Variations in the charge radii of indium isotopes between <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>N</mml:mi> <mml:mo>=</mml:mo> <mml:mn>52</mml:mn> </mml:mrow> </mml:math> and 82
Bibliographic record
Abstract
Measurements of the <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"> <a:mrow> <a:mn>5</a:mn> <a:mi>p</a:mi> <a:mspace width="0.16em"/> <a:mmultiscripts> <a:mi>P</a:mi> <a:mrow> <a:mn>3</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> <a:none/> <a:mprescripts/> <a:none/> <a:mn>2</a:mn> </a:mmultiscripts> <a:mo>→</a:mo> <a:mn>9</a:mn> <a:mi>s</a:mi> <a:mspace width="0.16em"/> <a:mmultiscripts> <a:mi>S</a:mi> <a:mrow> <a:mn>1</a:mn> <a:mo>/</a:mo> <a:mn>2</a:mn> </a:mrow> <a:none/> <a:mprescripts/> <a:none/> <a:mn>2</a:mn> </a:mmultiscripts> </a:mrow> </a:math> and <d:math xmlns:d="http://www.w3.org/1998/Math/MathML"> <d:mrow> <d:mn>5</d:mn> <d:mi>p</d:mi> <d:mspace width="0.16em"/> <d:mmultiscripts> <d:mi>P</d:mi> <d:mrow> <d:mn>1</d:mn> <d:mo>/</d:mo> <d:mn>2</d:mn> </d:mrow> <d:none/> <d:mprescripts/> <d:none/> <d:mn>2</d:mn> </d:mmultiscripts> <d:mo>→</d:mo> <d:mn>8</d:mn> <d:mi>s</d:mi> <d:mspace width="0.16em"/> <d:mmultiscripts> <d:mi>S</d:mi> <d:mrow> <d:mn>1</d:mn> <d:mo>/</d:mo> <d:mn>2</d:mn> </d:mrow> <d:none/> <d:mprescripts/> <d:none/> <d:mn>2</d:mn> </d:mmultiscripts> </d:mrow> </d:math> transitions in the indium atom, combined with new atomic physics calculations, were used to extract the changes in mean-square nuclear charge radii, <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"> <g:mrow> <g:mi>δ</g:mi> <g:mo>〈</g:mo> <g:msup> <g:mi>r</g:mi> <g:mn>2</g:mn> </g:msup> <g:mo>〉</g:mo> </g:mrow> </g:math> , of the indium ( <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"> <h:mrow> <h:mi>Z</h:mi> <h:mo>=</h:mo> <h:mn>49</h:mn> </h:mrow> </h:math> ) isotopes <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"> <i:mmultiscripts> <i:mi>In</i:mi> <i:mprescripts/> <i:none/> <i:mrow> <i:mn>101</i:mn> <i:mo>–</i:mo> <i:mn>111</i:mn> </i:mrow> </i:mmultiscripts> <i:mo>,</i:mo> <i:mo> </i:mo> <i:mmultiscripts> <i:mi>In</i:mi> <i:mprescripts/> <i:none/> <i:mrow> <i:mn>113</i:mn> <i:mo>–</i:mo> <i:mn>123</i:mn> </i:mrow> </i:mmultiscripts> </i:math> , and <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"> <j:mmultiscripts> <j:mi>In</j:mi> <j:mprescripts/> <j:none/> <j:mrow> <j:mn>125</j:mn> <j:mo>–</j:mo> <j:mn>131</j:mn> </j:mrow> </j:mmultiscripts> </j:math> . With a proton hole in the closed nuclear shell of <k:math xmlns:k="http://www.w3.org/1998/Math/MathML"> <k:mrow> <k:mi>Z</k:mi> <k:mo>=</k:mo> <k:mn>50</k:mn> </k:mrow> </k:math> , indium provides a detailed study of the effect of unpaired nucleons adjacent to the proton-shell closure, allowing investigation into the charge radii for isotopes between the two major neutron-shell closures at <l:math xmlns:l="http://www.w3.org/1998/Math/MathML"> <l:mrow> <l:mi>N</l:mi> <l:mo>=</l:mo> <l:mn>50</l:mn> </l:mrow> </l:math> and <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mrow> <m:mi>N</m:mi> <m:mo>=</m:mo> <m:mn>82</m:mn> </m:mrow> </m:math> . A study of the variations in charge radii between neighboring isotopes with neutron number (the ‘odd-even staggering') is presented and provides further insight and challenges for the theoretical description of the size of proton-hole nuclei. Two nuclear theories, density functional theory and the valence-space in-medium similarity renormalization group method, were employed to interpret the data. The new information obtained in this work provides valuable insights into the successes and shortcomings of the theoretical approaches employed.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.001 | 0.001 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.003 | 0.001 |
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".