Electron Broadening Operator Including Penetrating Collisions for Hydrogen
The expression of the electron broadening operator including the effect of penetrating collisions, i.e., for which the incoming electron enters the extent of bound-electron wave-functions, is rather complicated, even for hydrogen. It involves integrals of special functions, the evaluation of which d...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-01-01
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| Series: | Atoms |
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| Online Access: | https://www.mdpi.com/2218-2004/8/1/2 |
| _version_ | 1818133977936953344 |
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| author | Jean-Christophe Pain Franck Gilleron |
| author_facet | Jean-Christophe Pain Franck Gilleron |
| author_sort | Jean-Christophe Pain |
| collection | DOAJ |
| description | The expression of the electron broadening operator including the effect of penetrating collisions, i.e., for which the incoming electron enters the extent of bound-electron wave-functions, is rather complicated, even for hydrogen. It involves integrals of special functions, the evaluation of which deserves scrutiny. We present a simple approximate form of the electron collision operator for hydrogen including penetration effects, both in direct and interference terms. The new expression is accurate and easy to compute. In the Penetration Standard Theory, the collision operator is convergent whatever the value of the maximum impact parameter. However, when penetration theory is not valid anymore, it should be questioned. We discuss the problem of strong collisions when penetration effects are taken into account. |
| first_indexed | 2024-12-11T09:01:18Z |
| format | Article |
| id | doaj.art-c7657ba4d1564fae82e7dc9f7c7e774c |
| institution | Directory Open Access Journal |
| issn | 2218-2004 |
| language | English |
| last_indexed | 2024-12-11T09:01:18Z |
| publishDate | 2020-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atoms |
| spelling | doaj.art-c7657ba4d1564fae82e7dc9f7c7e774c2022-12-22T01:13:45ZengMDPI AGAtoms2218-20042020-01-0181210.3390/atoms8010002atoms8010002Electron Broadening Operator Including Penetrating Collisions for HydrogenJean-Christophe Pain0Franck Gilleron1CEA, DAM, DIF, F-91297 Arpajon, FranceCEA, DAM, DIF, F-91297 Arpajon, FranceThe expression of the electron broadening operator including the effect of penetrating collisions, i.e., for which the incoming electron enters the extent of bound-electron wave-functions, is rather complicated, even for hydrogen. It involves integrals of special functions, the evaluation of which deserves scrutiny. We present a simple approximate form of the electron collision operator for hydrogen including penetration effects, both in direct and interference terms. The new expression is accurate and easy to compute. In the Penetration Standard Theory, the collision operator is convergent whatever the value of the maximum impact parameter. However, when penetration theory is not valid anymore, it should be questioned. We discuss the problem of strong collisions when penetration effects are taken into account.https://www.mdpi.com/2218-2004/8/1/2line-shape profilestark broadeningelectron broadeningcollision operatorstandard theorypenetration standard theorystrong collisions |
| spellingShingle | Jean-Christophe Pain Franck Gilleron Electron Broadening Operator Including Penetrating Collisions for Hydrogen Atoms line-shape profile stark broadening electron broadening collision operator standard theory penetration standard theory strong collisions |
| title | Electron Broadening Operator Including Penetrating Collisions for Hydrogen |
| title_full | Electron Broadening Operator Including Penetrating Collisions for Hydrogen |
| title_fullStr | Electron Broadening Operator Including Penetrating Collisions for Hydrogen |
| title_full_unstemmed | Electron Broadening Operator Including Penetrating Collisions for Hydrogen |
| title_short | Electron Broadening Operator Including Penetrating Collisions for Hydrogen |
| title_sort | electron broadening operator including penetrating collisions for hydrogen |
| topic | line-shape profile stark broadening electron broadening collision operator standard theory penetration standard theory strong collisions |
| url | https://www.mdpi.com/2218-2004/8/1/2 |
| work_keys_str_mv | AT jeanchristophepain electronbroadeningoperatorincludingpenetratingcollisionsforhydrogen AT franckgilleron electronbroadeningoperatorincludingpenetratingcollisionsforhydrogen |