Benchmark PhotoIonization Cross-Sections of Neutral Scandium from the Ground and Excited States

The <i>B</i>-spline <i>R</i>-matrix method has been used to investigate cross-sections for photoionization of neutral scandium from the ground and excited states in the energy region from the 3<i>d</i> and 4<i>s</i> valence electron ionization threshol...

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Bibliographic Details
Main Authors: Swaraj S. Tayal, Oleg Zatsarinny
Format: Article
Language:English
Published: MDPI AG 2021-10-01
Series:Atoms
Subjects:
Online Access:https://www.mdpi.com/2218-2004/9/4/83
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Summary:The <i>B</i>-spline <i>R</i>-matrix method has been used to investigate cross-sections for photoionization of neutral scandium from the ground and excited states in the energy region from the 3<i>d</i> and 4<i>s</i> valence electron ionization thresholds to 25 eV. The initial bound states of Sc and the final residual Sc<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>+</mo></msup></semantics></math></inline-formula> ionic states have been accurately calculated by combining the multiconfiguration Hartree-Fock method with the frozen-core close-coupling approach. The lowest 20 bound states of Sc I belonging to the ground <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mi>d</mi><mn>4</mn><msup><mi>s</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> and excited <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>d</mi><mn>2</mn></msup><mn>4</mn><mi>s</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>d</mi><mn>2</mn></msup><mn>4</mn><mi>p</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><mi>d</mi><mn>4</mn><mi>s</mi><mn>4</mn><mi>p</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>4</mn><msup><mi>s</mi><mn>2</mn></msup><mn>4</mn><mi>p</mi></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>d</mi><mn>3</mn></msup></mrow></semantics></math></inline-formula> configurations have been considered as initial states. The 81 <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>L</mi><mi>S</mi></mrow></semantics></math></inline-formula> final ionic states of Sc<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>+</mo></msup></semantics></math></inline-formula> belonging to the terms of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>p</mi><mn>6</mn></msup><mn>3</mn><msup><mi>d</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>p</mi><mn>6</mn></msup><mn>3</mn><mi>d</mi><mn>4</mn><mi>l</mi></mrow></semantics></math></inline-formula> (<i>l</i> = 0–3), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>p</mi><mn>6</mn></msup><mn>3</mn><mi>d</mi><mn>5</mn><mi>l</mi></mrow></semantics></math></inline-formula> (<i>l</i> = 0–3), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>p</mi><mn>6</mn></msup><mn>3</mn><mi>d</mi><mn>6</mn><mi>s</mi></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>p</mi><mn>6</mn></msup><mn>4</mn><msup><mi>s</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>p</mi><mn>6</mn></msup><mn>4</mn><mi>s</mi><mn>4</mn><mi>l</mi></mrow></semantics></math></inline-formula> (<i>l</i> = 0–3), <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>p</mi><mn>6</mn></msup><mn>4</mn><mi>s</mi><mn>5</mn><mi>l</mi></mrow></semantics></math></inline-formula> (<i>l</i> = 0–1), and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>3</mn><msup><mi>p</mi><mn>6</mn></msup><mn>4</mn><msup><mi>p</mi><mn>2</mn></msup></mrow></semantics></math></inline-formula> configurations have been included in the final-state close-coupling expansion. The cross-sections are dominated by complicated resonance structures in the low energy region converging to several Sc<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>+</mo></msup></semantics></math></inline-formula> ionic thresholds. The inclusion of all these final ionic states has been noted to significantly impact the near-threshold resonance structures and background cross-sections. The important scattering channels for leaving the residual ion in various final states have been identified, and 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> electron ionization channels have been noted to dominate the cross-sections at higher photon energies.
ISSN:2218-2004