Charge-State Distributions after Beta Decay of <sup>6</sup>He to Form <sup>6</sup>Li<sup>+</sup>
The shake-off processes and charge-state fractions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-...
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-02-01
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| Series: | Atoms |
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| Online Access: | https://www.mdpi.com/2218-2004/11/3/41 |
| _version_ | 1827751287983177728 |
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| author | Aaron T. Bondy Gordon W. F. Drake |
| author_facet | Aaron T. Bondy Gordon W. F. Drake |
| author_sort | Aaron T. Bondy |
| collection | DOAJ |
| description | The shake-off processes and charge-state fractions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> were studied following the beta decay of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>He in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><msup><mi>s</mi><mn>2</mn></msup><msup><mspace width="0.277778em"></mspace><mn>1</mn></msup><msub><mi>S</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>s</mi><mn>2</mn><mi>s</mi><msup><mspace width="0.277778em"></mspace><mn>1</mn></msup><msub><mi>S</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>s</mi><mn>2</mn><mi>s</mi><msup><mspace width="0.277778em"></mspace><mn>3</mn></msup><msub><mi>S</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> initial states. The sudden approximation was used, together with fully correlated Hylleraas wave functions and pseudostates. A projection operator method was introduced to separate the charge-state fractions in the positive energy region of overlapping continua. The results show that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></semantics></math></inline-formula> (single-ionisation) remains dominant, even in the energy range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, where the formation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> (double-ionisation) is energetically allowed. The results reduce disagreements with the experiment for the fraction of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> by nearly an order of magnitude, but substantial disagreements remain that are inconsistent with the sudden approximation widely used in other similar work. |
| first_indexed | 2024-03-11T06:56:08Z |
| format | Article |
| id | doaj.art-0d4bb22da2b94b0bb2224d69979a5efa |
| institution | Directory Open Access Journal |
| issn | 2218-2004 |
| language | English |
| last_indexed | 2024-03-11T06:56:08Z |
| publishDate | 2023-02-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Atoms |
| spelling | doaj.art-0d4bb22da2b94b0bb2224d69979a5efa2023-11-17T09:34:08ZengMDPI AGAtoms2218-20042023-02-011134110.3390/atoms11030041Charge-State Distributions after Beta Decay of <sup>6</sup>He to Form <sup>6</sup>Li<sup>+</sup>Aaron T. Bondy0Gordon W. F. Drake1Department of Physics, University of Windsor, Windsor, ON N9B 3P4, CanadaDepartment of Physics, University of Windsor, Windsor, ON N9B 3P4, CanadaThe shake-off processes and charge-state fractions of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mo>+</mo></msup></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> were studied following the beta decay of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>He in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><msup><mi>s</mi><mn>2</mn></msup><msup><mspace width="0.277778em"></mspace><mn>1</mn></msup><msub><mi>S</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>, <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>s</mi><mn>2</mn><mi>s</mi><msup><mspace width="0.277778em"></mspace><mn>1</mn></msup><msub><mi>S</mi><mn>0</mn></msub></mrow></semantics></math></inline-formula>, and <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mi>s</mi><mn>2</mn><mi>s</mi><msup><mspace width="0.277778em"></mspace><mn>3</mn></msup><msub><mi>S</mi><mn>1</mn></msub></mrow></semantics></math></inline-formula> initial states. The sudden approximation was used, together with fully correlated Hylleraas wave functions and pseudostates. A projection operator method was introduced to separate the charge-state fractions in the positive energy region of overlapping continua. The results show that <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mo>+</mo><mo>+</mo></mrow></msup></semantics></math></inline-formula> (single-ionisation) remains dominant, even in the energy range <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>E</mi><mo>></mo><mn>0</mn></mrow></semantics></math></inline-formula>, where the formation of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> (double-ionisation) is energetically allowed. The results reduce disagreements with the experiment for the fraction of <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mn>6</mn></msup></semantics></math></inline-formula>Li<inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msup><mrow></mrow><mrow><mn>3</mn><mo>+</mo></mrow></msup></semantics></math></inline-formula> by nearly an order of magnitude, but substantial disagreements remain that are inconsistent with the sudden approximation widely used in other similar work.https://www.mdpi.com/2218-2004/11/3/41beta decaydouble-ionisationtwo-electron calculationsHylleraas wave functionsSturmian projectors |
| spellingShingle | Aaron T. Bondy Gordon W. F. Drake Charge-State Distributions after Beta Decay of <sup>6</sup>He to Form <sup>6</sup>Li<sup>+</sup> Atoms beta decay double-ionisation two-electron calculations Hylleraas wave functions Sturmian projectors |
| title | Charge-State Distributions after Beta Decay of <sup>6</sup>He to Form <sup>6</sup>Li<sup>+</sup> |
| title_full | Charge-State Distributions after Beta Decay of <sup>6</sup>He to Form <sup>6</sup>Li<sup>+</sup> |
| title_fullStr | Charge-State Distributions after Beta Decay of <sup>6</sup>He to Form <sup>6</sup>Li<sup>+</sup> |
| title_full_unstemmed | Charge-State Distributions after Beta Decay of <sup>6</sup>He to Form <sup>6</sup>Li<sup>+</sup> |
| title_short | Charge-State Distributions after Beta Decay of <sup>6</sup>He to Form <sup>6</sup>Li<sup>+</sup> |
| title_sort | charge state distributions after beta decay of sup 6 sup he to form sup 6 sup li sup sup |
| topic | beta decay double-ionisation two-electron calculations Hylleraas wave functions Sturmian projectors |
| url | https://www.mdpi.com/2218-2004/11/3/41 |
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