The Feshbach Resonances Applied to the Calculation of Stark Broadening of Ionized Spectral Lines: An Example of Interdisciplinary Research
In the present paper, we revisit the determination of Feshbach resonances in the elastic and fine-structure cross-sections of the spectral lines of ionized atoms colliding with electrons. The Gailitis approximation will be recalled and used to calculate the Feshbach resonances. A historical point of...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
MDPI AG
2025-01-01
|
| Series: | Atoms |
| Subjects: | |
| Online Access: | https://www.mdpi.com/2218-2004/13/1/7 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832589137838866432 |
|---|---|
| author | Sylvie Sahal-Bréchot Haykel Elabidi |
| author_facet | Sylvie Sahal-Bréchot Haykel Elabidi |
| author_sort | Sylvie Sahal-Bréchot |
| collection | DOAJ |
| description | In the present paper, we revisit the determination of Feshbach resonances in the elastic and fine-structure cross-sections of the spectral lines of ionized atoms colliding with electrons. The Gailitis approximation will be recalled and used to calculate the Feshbach resonances. A historical point of view will be used, emphasizing the interest of interdisciplinary research, with a back and forth between physics and astrophysics. First, the theory of Feshbach (arising at end of the 1950s and beginning of the 1960s) resonances will be briefly recalled and applied to the calculation of the cross-sections. In the beginning of the 1970s, the insertion of Feshbach resonances in spectroscopic diagnostics calculations permitted researchers to interpret the intensities of solar coronal lines. Then, in the middle of the 1970s, this gave rise to the idea of including the Feshbach resonances in the calculation of electron impact broadening (the so-called “Stark” broadening) of isolated spectral lines of ionized atoms. Finally, in the recent example of the Stark broadening of the Mo VI <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mi mathvariant="normal">d</mi><mrow><mo> </mo><mmultiscripts><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>2</mn></mmultiscripts><mo>−</mo><mn>5</mn><mi mathvariant="normal">p</mi><mo> </mo><mmultiscripts><mrow><mi>P</mi><mo>°</mo></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>2</mn></mmultiscripts></mrow></mrow></semantics></math></inline-formula> line, the S-matrices will be calculated using the semi-classical perturbation formalism and will be compared to those of the more recent quantum distorted wave formalism. |
| format | Article |
| id | doaj-art-aa24b55215924e7ba7fd8a53bbff6022 |
| institution | Kabale University |
| issn | 2218-2004 |
| language | English |
| publishDate | 2025-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atoms |
| spelling | doaj-art-aa24b55215924e7ba7fd8a53bbff60222025-01-24T13:22:06ZengMDPI AGAtoms2218-20042025-01-01131710.3390/atoms13010007The Feshbach Resonances Applied to the Calculation of Stark Broadening of Ionized Spectral Lines: An Example of Interdisciplinary ResearchSylvie Sahal-Bréchot0Haykel Elabidi1LERMA, Observatoire de Paris, PSL University, CNRS, Sorbonne Université, 92190 Meudon, FrancePhysics Department, College of Sciences, Umm AL-Qura University, P.O. Box 715, Makkah 24382, Saudi ArabiaIn the present paper, we revisit the determination of Feshbach resonances in the elastic and fine-structure cross-sections of the spectral lines of ionized atoms colliding with electrons. The Gailitis approximation will be recalled and used to calculate the Feshbach resonances. A historical point of view will be used, emphasizing the interest of interdisciplinary research, with a back and forth between physics and astrophysics. First, the theory of Feshbach (arising at end of the 1950s and beginning of the 1960s) resonances will be briefly recalled and applied to the calculation of the cross-sections. In the beginning of the 1970s, the insertion of Feshbach resonances in spectroscopic diagnostics calculations permitted researchers to interpret the intensities of solar coronal lines. Then, in the middle of the 1970s, this gave rise to the idea of including the Feshbach resonances in the calculation of electron impact broadening (the so-called “Stark” broadening) of isolated spectral lines of ionized atoms. Finally, in the recent example of the Stark broadening of the Mo VI <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>5</mn><mi mathvariant="normal">d</mi><mrow><mo> </mo><mmultiscripts><mrow><mi mathvariant="normal">D</mi></mrow><mrow><mn>5</mn><mo>/</mo><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>2</mn></mmultiscripts><mo>−</mo><mn>5</mn><mi mathvariant="normal">p</mi><mo> </mo><mmultiscripts><mrow><mi>P</mi><mo>°</mo></mrow><mrow><mn>3</mn><mo>/</mo><mn>2</mn></mrow><none></none><mprescripts></mprescripts><none></none><mn>2</mn></mmultiscripts></mrow></mrow></semantics></math></inline-formula> line, the S-matrices will be calculated using the semi-classical perturbation formalism and will be compared to those of the more recent quantum distorted wave formalism.https://www.mdpi.com/2218-2004/13/1/7stark broadeningimpact approximationisolated spectral lines of ionized atomselectronic collisionsFeshbach resonances |
| spellingShingle | Sylvie Sahal-Bréchot Haykel Elabidi The Feshbach Resonances Applied to the Calculation of Stark Broadening of Ionized Spectral Lines: An Example of Interdisciplinary Research Atoms stark broadening impact approximation isolated spectral lines of ionized atoms electronic collisions Feshbach resonances |
| title | The Feshbach Resonances Applied to the Calculation of Stark Broadening of Ionized Spectral Lines: An Example of Interdisciplinary Research |
| title_full | The Feshbach Resonances Applied to the Calculation of Stark Broadening of Ionized Spectral Lines: An Example of Interdisciplinary Research |
| title_fullStr | The Feshbach Resonances Applied to the Calculation of Stark Broadening of Ionized Spectral Lines: An Example of Interdisciplinary Research |
| title_full_unstemmed | The Feshbach Resonances Applied to the Calculation of Stark Broadening of Ionized Spectral Lines: An Example of Interdisciplinary Research |
| title_short | The Feshbach Resonances Applied to the Calculation of Stark Broadening of Ionized Spectral Lines: An Example of Interdisciplinary Research |
| title_sort | feshbach resonances applied to the calculation of stark broadening of ionized spectral lines an example of interdisciplinary research |
| topic | stark broadening impact approximation isolated spectral lines of ionized atoms electronic collisions Feshbach resonances |
| url | https://www.mdpi.com/2218-2004/13/1/7 |
| work_keys_str_mv | AT sylviesahalbrechot thefeshbachresonancesappliedtothecalculationofstarkbroadeningofionizedspectrallinesanexampleofinterdisciplinaryresearch AT haykelelabidi thefeshbachresonancesappliedtothecalculationofstarkbroadeningofionizedspectrallinesanexampleofinterdisciplinaryresearch AT sylviesahalbrechot feshbachresonancesappliedtothecalculationofstarkbroadeningofionizedspectrallinesanexampleofinterdisciplinaryresearch AT haykelelabidi feshbachresonancesappliedtothecalculationofstarkbroadeningofionizedspectrallinesanexampleofinterdisciplinaryresearch |