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Register a new user$^{12}$C properties with evolved chiral three-nucleon interactions
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We investigate selected static and transition properties of $^{12}$C using ab initio No-Core Shell Model (NCSM) methods with chiral two- and three-nucleon interactions. We adopt the Similarity Renormalization Group (SRG) to assist convergence including up to three-nucleon (3N) contributions. We examine the dependences of the $^{12}$C observables on the SRG evolution scale and on the model-space parameters. We obtain nearly converged low-lying excitation spectra. We compare results of the full NCSM with the Importance Truncated NCSM in large model spaces for benchmarking purposes. We highlight the effects of the chiral 3N interaction on several spectroscopic observables. The agreement of some observables with experiment is improved significantly by the inclusion of 3N interactions, e.g., the B(M1) from the first $J^pi T = 1^+ 1$ state to the ground state. However, in some cases the agreement deteriorates, e.g., for the excitation energy of the first $1^+ 0$ state, leaving room for improved next-generation chiral Hamiltonians.
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A discussion is presented of the dynamics underlying three-body nuclear forces, with emphasis on changes which occurred over several decades.
We compute the binding energies, radii, and densities for selected medium-mass nuclei within coupled-cluster theory and employ the bare chiral nucleon-nucleon interaction at order N3LO. We find rather well-converged results in model spaces consisting of 15 oscillator shells, and the doubly magic nuclei 40Ca, 48Ca, and the exotic 48Ni are underbound by about 1 MeV per nucleon within the CCSD approximation. The binding-energy difference between the mirror nuclei 48Ca and 48Ni is close to theoretical mass table evaluations. Our computation of the one-body density matrices and the corresponding natural orbitals and occupation numbers provides a first step to a microscopic foundation of the nuclear shell model.
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.
We study ground- and excited-state properties of all sd-shell nuclei with neutron and proton numbers 8 <= N,Z <= 20, based on a set of low-resolution two- and three-nucleon interactions that predict realistic saturation properties of nuclear matter. We focus on estimating the theoretical uncertainties due to variation of the resolution scale, the low-energy couplings, as well as from the many-body method. The experimental two-neutron and two-proton separation energies are reasonably well reproduced, with an uncertainty range of about 5 MeV. The first excited 2+ energies also show overall agreement, with a more narrow uncertainty range of about 500 keV. In most cases, this range is dominated by the uncertainties in the Hamiltonian.
We present a family of nucleon-nucleon (NN) plus three-nucleon (3N) interactions up to N3LO in the chiral expansion that provides an accurate ab initio description of ground-state energies and charge radii up to the medium-mass regime with quantified theory uncertainties. Starting from the NN interactions proposed by Entem, Machleidt and Nosyk, we construct 3N interactions with consistent chiral order, non-local regulator, and cutoff value and explore the dependence of nuclear observables over a range of mass numbers on the 3N low-energy constants. By fixing these constants using the 3-H and 16-O ground-state energies, we obtain interactions that robustly reproduce experimental energies and radii for large range from p-shell nuclei to the nickel isotopic chain and resolve many of the deficiencies of previous interactions. Based on the order-by-order convergence and the cutoff dependence of nuclear observables, we assess the uncertainties due the interaction, which yield a significant contribution to the total theory uncertainty.
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