Bibliographic record
Abstract
Abstract The total energy and other bound state properties of the ground (bound) 1 1 S -state in the Ps − (or e − e + e − ) ion are determined to very high accuracy. Our best variational energy for the ground state in this ion equals E =-0.26200507023298010777040225 a . u . , which is the lowest variational energy ever obtained for this ion. By using our highly wave functions we evaluated (to very high accuracy) a large number of different expectation values (or properties) of the Ps − ion which have never been considered in earlier studies. This includes a number of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">〈</mml:mo> <mml:msubsup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">ij</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>k</mml:mi> </mml:mrow> </mml:msubsup> <mml:mo stretchy="false">〉</mml:mo> </mml:math> expectation values (where 5 ≤ k ≤ 11), all independent quasi-singular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">〈</mml:mo> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mrow> <mml:msub> <mml:mrow> <mml:mi mathvariant="bold">r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">ij</mml:mi> </mml:mrow> </mml:msub> <mml:msub> <mml:mrow> <mml:mi mathvariant="bold">r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">jk</mml:mi> </mml:mrow> </mml:msub> </mml:mrow> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">ij</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:mfrac> </mml:mstyle> <mml:mo stretchy="false">〉</mml:mo> </mml:math> and singular <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">〈</mml:mo> <mml:mstyle displaystyle="false"> <mml:mfrac> <mml:mrow> <mml:mn>1</mml:mn> </mml:mrow> <mml:mrow> <mml:msubsup> <mml:mrow> <mml:mi>r</mml:mi> </mml:mrow> <mml:mrow> <mml:mi mathvariant="italic">ij</mml:mi> </mml:mrow> <mml:mrow> <mml:mn>3</mml:mn> </mml:mrow> </mml:msubsup> </mml:mrow> </mml:mfrac> </mml:mstyle> <mml:mo stretchy="false">〉</mml:mo> </mml:math> expectation values, etc. Our highly accurate expectation values of the electron-positron delta-function of the Ps − ion are used to evaluate (to very high accuracy) the rates of two-, three-, four- and five-photon annihilation. The numerical values of these rates provide the highly accurate and complete solution of the multi-photon annihilation in the negatively charged positronium ion.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.004 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".