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Register a new userQuantifying uncertainties in neutron-alpha scattering with chiral nucleon-nucleon and three-nucleon forces
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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 (N4LO) 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 (cE and cD) contribute to the overall uncertainty budget of many-body calculations of neutron-He 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 an 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.
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We investigate the roles of chiral three-nucleon force (3NF) in nucleon-nucleus elastic scattering, using the standard framework based on the Brueckner-Hartree-Fock method for nuclear matter and the $g$-matrix folding model for the nucleon-nucleus scattering. In nuclear matter, chiral 3NF at NNLO level (mainly the 2$pi$-exchange diagram) makes the single particle potential less attractive for the singlet-even channel and more absorptive for the triplet channels. The single-particle potential calculated from chiral two-nucleon force (2NF) at N$^{3}$LO level is found to be close to that from Bonn-B 2NF. The Melbourne $g$-matrix interaction is a practical effective interaction constructed by localizing the $g$-matrices calculated from Bonn-B 2NF. We then introduce the chiral-3NF effects to the local Melbourne $g$-matrix interaction. For nucleon-nucleus elastic scattering on various targets at 65 MeV, chiral 3NF makes the folding potential less attractive and more absorptive. The novel property for the imaginary part is originated in the enhancement of tensor correlations due to chiral 3NF. The two effects are small for differential cross sections and vector analyzing powers at the forward and middle angles where the experimental data are available. If backward measurements are done, the data will reveal the effects of chiral 3NF.
We apply improved nucleon-nucleon potentials up to fifth order in chiral effective field theory, along with a new analysis of the theoretical truncation errors, to study nucleon-deuteron (Nd) scattering and selected low-energy observables in 3H, 4He, and 6Li. Calculations beyond second order differ from experiment well outside the range of quantified uncertainties, providing truly unambiguous evidence for missing three-nucleon forces within the employed framework. The sizes of the required three-nucleon force contributions agree well with expectations based on Weinbergs power counting. We identify the energy range in elastic Nd scattering best suited to study three-nucleon force effects and estimate the achievable accuracy of theoretical predictions for various observables.
The existence of superfluidity of the neutron component in the core of a neutron star, associated specifically with triplet $P-$wave pairing, is currently an open question that is central to interpretation of the observed cooling curves and other neutron-star observables. Ab initio theoretical calculations aimed at resolving this issue face unique challenges in the relevant high-density domain, which reaches beyond the saturation density of symmetrical nuclear matter. These issues include uncertainties in the three-nucleon (3N) interaction and in the effects of strong short-range correlations -- and more generally of in-medium modification of nucleonic self-energies and interactions. A survey of existing solutions to the gap equations in the triplet channel shows that the separate or combined impacts of 3N forces, coupled channels, and mass renormalization range from moderate to strong to devastating, thus motivating a detailed analysis of the competing effects. In the present work we track the effects of the 3N force and in-medium modifications in the representative case of the $^3P_2$ channel, based on the Argonne V18 two-nucleon (2N) interaction supplemented by 3N interactions of the Urbana IX family. Sensitivity of the results to the input interaction is clearly demonstrated, while consistency issues arise with respect to the simultaneous treatment of 3N forces and in-medium effects. We consider this pilot study as the first step towards a systematic and comprehensive exploration of coupled-channel $^3P F_2$ pairing using a broad range of 2N and 3N interactions from the current generation of refined semi-phenomenological models and models derived from chiral effective field theory.
We employ a variety of ab initio methods including Faddeev-Yakubovsky equations, No-Core Configuration Interaction Approach, Coupled-Cluster Theory and In-Medium Similarity Renormalization Group to perform a comprehensive analysis of the nucleon-deuteron elastic and breakup reactions and selected properties of light and medium-mass nuclei up to 48Ca using the recently constructed semilocal coordinate-space regularized chiral nucleon-nucleon potentials. We compare the results with those based on selected phenomenological and chiral EFT two-nucleon potentials, discuss the convergence pattern of the chiral expansion and estimate the achievable theoretical accuracy at various chiral orders using the novel approach to quantify truncation errors of the chiral expansion without relying on cutoff variation. We also address the robustness of this method and explore alternative ways to estimate the theoretical uncertainty from the truncation of the chiral expansion.
Chiral symmetry allows two and three nucleon forces to be treated in a single theoretical framework. We discuss two new features of this research programme at $cO(q^4)$ and the consistency of the overall chiral picture.
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