<i>Ab initio</i> no-core shell-model description of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">C</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>10</mml:mn><mml:mo>–</mml:mo><mml:mn>14</mml:mn></mml:mrow></mml:mmultiscripts></mml:math> isotopes
Bibliographic record
Abstract
We present a systematic study of the $^{10--14}\mathrm{C}$ isotopes within the ab initio no-core shell-model theory. We apply four different realistic nucleon-nucleon $(NN)$ interactions: (i) the charge-dependent Bonn 2000 (CDB2K) potential; (ii) the inside nonlocal outside Yukawa (INOY) potential; (iii) the next-to-next-to-next-to-leading order $({\mathrm{N}}^{3}\mathrm{LO})$ potential; and (iv) the optimized next-to-next-to-leading order $({\mathrm{N}}^{2}{\mathrm{LO}}_{\mathrm{opt}})$ potential. We report the low-lying energy spectra of both positive- and negative-parity states for $^{10--14}\mathrm{C}$ isotopes and investigate the level structures. We also calculate electromagnetic properties such as transition strengths, quadrupole moments, and magnetic moments. The dependence of point-proton radii on the harmonic-oscillator frequency and basis space is shown. We present calculations of the translation invariant one-body density matrix in the no-core shell-model and discuss isotopic trends in the density distribution. The maximum basis space reached is $10\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}$ for $^{10}\mathrm{C}$ and $8\ensuremath{\hbar}\mathrm{\ensuremath{\Omega}}$ for $^{11--14}\mathrm{C}$, with a maximum M-scheme dimension of $1.3\ifmmode\times\else\texttimes\fi{}{10}^{9}$ for $^{10}\mathrm{C}$. We found that, while the INOY interaction gives the best description of the ground-state energies, the ${\mathrm{N}}^{3}\mathrm{LO}$ interaction best reproduces the point-proton radii.
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How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.002 |
| Meta-epidemiology (narrow) | 0.002 | 0.003 |
| Meta-epidemiology (broad) | 0.001 | 0.004 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.002 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.003 | 0.005 |
| Research integrity | 0.002 | 0.003 |
| Insufficient payload (model declined to judge) | 0.048 | 0.011 |
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; both teacher heads agree on what is shown here.
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".