Radii and Binding Energies in Oxygen Isotopes: A Challenge for Nuclear Forces

Trends of Neutron Skins and Radii of Mirror Nuclei from First Principles

The neutron skin of atomic nuclei impacts the structure of neutron-rich nuclei, the equation of state of nucleonic matter, and the size of neutron stars. Here we predict the neutron skin of selected light- and medium-mass nuclei using coupled-cluster theory and the auxiliary field diffusion Monte Carlo method with two- and three-nucleon forces from chiral effective field theory. We find a linear correlation between the neutron skin and the isospin asymmetry in agreement with the liquid-drop model and compare with data. We also extract the linear relationship that describes the difference between neutron and proton radii of mirror nuclei and quantify the effect of charge symmetry breaking terms in the nuclear Hamiltonian. Our results for the mirror-difference charge radii and binding energies per nucleon agree with existing data.

Extended p_{3/2} Neutron Orbital and the N=32 Shell Closure in ^{52}Ca

The one-neutron knockout from ^{52}Ca in inverse kinematics onto a proton target was performed at ∼230  MeV/nucleon combined with prompt γ spectroscopy. Exclusive quasifree scattering cross sections to bound states in ^{51}Ca and the momentum distributions corresponding to the removal of 1f_{7/2} and 2p_{3/2} neutrons were measured. The cross sections, interpreted within the distorted-wave impulse approximation reaction framework, are consistent with a shell closure at the neutron number N=32, found as strong as at N=28 and N=34 in Ca isotopes from the same observables. The analysis of the momentum distributions leads to a difference of the root-mean-square radii of the neutron 1f_{7/2} and 2p_{3/2} orbitals of 0.61(23) fm, in agreement with the modified-shell-model prediction of 0.7 fm suggesting that the large root-mean-square radius of the 2p_{3/2} orbital in neutron-rich Ca isotopes is responsible for the unexpected linear increase of the charge radius with the neutron number.

Proton Distribution Radii of ^{16-24}O: Signatures of New Shell Closures and Neutron Skin

The root mean square radii of the proton density distribution in ^{16-24}O derived from measurements of charge changing cross sections with a carbon target at ∼900A  MeV together with the matter radii portray thick neutron skin for ^{22-24}O despite ^{22,24}O being doubly magic. Imprints of the shell closures at N=14 and 16 are reflected in local minima of their proton radii that provide evidence for the tensor interaction causing them. The radii agree with ab initio calculations employing the chiral NNLO_{sat} interaction, though skin thickness predictions are challenged. Shell model predictions agree well with the data.

Convergence of Eigenvector Continuation

Eigenvector continuation is a computational method that finds the extremal eigenvalues and eigenvectors of a Hamiltonian matrix with one or more control parameters. It does this by projection onto a subspace of eigenvectors corresponding to selected training values of the control parameters. The method has proven to be very efficient and accurate for interpolating and extrapolating eigenvectors. However, almost nothing is known about how the method converges, and its rapid convergence properties have remained mysterious. In this Letter, we present the first study of the convergence of eigenvector continuation. In order to perform the mathematical analysis, we introduce a new variant of eigenvector continuation that we call vector continuation. We first prove that eigenvector continuation and vector continuation have identical convergence properties and then analyze the convergence of vector continuation. Our analysis shows that, in general, eigenvector continuation converges more rapidly than perturbation theory. The faster convergence is achieved by eliminating a phenomenon that we call differential folding, the interference between nonorthogonal vectors appearing at different orders in perturbation theory. From our analysis we can predict how eigenvector continuation converges both inside and outside the radius of convergence of perturbation theory. While eigenvector continuation is a nonperturbative method, we show that its rate of convergence can be deduced from power series expansions of the eigenvectors. Our results also yield new insights into the nature of divergences in perturbation theory.

Ab Initio Computation of Charge Densities for Sn and Xe Isotopes

We present the first ab initio calculations for open-shell nuclei past the tin isotopic line, focusing on Xe isotopes as well as doubly magic Sn isotopes. We show that, even for moderately hard interactions, it is possible to obtain meaningful predictions and that the NNLO_{sat} chiral interaction predicts radii and charge density distributions close to the experiment. We then make a new prediction for ^{100}Sn. This paves the way for ab initio studies of exotic charge density distributions at the limit of the present ab initio mass domain, where experimental data is becoming available. The present study closes the gap between the largest isotopes reachable by ab initio methods and the smallest exotic nuclei accessible to electron scattering experiments.

