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Transition metals are defined as those elements that have partially filled d orbitals. As shown in Figure 1, the d-block elements in groups 3–12 are transition elements. The f-block elements, also called inner transition metals (the lanthanides and actinides), also meet this criterion because the d orbital is partially occupied before the f orbitals.
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Updated: Dec 18, 2025

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Excitonic Effects in X-Ray Transitions in Metals.

G D Mahan1

  • 1Institute of Theoretical Science and Department of Physics, University of Oregon, Eugene, Oregon 94703 and General Electric Research and Development Center, Schenectady, New York 12301.

Journal of Research of the National Bureau of Standards. Section A, Physics and Chemistry
|June 12, 2020
PubMed
Summary
This summary is machine-generated.

Soft x-ray transitions in solids do not directly measure the density of states due to matrix element variations and final state interactions. Calculations show these effects significantly impact results.

Keywords:
Density of statesexcitonmany body effectsphase shiftssoft x-raytransition probability

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Area of Science:

  • Solid-state physics
  • Atomic and molecular physics

Background:

  • Soft x-ray spectroscopy is used to study electronic structures in solids.
  • Traditionally, it was hoped that results directly reflect the density of states.
  • This relied on assumptions of small matrix element variations and negligible final state interactions.

Purpose of the Study:

  • To investigate the validity of using soft x-ray transitions as a direct measure of the density of states in solids.
  • To illustrate the impact of matrix element variations and final state interactions on spectroscopic results.

Main Methods:

  • Calculated the one-electron oscillator strength of a body-centered cubic (bcc) metal as a function of energy.
  • Estimated the strength of the Nozieres-DeDominicis singularity at the spectral threshold.
  • Utilized an assumed Yukawa interaction between conduction electrons and core holes to determine phase shifts.

Main Results:

  • Demonstrated that matrix element variations across the band are significant.
  • Showed that final state interactions, particularly the Nozieres-DeDominicis singularity, strongly influence spectral features.
  • Quantified the deviation from a direct density of states measure.

Conclusions:

  • The assumptions that matrix element variations and final state interactions are negligible in soft x-ray transitions are incorrect.
  • These effects significantly alter the interpretation of soft x-ray spectra, moving away from a direct density of states measure.
  • Accurate interpretation requires accounting for these electron correlation and matrix element effects.