I. General Formalism BY Yu. A. BABANOV (a), V. V. VASIN (b), A. L. AGEEV (b), and N. V. ERSHOV (a)It is shown that the problem of determining the function of radial atomic distribution around an absorbing atom by oscillations of the X-ray absorption coefficient belongs to a family of incorrect problems. A regularization algorithm is proposed for the problem concerned. Computational schemes realized involving the use of computers are described. Some results of model calculations are given.Es wird gezeigt, daB das Problem der Bestimmung der radialen atomaren Verteilungsfunktion urn ein absorbierendes Atom durch Oszillationen des Rontgenabsorptionskoeffizienten zur Familie der inkorrekten Probleme gehort. Ein Regulierungsalgorithmus wird fur das betrachtete Problem vorgeschlagen. Realisierte Berechnungsschemata, die die Benutzung von Computern einschlielen, werden beschrieben. Einige Ergebnisse von Modellberechnungen werden mitgeteilt.
The errors in the initial EXAFS data are simulated numerically. The comparative sensitivity of the regular methods and of the Fourier transformation method to these errors is analyzed. The theoretically calculated normalized oscillating part of the absorption coefficient X(k) for polycrystalline copper a t T = 77.4 K is compared with the experimental spectrum obtained with the use of a synchrotron facility. The spectrum involved is processed using regular methods.
Theresults of a numerical analysis of the effect of the hole potential on the form of the X-ray spectra of narrow band metals are given. The dependence of the spectra on the magnitude of conduction band filling as well as on the magnitude of intratomic interaction between conduction band electrons and the hole is investigated. It is shown that when the band is filled, the emission and absorption spectra vary from a form of the spectra, which occurs if the hole potential is engaged adiabatically, to a form where the interaction with the hole is not taken into account. I n the first case the spectra reflect the local impurity density, and in the second one the density of states of the unperturbed matrix. If the hole potential is strong enough, then the formation of a local level is possible. The most interesting consequence of this is the presence of two lines in core XPS. The systematic change is recorded of the intensities of these lines as the band is filled. The results of the investigation are drawn into a qualitative interpretation of the width of emission bands and of the shift of the inner lines of d-metals. Es werden Ergebnisse einer numerischen Analyse des Einflusses des Lochpotentials auf dieForm von Rontgenspektren von Schrnalbandrnetallen angegeben. Die Abhangigkeit der Spektren sowohl vom Wert der Leitungsbandbesetzung als auch von der GroDe der interatornaren Wechselwirkung zwischen Leitungsbandelektronen und Lochern wird untersucht. Es wird gezeigt, daD die Fiillung der Biinder die Emissions-und Absorptionsspektren sich von der Spektrenform, die dann auftritt, wenn das Lochpotential adiabatisch eingeht, in eine Form Bndert, wo Wechselwirkung mit dem Loch nicht beriicksichtigt wird. Im ersten Fall spiegeln die Spektren die lokale Storstellendichte, und im zweiten die Zustandsdichte der ungestorten Matrix wider. Wenn das Lochpotential stark genug ist, ist die Bildung eines lokalen Niveaus moglich. Die interessanteste Konsequep ist die Anwesenheit von zwei Linien in den Rumpf -Rontgenphotospektren. Die systematische Anderung der Intensitiiten dieser Linien, wenn das Band gefullt wird, wird aufgezeichnet. Die Ergebnisse der Untersuchung werden in eine qualitative Interpretation der Breite der Emissionsbanden und der Verschiebung der inneren Linien der d-Metalle einbezogen.
The results of a numerical analysis of the effect of the hole potential on the form of the X‐ray spectra of narrow band metals are given. The dependence of the spectra on the magnitude of conduction band filling as well as on the magnitude of intratomic interaction between conduction band electrons and the hole is investigated. It is shown that when the band is filled, the emission and absorption spectra vary from a form of the spectra, which occurs if the hole potential is engaged adiabatically, to a form where the interaction with the hole is not taken into account. In the first case the spectra reflect the local impurity density, and in the second one the density of states of the unperturbed matrix. If the hole potential is strong enough, then the formation of a local level is possible. The most interesting consequence of this is the presence of two lines in core XPS. The systematic change is recorded of the intensities of these lines as the band is filled. The results of the investigation are drawn into a qualitative interpretation of the width of emission bands and of the shift of the inner lines of d‐metals.
Generalizing the regular solution algorithm the inverse problem of Mossbauer spectroscopy is proposed for obtaining the distribution function of the hyperfine interaction parameters from the spectrum. By model calculations it is shown that the algorithm is stable with respect to statistical noise and errors in the spectrum parameters. It is noticed that the algorithm is applicable strictly only to objects which properties can be described by a continuous distribution of one of the hyperfine interaction parameters. The condition of the normalization is introduced as an additional criterion of the correctness of the solution. There is a possibility of investigating the spectra with paramagnetic components. The algorithm may be applied to an analysis of both, poorly resolved and well resolved spectra. npemomeH 0604embIji perynnpHbIji ~O P H T M peluemn 06paTHOfi sanaqu MeCC6ay3pOB3KO6 CIIeKTpOCKOIIHH AJIUIII IIOJIy9eHm I$yHKqEIU PaCIIpeneJIeHUR IIapaMeTpOB CBepXTOHKOrO B3aUMOAefiCTBHX U3 CneKTpa. Ha MOneJIbJibIX paCWTZlX nOKa3IW0, 9TO WrOpHTM YCTOkIUB IIO OTHOIIIeHHH) K &iTOp€iTM CTpOrO IIpHMeHHM Nub K 06%eKTaM, CBOkTBa KOTOPbIX MOrYT 6bITb OIIECaHbI He-YCJIOBHe HOPMWPOBKH KBK nOlIOJIHuTenb& KpIlTepd KOppeKTHOCTH PeIIIeHUX. kiMeeTCR B03MOX-HOCTb UCCJEnOBaHUII CIIeKTpOB C IlapaMarHuTHbIMIl COCTaBJIXIOIIpiMH. AnropuTM MOXHO npuMeHIlTb cTaTucTuqecKoii norpemaocni w K o r u u 6 r a~ B onpenenearn napaMeTpoe cnempa. 3 a~e q e~0 , w o I I~~P~I B H~I M pacnpeneneJiweM o p o r o ~3 napaMeTpoB csepxTomoro ~s a w l o n e i i c~~w a . BBeneHO a~anu3a K a K cna60pa3peme~1mx TaK H xop0111opa3peme~m1x cnex-ipoB. ') Kirov street 132, SU-426OOO Izhevsk, USSR.
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