Quantifying uncertainties in neutron-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mi>α</mml:mi></mml:math> scattering with chiral nucleon-nucleon and three-nucleon forces
Bibliographic record
Abstract
Background: Modern ab initio theory combined with high-quality nucleon-nucleon (NN) and three-nucleon (3N) interactions from chiral effective field theory (EFT) can provide a predictive description of low-energy light-nuclei reactions relevant for astrophysics and fusion-energy applications. However, the high cost of computations has so far impeded a complete analysis of the uncertainty budget of such calculations.Purpose: Starting from NN potentials up to fifth order (${\mathrm{N}}^{4}\mathrm{LO}$) combined with leading-order 3N forces, we study how the order-by-order convergence of the chiral expansion and confidence intervals for the 3N contact and contact-plus-one-pion-exchange low-energy constants (${c}_{E}$ and ${c}_{D}$) contribute to the overall uncertainty budget of many-body calculations of neutron $^{4}\mathrm{He}$ ($n\ensuremath{-}\ensuremath{\alpha}$) elastic scattering.Methods: We compute structure and reaction observables for three-, four-, and five-nucleon systems within the ab initio frameworks of the no-core shell model and no-core shell model with continuum. Using a small set of design runs, we construct a Gaussian process model (GPM) that acts as a statistical emulator for the theory. With this, we gain insight into how uncertainties in the 3N low-energy constants propagate throughout the calculation and determine the Bayesian posterior distribution of these parameters with Markov-Chain Monte Carlo.Results: We find rapidly converging $n\ensuremath{-}\ensuremath{\alpha}$ phase shifts with respect to the chiral order. With the adopted leading-order 3N force, calculations based on the NN interaction at ${\mathrm{N}}^{4}\mathrm{LO}$ of Entem, Machleidt, and Nosyk [Phys. Rev. C 96, 024004 (2017)] are unable to reproduce the experimental phase shifts in the $3/{2}^{\ensuremath{-}}$ channel within the estimated chiral truncation errors. Closer agreement with empirical data is found when using an older parametrization of the NN interaction at order ${\mathrm{N}}^{3}\mathrm{LO}$ [Entem and Machledit, Phys. Rev. C 68, 041001(R) (2017)], and the position and width of the $P$-wave resonances can be used to reduce the uncertainty of the 3N low-energy constants.Conclusions: The present results point to a lack of spin-orbit strength when the newer parametrization of the chiral NN force up to fifth order is combined with the leading-order 3N force. The inclusion of higher-order 3N-force terms may be required to recover the missing strength. GPMs can act as fast and accurate emulators of ab initio many-body calculations of low-energy scattering and reactions of light nuclei, opening the way to a robust quantification of theoretical uncertainties grounded in the description of the underlying chiral Hamiltonian.
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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 | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| 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".