Inverse problem in the theory of many-centre shape resonances

Migal, Yu. F.

doi:10.1088/0953-4075/27/8/012

Cited by 14 publications

(3 citation statements)

References 8 publications

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“…In general case the selection of such peaks from all peaks in XANES can be a difficult problem. Methods of the selection of the peaks are described in Migal (1994). The situation is simple if previously a direct problem calculation within the MT approach for a given object was performed (it can be done by means of available codes), and an accordance between experimental and calculated peaks was settled.…”

Section: Methodsmentioning

confidence: 99%

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Determination of parameters of valence states by using XANES

Migal

Kovaleva

2001

J Synchrotron Radiat

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A new approach for the parametrization of valence states of atoms in molecules and solids, facilitating the deciphering of experimental XANES spectra, is proposed. It is shown that energies and halfwidths of XANES maxima of the one-electron origin depend mainly on the arrangement of atoms and energies and mean radii of atomic valence states. Just these quantities having distinct physical meaning must be determined above all from experiment. A procedure for such a determination is developed. Values of energies and mean radii of the nitrogen and oxygen atoms in some molecules are obtained. Keywords: XANES, valence states ProblemOur aim is to investigate valence states of separate atoms in manyatom systems. Such systems can be molecules, free or adsorbed, solid clusters and so on. This problem is a part of the more general question which we try to examine (Migal, 1994): what information about objects under consideration is contained in XANES and how to extract this information.Analysing XANES we choose peaks of the one-electron origin. As usual such peaks are the most distinctive details of spectra. They correspond to the transition of the photoelectron to both unoccupied collective states of the discrete spectrum and so called shape resonances. The latter are one-electron quasi-stationary states with small positive energies. We consider only such peaks which correspond to states localized or quasi-localized within many-atom systems (i.e., the Rydberg series is excepted). Position and form of these peaks essentially depend on arrangements and types of atoms, magnetic microstructure, the presence and nature of defects, the distribution of electric charge, etc. This fact allows us, in principle, to obtain structure information by analysing characteristics of the peaks. However, unfortunately, general methods for extracting this information are still not developed.Before considering concrete questions about atomic valence states we would like to make three general remarks. Firstly, an amount of information coded in XANES is essentially greater than in EXAFS. It is caused by the fact that in the case of XANES the photoelectron, moving through a many-atom system with a comparatively small speed, interacts with the system for much longer time than in the case of EXAFS. Due to that, by using XANES it is possible to obtain, along with geometric parameters of the system, also parameters of the potential V(r) describing the interaction between the photoelectron and the system. Secondly, since position and form of peaks in XANES depend on a lot of factors, in order to extract information from XANES one must solve a many-parameter inverse problem. In a number of works, where for deciphering structure information from XANES

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Section: Methodsmentioning

confidence: 99%

“…Such systems can be molecules, free or adsorbed, solid clusters and so on. This problem is a part of the more general question which we try to examine (Migal, 1994): what information about objects under consideration is contained in XANES and how to extract this information.…”

Section: Problemmentioning

confidence: 99%

Determination of parameters of valence states by using XANES

Migal

Kovaleva

2001

J Synchrotron Radiat

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show abstract

“…Previously it has been shown that the scheme is steady with respect to geometric parameters as the input data E j and G j change a little [4]. Buth with respect to the MT potential construction the scheme can be not steady if there are some coefficients b n for the same atom.…”

Section: Scheme Of Inverse Problem Solutionmentioning

confidence: 99%