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Ab Initio Manganese K<i>α</i> and K<i>β</i> Energy Eigenvalues, Shake-Off Probabilities, Auger Rates, with Convergence Tests
oleh: Jonathan William Dean, Scott Neil Thompson, Christopher Thomas Chantler
Format: | Article |
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Diterbitkan: | MDPI AG 2024-09-01 |
Deskripsi
This work presents ab initio calculations for the K<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi>α</mi></semantics></math></inline-formula> spectrum of manganese (Z = 25, [Ar]<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>d</mi><mn>5</mn></msup><mn>4</mn><msup><mi>s</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>), a highly complex system due to the five open orbitals in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mi>d</mi></mrow></semantics></math></inline-formula> shell. The spectrum is composed of the canonical diagram line <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>1</mn><mi>s</mi><mo>]</mo><mo>→</mo><mo>[</mo><mn>2</mn><mi>p</mi><mo>]</mo></mrow></semantics></math></inline-formula> and shake-off satellite lines <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mo>[</mo><mn>1</mn><mi>s</mi><mi>n</mi><mi>l</mi><mo>]</mo><mo>→</mo><mo>[</mo><mn>2</mn><mi>p</mi><mi>n</mi><mi>l</mi><mo>]</mo></mrow></semantics></math></inline-formula> (<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>n</mi><mi>l</mi><mo>∈</mo><mo>{</mo><mn>2</mn><mi>s</mi><mo>,</mo><mn>2</mn><mi>p</mi><mo>,</mo><mn>3</mn><mi>s</mi><mo>,</mo><mn>3</mn><mi>p</mi><mo>,</mo><mn>3</mn><mi>d</mi><mo>,</mo><mn>4</mn><mi>s</mi><mo>}</mo></mrow></semantics></math></inline-formula>), where square brackets denote a hole state. The multiconfiguration Dirac–Hartree–Fock method with the active set approach provides the initial and final atomic wavefunctions. Results are presented as energy eigenvalue spectra for the diagram and satellite transitions. The calculated wavefunctions include over one hundred million configuration state functions and over 280,000 independent transition energies for the seven sets of spectra considered. Shake-off probabilities and Auger transition rates determine satellite intensities. The number of configuration state functions ensures highly-converged wavefunctions. Several measures of convergence demonstrate convergence in the calculated parameters. We obtain convergence of the transition energies in all eight transitions to within 0.06 eV and shake-off probabilities to within 4.5%.