Calculation of Low-Energy Positron-Atom Scattering with Square-Integrable Wavefunctions
The variational method is applied to the low-energy positron scattering and annihilation problem. The ultimate aim of the investigation is to find a computationally economical way of accounting for strong electron–positron correlations, including the effect of virtual positronium formation. The meth...
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MDPI AG
2022-09-01
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| Online Access: | https://www.mdpi.com/2218-2004/10/4/97 |
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| author | Sarah Gregg Gleb Gribakin |
| author_facet | Sarah Gregg Gleb Gribakin |
| author_sort | Sarah Gregg |
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| description | The variational method is applied to the low-energy positron scattering and annihilation problem. The ultimate aim of the investigation is to find a computationally economical way of accounting for strong electron–positron correlations, including the effect of virtual positronium formation. The method is applied to the study of elastic <i>s</i>-wave positron scattering from a hydrogen atom. A generalized eigenvalue problem is set up and solved to obtain <i>s</i>-wave positron–hydrogen scattering phase shifts within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> rad of accepted values. This is achieved using a small number of terms in the variational wavefunction; in particular, only nine terms that depend on the electron–positron distance are included. The annihilation parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Z</mi><mi>eff</mi></msub></semantics></math></inline-formula> is also calculated and is found to be in good agreement with benchmark calculations. |
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| institution | Directory Open Access Journal |
| issn | 2218-2004 |
| language | English |
| last_indexed | 2024-03-09T17:20:37Z |
| publishDate | 2022-09-01 |
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| spelling | doaj.art-eb4b25ad336e43fea0650b5525c0f81a2023-11-24T13:13:33ZengMDPI AGAtoms2218-20042022-09-011049710.3390/atoms10040097Calculation of Low-Energy Positron-Atom Scattering with Square-Integrable WavefunctionsSarah Gregg0Gleb Gribakin1School of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UKSchool of Mathematics and Physics, Queen’s University Belfast, Belfast BT7 1NN, UKThe variational method is applied to the low-energy positron scattering and annihilation problem. The ultimate aim of the investigation is to find a computationally economical way of accounting for strong electron–positron correlations, including the effect of virtual positronium formation. The method is applied to the study of elastic <i>s</i>-wave positron scattering from a hydrogen atom. A generalized eigenvalue problem is set up and solved to obtain <i>s</i>-wave positron–hydrogen scattering phase shifts within <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>8</mn><mo>×</mo><msup><mn>10</mn><mrow><mo>−</mo><mn>3</mn></mrow></msup></mrow></semantics></math></inline-formula> rad of accepted values. This is achieved using a small number of terms in the variational wavefunction; in particular, only nine terms that depend on the electron–positron distance are included. The annihilation parameter <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><msub><mi>Z</mi><mi>eff</mi></msub></semantics></math></inline-formula> is also calculated and is found to be in good agreement with benchmark calculations.https://www.mdpi.com/2218-2004/10/4/97theoretical atomic and molecular physicspositronhydrogenannihilationphase shiftscattering |
| spellingShingle | Sarah Gregg Gleb Gribakin Calculation of Low-Energy Positron-Atom Scattering with Square-Integrable Wavefunctions Atoms theoretical atomic and molecular physics positron hydrogen annihilation phase shift scattering |
| title | Calculation of Low-Energy Positron-Atom Scattering with Square-Integrable Wavefunctions |
| title_full | Calculation of Low-Energy Positron-Atom Scattering with Square-Integrable Wavefunctions |
| title_fullStr | Calculation of Low-Energy Positron-Atom Scattering with Square-Integrable Wavefunctions |
| title_full_unstemmed | Calculation of Low-Energy Positron-Atom Scattering with Square-Integrable Wavefunctions |
| title_short | Calculation of Low-Energy Positron-Atom Scattering with Square-Integrable Wavefunctions |
| title_sort | calculation of low energy positron atom scattering with square integrable wavefunctions |
| topic | theoretical atomic and molecular physics positron hydrogen annihilation phase shift scattering |
| url | https://www.mdpi.com/2218-2004/10/4/97 |
| work_keys_str_mv | AT sarahgregg calculationoflowenergypositronatomscatteringwithsquareintegrablewavefunctions AT glebgribakin calculationoflowenergypositronatomscatteringwithsquareintegrablewavefunctions |