K. Wendt

Uncertainty Analysis and Order-by-Order Optimization of Chiral Nuclear Interactions

Chiral effective field theory (chi EFT) provides a systematic approach to describe low-energy nuclear forces. Moreover, chi EFT is able to provide well-founded estimates of statistical and systematic uncertainties-although this unique advantage has not yet been fully exploited. We fill this gap by performing an optimization and statistical analysis of all the low-energy constants (LECs) up to next-to-next-to-leading order. Our optimization protocol corresponds to a simultaneous fit to scattering and bound-state observables in the pion-nucleon, nucleon-nucleon, and few-nucleon sectors, thereby utilizing the full model capabilities of chi EFT. Finally, we study the effect on other observables by demonstrating forward-error-propagation methods that can easily be adopted by future works. We employ mathematical optimization and implement automatic differentiation to attain efficient and machine-precise first-and second-order derivatives of the objective function with respect to the LECs. This is also vital for the regression analysis. We use power-counting arguments to estimate the systematic uncertainty that is inherent to chi EFT, and we construct chiral interactions at different orders with quantified uncertainties. Statistical error propagation is compared with Monte Carlo sampling, showing that statistical errors are, in general, small compared to systematic ones. In conclusion, we find that a simultaneous fit to different sets of data is critical to (i) identify the optimal set of LECs, (ii) capture all relevant correlations, (iii) reduce the statistical uncertainty, and (iv) attain order-by-order convergence in chi EFT. Furthermore, certain systematic uncertainties in the few-nucleon sector are shown to get substantially magnified in the many-body sector, in particular when varying the cutoff in the chiral potentials. The methodology and results presented in this paper open a new frontier for uncertainty quantification in ab initio nuclear theory.

Effects of Three-Nucleon Forces and Two-Body Currents on Gamow-Teller Strengths

We optimize chiral interactions at next-to-next-to leading order to observables in two- and three-nucleon systems and compute Gamow-Teller transitions in 14C and (22,24)O using consistent two-body currents. We compute spectra of the daughter nuclei 14N and (22,24)F via an isospin-breaking coupled-cluster technique, with several predictions. The two-body currents reduce the Ikeda sum rule, corresponding to a quenching factor q2≈0.84-0.92 of the axial-vector coupling. The half-life of 14C depends on the energy of the first excited 1+ state, the three-nucleon force, and the two-body current.

Coupled-cluster calculations of nucleonic matter

Background: The equation of state (EoS) of nucleonic matter is central for the understanding of bulk nuclear properties, the physics of neutron star crusts, and the energy release in supernova explosions. Because nuclear matter exhibits a nely tuned saturation point, its EoS also constrains nuclear interactions. Purpose: This work presents coupled-cluster calculations of innite nucleonic matter using modern interactions from chiral eective eld theory (EFT). It assesses the role of correlations beyond particle-particle and hole-hole ladders, and the role of three-nucleon-forces (3NFs) in nuclear matter calculations with chiral interactions. Methods: This work employs the optimized nucleon-nucleon (NN) potential NNLOopt at next-tonext-to leading-order, and presents coupled-cluster computations of the EoS for symmetric nuclear matter and neutron matter. The coupled-cluster method employs up to selected triples clusters and the single-particle space consists of a momentum-space lattice. We compare our results with benchmark calculations and control nite-size eects and shell oscillations via twist-averaged boundary conditions. Results: We provide several benchmarks to validate the formalism and show that our results exhibit a good convergence toward the thermodynamic limit. Our calculations agree well with recent coupled-cluster results based on a partial wave expansion and particle-particle and hole-hole ladders. For neutron matter at low densities, and for simple potential models, our calculations agree with results from quantum Monte Carlo computations. While neutron matter with interactions from chiral EFT is perturbative, symmetric nuclear matter requires nonperturbative approaches. Correlations beyond the standard particle-particle ladder approximation yield non-negligible contributions. The saturation point of symmetric nuclear matter is sensitive to the employed 3NFs and the employed regularization scheme. 3NFs with nonlocal cutos exhibit a considerably improved convergence than their local cousins. We are unable to nd values for the parameters of the short-range part of the local 3NF that simultaneously yield acceptable values for the saturation point in symmetric nuclear matter and the binding energies of light nuclei. Conclusions: Coupled-cluster calculations with nuclear interactions from chiral EFT yield nonperturbative results for the EoS of nucleonic matter. Finite-size eects and eects

Infrared length scale and extrapolations for the no-core shell model

We precisely determine the infrared (IR) length scale of the no-core shell model (NCSM). In the NCSM, the A-body Hilbert space is truncated by the total energy, and the IR length can be determined by equating the intrinsic kinetic energy of A nucleons in the NCSM space to that of A nucleons in a 3(A - 1)-dimensional hyper-radial well with a Dirichlet boundary condition for the hyper radius. We demonstrate that this procedure indeed yields a very precise IR length by performing large-scale NCSM calculations for Li-6. We apply our result and perform accurate IR extrapolations for bound states of He-4, He-6, Li-6, and Li-7. We also attempt to extrapolate NCSM results for B-10 and O-16 with bare interactions from chiral effective field theory over tens of MeV.

Infrared extrapolations for atomic nuclei

Harmonic oscillator model-space truncations introduce systematic errors to the calculation of binding energies and other observables. We identify the relevant infrared (IR) scaling variable and give values for this nucleus-dependent quantity. We consider isotopes of oxygen computed with the coupled-cluster method from chiral nucleon–nucleon interactions at next-to-next-to-leading order and show that the IR component of the error is sufficiently understood to permit controlled extrapolations. By employing oscillator spaces with relatively large frequencies, well above the energy minimum, the ultraviolet corrections can be suppressed while IR extrapolations over tens of MeVs are accurate for ground-state energies. However, robust uncertainty quantification for extrapolated quantities that fully accounts for systematic errors is not yet developed.

Statistical uncertainties of a chiral interaction at next-to-next-to leading order

We have quantified the statistical uncertainties of the low-energy coupling-constants (LECs) of an optimized nucleon-nucleon interaction from chiral effective field theory at next-to-next-to-leading order. In addition, we have propagated the impact of the uncertainties of the LECs to two-nucleon scattering phase shifts, effective range parameters, and deuteron observables.

arXiv : Dipole and quadrupole moments of

Nuclear spins and precise values of the magnetic dipole and electric quadrupole moments of the ground-states of neutron-rich

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Cu as a test of the robustness of the

Cu isotopes were measured using the Collinear Resonance Ionization Spectroscopy (CRIS) experiment at ISOLDE, CERN. The nuclear moments of the less exotic

Z=28

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