Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion <span style="text-decoration: overline">H</span><sup>+</sup>
To overcome the numerical difficulties inherent in the Maxwell–Boltzmann integral of the velocity-weighted cross section that gives the radiative attachment rate coefficient <inline-formula> <math display="inline"> <semantics> <msub> <mi>α</mi> <mrow&...
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MDPI AG
2020-04-01
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| author | Jack C. Straton |
| author_facet | Jack C. Straton |
| author_sort | Jack C. Straton |
| collection | DOAJ |
| description | To overcome the numerical difficulties inherent in the Maxwell–Boltzmann integral of the velocity-weighted cross section that gives the radiative attachment rate coefficient <inline-formula> <math display="inline"> <semantics> <msub> <mi>α</mi> <mrow> <mi>R</mi> <mi>A</mi> </mrow> </msub> </semantics> </math> </inline-formula> for producing the negative hydrogen ion H<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mo>−</mo> </msup> </semantics> </math> </inline-formula> or its antimatter equivalent, the positive antihydrogen ion <inline-formula> <math display="inline"> <semantics> <msup> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> <mo>+</mo> </msup> </semantics> </math> </inline-formula>, we found the analytic form for this integral. This procedure is useful for temperatures below 700 K, the region for which the production of <inline-formula> <math display="inline"> <semantics> <msup> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> <mstyle displaystyle="false" scriptlevel="1"> <mo>+</mo> </mstyle> </msup> </semantics> </math> </inline-formula> has potential use as an intermediate stage in the cooling of antihydrogen to ultra-cold (sub-mK) temperatures for spectroscopic studies and probing the gravitational interaction of the anti-atom. Our results, utilizing a 50-term explicitly correlated exponential wave function, confirm our prior numerical results. |
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| id | doaj.art-cd96e1b607bc4fbea3405be5e55389e7 |
| institution | Directory Open Access Journal |
| issn | 2218-2004 |
| language | English |
| last_indexed | 2024-03-10T20:21:40Z |
| publishDate | 2020-04-01 |
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| series | Atoms |
| spelling | doaj.art-cd96e1b607bc4fbea3405be5e55389e72023-11-19T22:11:07ZengMDPI AGAtoms2218-20042020-04-01821310.3390/atoms8020013Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion <span style="text-decoration: overline">H</span><sup>+</sup>Jack C. Straton0Department of Physics, Portland State University, Portland, OR 97207-0751, USATo overcome the numerical difficulties inherent in the Maxwell–Boltzmann integral of the velocity-weighted cross section that gives the radiative attachment rate coefficient <inline-formula> <math display="inline"> <semantics> <msub> <mi>α</mi> <mrow> <mi>R</mi> <mi>A</mi> </mrow> </msub> </semantics> </math> </inline-formula> for producing the negative hydrogen ion H<inline-formula> <math display="inline"> <semantics> <msup> <mrow></mrow> <mo>−</mo> </msup> </semantics> </math> </inline-formula> or its antimatter equivalent, the positive antihydrogen ion <inline-formula> <math display="inline"> <semantics> <msup> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> <mo>+</mo> </msup> </semantics> </math> </inline-formula>, we found the analytic form for this integral. This procedure is useful for temperatures below 700 K, the region for which the production of <inline-formula> <math display="inline"> <semantics> <msup> <mover> <mi mathvariant="normal">H</mi> <mo>¯</mo> </mover> <mstyle displaystyle="false" scriptlevel="1"> <mo>+</mo> </mstyle> </msup> </semantics> </math> </inline-formula> has potential use as an intermediate stage in the cooling of antihydrogen to ultra-cold (sub-mK) temperatures for spectroscopic studies and probing the gravitational interaction of the anti-atom. Our results, utilizing a 50-term explicitly correlated exponential wave function, confirm our prior numerical results.https://www.mdpi.com/2218-2004/8/2/13antihydrogenradiative attachmentphotodetachmentantihydrogen ionanalyticalhydrogen ion |
| spellingShingle | Jack C. Straton Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion <span style="text-decoration: overline">H</span><sup>+</sup> Atoms antihydrogen radiative attachment photodetachment antihydrogen ion analytical hydrogen ion |
| title | Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion <span style="text-decoration: overline">H</span><sup>+</sup> |
| title_full | Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion <span style="text-decoration: overline">H</span><sup>+</sup> |
| title_fullStr | Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion <span style="text-decoration: overline">H</span><sup>+</sup> |
| title_full_unstemmed | Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion <span style="text-decoration: overline">H</span><sup>+</sup> |
| title_short | Analytical Results for the Three-Body Radiative Attachment Rate Coefficient, with Application to the Positive Antihydrogen Ion <span style="text-decoration: overline">H</span><sup>+</sup> |
| title_sort | analytical results for the three body radiative attachment rate coefficient with application to the positive antihydrogen ion span style text decoration overline h span sup sup |
| topic | antihydrogen radiative attachment photodetachment antihydrogen ion analytical hydrogen ion |
| url | https://www.mdpi.com/2218-2004/8/2/13 |
| work_keys_str_mv | AT jackcstraton analyticalresultsforthethreebodyradiativeattachmentratecoefficientwithapplicationtothepositiveantihydrogenionspanstyletextdecorationoverlinehspansupsup |