Global Sensitivity Analysis of Bulk Properties of an Atomic Nucleus

We perform a global sensitivity analysis of the binding energy and the charge radius of the nucleus ^{16}O to identify the most influential low-energy constants in the next-to-next-to-leading order chiral Hamiltonian with two- and three-nucleon forces. For this purpose, we develop a subspace-projected coupled-cluster method using eigenvector continuation [Frame D. et al., Phys. Rev. Lett. 121, 032501 (2018)PRLTAO0031-900710.1103/PhysRevLett.121.032501]. With this method, we compute the binding energy and charge radius of ^{16}O at more than 10^{6} different values of the 16 low-energy constants in one hour on a standard laptop computer. For relatively small subspace projections, the root-mean-square error is about 1% compared to full-space coupled-cluster results. We find that 58(1)% of the variance in energy can be apportioned to a single contact term in the ^{3}S_{1} wave, whereas the radius depends sensitively on several low-energy constants and their higher-order correlations. The results identify the most important parameters for describing nuclear saturation and help prioritize efforts for uncertainty reduction of theoretical predictions. The achieved acceleration opens up an array of computational statistics analyses of the underlying description of the strong nuclear interaction in nuclei across the Segrè chart.

Quasifree Neutron Knockout from ^{54}Ca Corroborates Arising N=34 Neutron Magic Number

Exclusive cross sections and momentum distributions have been measured for quasifree one-neutron knockout reactions from a ^{54}Ca beam striking on a liquid hydrogen target at ∼200  MeV/u. A significantly larger cross section to the p_{3/2} state compared to the f_{5/2} state observed in the excitation of ^{53}Ca provides direct evidence for the nature of the N=34 shell closure. This finding corroborates the arising of a new shell closure in neutron-rich calcium isotopes. The distorted-wave impulse approximation reaction formalism with shell model calculations using the effective GXPF1Bs interaction and ab initio calculations concur our experimental findings. Obtained transverse and parallel momentum distributions demonstrate the sensitivity of quasifree one-neutron knockout in inverse kinematics on a thick liquid hydrogen target with the reaction vertex reconstructed to final state spin-parity assignments.

Ab Initio Optical Potentials and Nucleon Scattering on Medium Mass Nuclei

We derive ab initio optical potentials from self-consistent Green's function theory and compute the elastic scattering of neutrons off oxygen and calcium isotopes. The comparison with scattering data is satisfactory at low scattering energies. The method is benchmarked against the no-core shell model with continuum calculations, showing that virtual excitations of the target are crucial to predict proper fragmentation and absorption at higher energies. This is a significant step toward deriving optical potentials for medium mass nuclei and complex many-body systems in general.

Quasifree (p, 2p) Reactions on Oxygen Isotopes: Observation of Isospin Independence of the Reduced Single-Particle Strength

Quasifree one-proton knockout reactions have been employed in inverse kinematics for a systematic study of the structure of stable and exotic oxygen isotopes at the R^{3}B/LAND setup with incident beam energies in the range of 300-450  MeV/u. The oxygen isotopic chain offers a large variation of separation energies that allows for a quantitative understanding of single-particle strength with changing isospin asymmetry. Quasifree knockout reactions provide a complementary approach to intermediate-energy one-nucleon removal reactions. Inclusive cross sections for quasifree knockout reactions of the type ^{A}O(p,2p)^{A-1}N have been determined and compared to calculations based on the eikonal reaction theory. The reduction factors for the single-particle strength with respect to the independent-particle model were obtained and compared to state-of-the-art ab initio predictions. The results do not show any significant dependence on proton-neutron asymmetry.

The equation of motion phonon method and its application in the neutron rich oxygen region

An equation of motion phonon method, developed for even-even nuclear systems and extended to odd nuclei, is applied to 22O and to its odd neighbors 23O and 23F. A calculation using the chiral potential NNLOopt is carried out in a space encompassing up to two phonons. The computed dipole cross section in 22O and the spectra of 22O and 23O are in a satisfactory agreement with the experimental data. However, the calculation describes poorly the spectrum of 23F. This discrepancy originates from the strong coupling between the odd proton and the 22O phonons of neutron nature. This coupling pushes down in energy several states enhancing the level density at low energy. We suggest that a viable route for the solution of this problem could be the inclusion of the three-body interaction using the new chiral potential NNLOsat.

Status and future of nuclear matrix elements for neutrinoless double-beta decay: a review

The nuclear matrix elements that govern the rate of neutrinoless double beta decay must be accurately calculated if experiments are to reach their full potential. Theorists have been working on the problem for a long time but have recently stepped up their efforts as ton-scale experiments have begun to look feasible. Here we review past and recent work on the matrix elements in a wide variety of nuclear models and discuss work that will be done in the near future. Ab initio nuclear-structure theory, which is developing rapidly, holds out hope of more accurate matrix elements with quantifiable error bars.