engleski

ASYMPTOTIC FOURIER TRANSFORM APPROACH TO HIGH ENERGY PHOTOEFFECT IN MOLECULES: EXAMPLE OF FIXED IN SPACE H$_{; ; 2}; ; ^{; ; +}; ; $.

The theoretical description of high energy photoeffect processes requires in general a good description of the bound and continuum states of the system. It is now understood \cite{;suric03}; that in helium-like systems, and for high photon energies $\omega$, the wave functions must be sufficiently accurate in the vicinity of the coalescence points (i.e. when two of the charged particles, an electron and nucleus or two electrons, are close to each other), in order to obtain accurately the leading contributions to the total cross section for ionization with or without excitations, and the spectrum for double ionization. This has been discussed for different gauges \cite{;suric03, suric04}; using a generalized asymptotic Fourier transform approach (AFT), which connects the high energy photoabsorption matrix elements with the behavior of the wave functions and interaction operator in the vicinity of the singularities, i.e the points where wave functions and opperators are not differentiable. Coalescence points are such singularities. In the AFT approach the vicinities of singularities of the exact wave functions are described in terms of simpler functions and remainders. The simpler functions allow analytic calculation while the remainders determine the order (characterized in powers of $1/\sqrt{;\omega};$) of the neglected terms. We apply the AFT approach for the description of high energy photoeffect from molecules. Initially we consider single ionization, and our goal is to understand the behavior of the wave functions in the vicinity of nuclei, and to find simpler functions (both for initial and final states) which are sufficient for an accuracy of matrix elements neglecting terms O($1/\omega$). The often used simple description of Cohen and Fano \cite{;cohen66}; for the total cross section does not achieve such an accuracy. As a first step we study the system of one electron moving in the field of two fixed Coulombic centers with charges Z=1. This system, often called fixed in space H$_{;2};^{;+};$, can be treated exactly, and it also serves as a model of a diatomic molecule in situations when the Born-Oppenheimer molecular model is applicable, as in the case of high energy photoionization. For such a system we study the quality of simplified wave functions and remainders in the vicinity of nuclei, by direct comparison with the exact wave functions and by comparison of the cross sections obtained with exact wave functions and with simplified wave functions, for various orientations of the molecular axes with respect to photon polarization. We also discuss interference effects due to the coherent ionization from the two centers. The interference effects are most easily observed in ratios of molecular and atomic cross sections, or in the ratios of molecular cross sections for different orientations of the diatomic molecule with respect to photon polarization. The simplified model of Cohen and Fano provides only a rough qualitative description of the interference effects in the ratios, failing to predict the positions of maxima and minima as well as the average positions of the ratios. We discuss this simplified model from the point of view of the AFT approach. We compare our results with the results of other studies

Fourier transform; photoabsorption; high energy

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