Coulomb excitation of radioactive<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Na</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>21</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>and its stable mirror<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mmultiscripts><mml:mi mathvariant="normal">Ne</mml:mi><mml:mprescripts/><mml:none/><mml:mrow><mml:mn>21</mml:mn></mml:mrow></mml:mmultiscripts></mml:math>
Bibliographic record
Abstract
The low-energy structures of the mirror nuclei $^{21}\mathrm{Ne}$ and radioactive $^{21}\mathrm{Na}$ have been examined by using Coulomb excitation at the TRIUMF-ISAC radioactive ion beam facility. Beams of $~5\ifmmode\times\else\texttimes\fi{}{10}^{6}$ ions/s were accelerated to 1.7 MeV/$A$ and Coulomb excited in a 0.5 mg/${\mathrm{cm}}^{2}$ ${}^{\mathrm{nat}}$Ti target. Scattered beam and target particles were detected by the segmented Si detector BAMBINO, while $\ensuremath{\gamma}$ rays were observed by using two TIGRESS HPGe clover detectors perpendicular to the beam axis. For each isobar, Coulomb excitation from the ${\frac{3}{2}}^{+}$ ground state to the first excited ${\frac{5}{2}}^{+}$ state was observed and $B(E2)$ values were determined by using the ${2}^{+}\ensuremath{\rightarrow}{0}^{+}$ de-excitation in $^{48}\mathrm{Ti}$ as a reference. The \ensuremath{\phi} segmentation of BAMBINO was used to deduce tentative assignments for the signs of the mixing ratios between the $E2$ and $M1$ components of the transitions. The resulting $B(E2)\ensuremath{\uparrow}$ values are $131\ifmmode\pm\else\textpm\fi{}9 {e}^{2}$ ${\mathrm{fm}}^{4}$ ($25.4\ifmmode\pm\else\textpm\fi{}1.7$ W.u.) for $^{21}\mathrm{Ne}$ and $205\ifmmode\pm\else\textpm\fi{}14 {e}^{2}$ ${\mathrm{fm}}^{4}$ ($39.7\ifmmode\pm\else\textpm\fi{}2.7$ W.u.) for $^{21}\mathrm{Na}$. The fit to the present data and the known lifetimes determined $E2/M1$ mixing ratios and $B(M1)\ensuremath{\downarrow}$ values of $\ensuremath{\delta}=(\ensuremath{-})0.0767\ifmmode\pm\else\textpm\fi{}0.0027$ and $0.1274\ifmmode\pm\else\textpm\fi{}0.0025 {\ensuremath{\mu}}_{N}{\text{}}^{2}$ and $\ensuremath{\delta}=(+)0.0832\ifmmode\pm\else\textpm\fi{}0.0028$ and $0.1513\ifmmode\pm\else\textpm\fi{}0.0017 {\ensuremath{\mu}}_{N}{\text{}}^{2}$ for $^{21}\mathrm{Ne}$ and $^{21}\mathrm{Na}$, respectively (with Krane and Steffen sign convention). By using the effective charges ${e}_{p}=1.5e$ and ${e}_{n}=0.5e$, the $B(E2)$ values produced by the $p$-$\mathit{sd}$ shell model are 30.7 and 36.4 W.u. for $^{21}\mathrm{Ne}$ and $^{21}\mathrm{Na}$, respectively. This analysis resolves a significant discrepancy between a previous experimental result for $^{21}\mathrm{Na}$ and shell-model calculations.
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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 | 0.004 | 0.003 |
| Meta-epidemiology (narrow) | 0.003 | 0.005 |
| Meta-epidemiology (broad) | 0.002 | 0.005 |
| Bibliometrics | 0.001 | 0.003 |
| Science and technology studies | 0.005 | 0.005 |
| Scholarly communication | 0.003 | 0.006 |
| Open science | 0.006 | 0.006 |
| Research integrity | 0.004 | 0.006 |
| Insufficient payload (model declined to judge) | 0.058 | 0.006 |
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".