switching functions, is given for systems which are electrically either asymmetric or symmetric (with or without mass asymmetry). The main result is that the close-coupled scattering equations obtained in the perturbed-stationary-states theory must be replaced by equations of identical form, but having modified nonadiabatic coupling matrices. In general, the corrections involved are substantial; their nature, and effect on coupling matrices, is discussed, and conditions when they are likely to be important are described. The remaining problem of determining the switching function is discussed briefly. The correct form for ETF\u27s, their quantum-mechanical formulation, and the resulting correct form for the coupled equations, have not been given previously

    Semiclassical Theory of Inelastic Collisions I. Classical Picture and Semiclassical

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    This series of papers is concerned with the derivation of the equations of the classical picture of atomic collisions, iℏddtdi(t)=Σjhij(t)dj(t), which describe the time dependence of electronic-quantum-state amplitudes as the nuclei move along a classical trajectory. These equations are derived in two ways. In the first formulation, which coincides with the intuitive classical picture of the collision, the nuclear part of the wave function is treated as a superposition of narrow wave packets, each traveling along a classical trajectory. In the second formulation, a semiclassical approach is used. The validity and meaning of the two formulations are discussed and compared
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