Nuclear shape coexistence from the perspective of an algebraic many-nucleon version of the Bohr-Mottelson unified model
Bibliographic record
Abstract
A fully quantal algebraic version of the Bohr-Mottelson unified model is presented with the important property that its quantization is defined by the fully antisymmetric many-nucleon unitary irreps (irreducible representations), which span the many-nucleon Hilbert space of a nucleus. The spatial component of this model, with added spin $\mathrm{SU}{(2)}_{S}$ and isospin $\mathrm{SU}{(2)}_{T}$ degrees of freedom, is uniquely defined by the requirement that its Lie algebra of observables includes the nuclear quadrupole moments, its angular momenta, and kinetic energy. Thus, it is determined to be an $\mathrm{Sp}(3,\mathbb{R})$ Lie algebra, which is then combined with the spin and isospin algebras of a Lie algebra for an $\mathrm{Sp}(3,\mathbb{R})\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{S}\ifmmode\times\else\texttimes\fi{}{\mathrm{SU}(2)}_{T}$ dynamical group of the desired algebraic unified model. The irreps of this model are uniquely defined by their $\mathrm{Sp}(3,\mathbb{R})$ lowest weights, spins, and isospins, and have the property that observed transitions between rotational states of nuclei can be expressed in terms of these irreps and their mixtures. The algebraic unified model parallels the Bohr-Mottelson version in almost all respects, including the possibility of taking into account the effects of Coriolis and centrifugal forces as subsequent perturbations. In addition, it defines the admissible fully antisymmetric many-nucleon irreps and puts a new perspective on the phenomenon of shape coexistence. It avoids use of an overcomplete set of coordinates and corrects the phenomenological unified model treatment of angular momentum quantization. These changes have significant implications for the dynamics of nuclear rotations, which are hidden when its moments of inertia are considered as adjustable parameters in the standard expression of rotational kinetic energies.
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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 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 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".