Bibliographic record
Abstract
In this article, a semiclassical, microscopic model (dubbed SMRM) is derived to describe collective rotation in deformed nuclei. The SMRM is derived by transforming the time-dependent, multiparticle Schrodinger equation to a rotating frame whose axes are chosen to coincide with the principal axes of the expectation value of an arbitrary, second-rank, symmetric, tensor (nuclear shape) operator [Formula: see text]. This transformation circumvents the difficulty associated with the introduction of redundant particle coordinates in the Villars' transformation. The SMRM Schrodinger equation, which resembles the cranking model (CM) equation, is a time-dependent, time-reversal-invariant, nonlinear integro-differential equation. In this equation, the angular velocity is determined by the wave function and deformation–rotation shear operators, and this introduces the nonlinearity in the equation. A variational method is proposed and justified to obtain: a stationary solution of the SMRM Schrodinger equation in the Rayleigh–Ritz Hartree–Fock particle–hole formalism, the rotational energy increment, and the associated moment of inertia. When exchange interaction terms are neglected or a separable interaction is used, the SMRM moment of inertia is shown to reduce to that given by the CM provided that a certain relationship exists between the moment of inertia and the expectation value of [Formula: see text]. However, the SMRM and CM wave functions are not the same (SMRM preserves and CM violates time-reversal invariance) implying that the calculated values of other parameters, including the moment of inertia at higher values of the angular momentum, may not be the same in the two models. In any case, the SMRM derives the CM moment of inertia from a microscopic, time-reversal invariant, nonlinear theory.PACS Nos.: 21.60.Ev, 21.60.Fw, 21.60.Jz
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
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 | 0.000 | 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".