Microscopic derivation of the generalized collective Hamiltonian
Bibliographic record
Abstract
The nucleus in the center-of-mass frame is described by <a:math xmlns:a="http://www.w3.org/1998/Math/MathML"><a:mrow><a:mn>3</a:mn><a:mi>A</a:mi><a:mtext>−</a:mtext><a:mn>3</a:mn></a:mrow></a:math> independent coordinates, including three Euler angles and three variables <b:math xmlns:b="http://www.w3.org/1998/Math/MathML"><b:mrow><b:mi>ρ</b:mi><b:mo>,</b:mo><b:mspace width="0.28em"/><b:mi>β</b:mi><b:mo>,</b:mo><b:mspace width="4.pt"/><b:mtext>and</b:mtext><b:mspace width="4.pt"/><b:mi>γ</b:mi></b:mrow></b:math> to describe orientation, size, and shape of the nuclear inertia ellipsoid as well as <f:math xmlns:f="http://www.w3.org/1998/Math/MathML"><f:mrow><f:mn>3</f:mn><f:mi>A</f:mi><f:mtext>−</f:mtext><f:mn>9</f:mn></f:mrow></f:math> generalized Euler angles to describe internal motion of the nucleons. Based on the idea that the incompressible nucleus has constant density, we suggest a definition of the deformation parameter <g:math xmlns:g="http://www.w3.org/1998/Math/MathML"><g:mi>β</g:mi></g:math>. It allows us to derive the Hamiltonian, which describes large-amplitude collective motions. At <h:math xmlns:h="http://www.w3.org/1998/Math/MathML"><h:mrow><h:mi>β</h:mi><h:mo>≪</h:mo><h:mn>1</h:mn></h:mrow></h:math> it reduces to a sum of the Bohr Hamiltonian and the Hamiltonian of monopole <i:math xmlns:i="http://www.w3.org/1998/Math/MathML"><i:mi>ρ</i:mi></i:math> vibrations. As a result of straightforward calculations we obtain explicit expressions for all the inertial parameters as functions of the variables <j:math xmlns:j="http://www.w3.org/1998/Math/MathML"><j:mrow><j:mi>ρ</j:mi><j:mo>,</j:mo><j:mspace width="0.28em"/><j:mi>β</j:mi><j:mo>,</j:mo><j:mspace width="4.pt"/><j:mtext>and</j:mtext><j:mspace width="4.pt"/><j:mi>γ</j:mi></j:mrow></j:math>. Published by the American Physical Society 2024
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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 | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 teacher head, 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".