Abstract
The matrix elements of the coordinate, the momentum and the gradient of the potential give equivalent interband transition probabilities when the initial and the final states are exactly known. In calculations based on the muffin-tin potential the approximate core state is assumed to be completely localized in one muffin-tin. Then the different matrix elements are no longer equivalent. They are related by expressions involving the amplitudes of the wave functions and their logarithmic derivatives at the muffin-tin radius. The discussion and the numerical example show that the most appropriate form for the numerical calculation turns out to be the matrix element of the gradient of the potential.
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Nemoškalenko V. V., Aljošin V. G., Antonov V. N., Metody raščota energetičeskoj struktury i flzičeskich svojstv kristallov, Naukovaja Dumka, Kiev 1977, p. 10 (in Russian).
Bethe H. A., Salpeter E. E., Quantum Mechanics of One-and Two-Electron Atoms, Springer, Berlin 1957.
Tomboulian D. H., Hanb. Physik30 (1957), 246.
Smrčka L., Czech. J. Phys. B21 (1971), 683.
Neckel A. et al., Microchimica Acta (Wien), Suppl. 6, 257–291 (1975).
Nemoškalenko V. V. et al., phys. stat. sol. (b)93 (1979), 575.
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Smrčka, L. Soft x-ray transition probability: Calculation based on the muffin-tin potential. Czech J Phys 30, 1012–1018 (1980). https://doi.org/10.1007/BF01596174
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DOI: https://doi.org/10.1007/BF01596174