A. Ekström

0(gs)+ -->2(1)+ transition strengths in 106Sn and 108Sn.

The reduced transition probabilities, B(E2; 0(gs)+ -->2(1)+), have been measured in the radioactive isotopes (108,106)Sn using subbarrier Coulomb excitation at the REX-ISOLDE facility at CERN. Deexcitation gamma rays were detected by the highly segmented MINIBALL Ge-detector array. The results, B(E2;0(gs)+ -->2(1)+)=0.222(19)e2b2 for 108Sn and B(E2; 0(gs)+-->2(1)+)=0.195(39)e2b2 for 106Sn were determined relative to a stable 58Ni target. The resulting B(E2) values are approximately 30% larger than shell-model predictions and deviate from the generalized seniority model. This experimental result may point towards a weakening of the N=Z=50 shell closure.

Universal properties of infrared oscillator basis extrapolations

these formulas by studying two-body models and the deuteron. We accurately determine the box size as a function of the model space parameters, and compute scattering phase shifts in the harmonic oscillator basis. We show that the energy shift can be well approximated in terms of the asymptotic normalization coecient and the bound-state momentum, discuss higher-order corrections for weakly bound systems, and illustrate this universal property using unitarily equivalent calculations of the deuteron.

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.

Spectroscopic Quadrupole Moments in {96,98}Sr: Evidence for Shape Coexistence in Neutron-Rich Strontium Isotopes at N=60.

Neutron-rich {96,98}Sr isotopes have been investigated by safe Coulomb excitation of radioactive beams at the REX-ISOLDE facility. Reduced transition probabilities and spectroscopic quadrupole moments have been extracted from the differential Coulomb excitation cross sections. These results allow, for the first time, the drawing of definite conclusions about the shape coexistence of highly deformed prolate and spherical configurations. In particular, a very small mixing between the coexisting states is observed, contrary to other mass regions where strong mixing is present. Experimental results have been compared to beyond-mean-field calculations using the Gogny D1S interaction in a five-dimensional collective Hamiltonian formalism, which reproduce the shape change at N=60.

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.

Δ isobars and nuclear saturation

We construct a nuclear interaction in chiral effective field theory with explicit inclusion of the Δ-isobar Δ(1232) degree of freedom at all orders up to next-to-next-to-leading order (NNLO). We use pion-nucleon (πN) low-energy constants (LECs) from a Roy-Steiner analysis of πN scattering data, optimize the LECs in the contact potentials up to NNLO to reproduce low-energy nucleon-nucleon scattering phase shifts, and constrain the three-nucleon interaction at NNLO to reproduce the binding energy and point-proton radius of He4. For heavier nuclei we use the coupled-cluster method to compute binding energies, radii, and neutron skins. We find that radii and binding energies are much improved for interactions with explicit inclusion of Δ(1232), while Δ-less interactions produce nuclei that are not bound with respect to breakup into α particles. The saturation of nuclear matter is significantly improved, and its symmetry energy is consistent with empirical estimates.

Uncertainty quantification for proton-proton fusion in chiral effective field theory

We compute the S-factor of the proton-proton (pp) fusion reaction using chiral effective field theory (chi EFT) up to next-to-next-to-leading order (NNLO) and perform a rigorous uncertainty analysis of the results. We quantify the uncertainties due to (i) the computational method used to compute the pp cross section in momentum space, (ii) the statistical uncertainties in the low-energy coupling constants of chi EFT, (iii) the systematic uncertainty due to the chi EFT cutoff, and (iv) systematic variations in the database used to calibrate the nucleon-nucleon interaction. We also examine the robustness of the polynomial extrapolation procedure, which is commonly used to extract the threshold S-factor and its energy-derivatives. By performing a statistical analysis of the polynomial fit of the energy-dependent S-factor at several different energy intervals, we eliminate a systematic uncertainty that can arise from the choice of the fit interval in our calculations. In addition, we explore the statistical correlations between the S-factor and few-nucleon observables such as the binding energies and point-proton radii of H-2,H-3 and He-3 as well as the D-state probability and quadrupole moment of H-2, and the beta-decay of 3H. We find that, with the state-of-the-art optimization of the nuclear Hamiltonian, the statistical uncertainty in the threshold S-factor cannot be reduced beyond 0.7%.

Collectivity in the light radon nuclei measured directly via Coulomb excitation

Background: Shape coexistence in heavy nuclei poses a strong challenge to state-of-the-art nuclear models, where several competing shape minima are found close to the ground state. A classic region for investigating this phenomenon is in the region around Z = 82 and the neutron midshell at N = 104. Purpose: Evidence for shape coexistence has been inferred from a-decay measurements, laser spectroscopy, and in-beam measurements. While the latter allow the pattern of excited states and rotational band structures to be mapped out, a detailed understanding of shape coexistence can only come from measurements of electromagnetic matrix elements. Method: Secondary, radioactive ion beams of Rn-202 and Rn-204 were studied by means of low-energy Coulomb excitation at the REX-ISOLDE in CERN. Results: The electric-quadrupole (E2) matrix element connecting the ground state and first excited 2(1)(+) state was extracted for both Rn-202 and Rn-204, corresponding to B(E2; 2(1)(+) -> 0(1)(+)) = 29(-8)(+8) and 43(-12)(+17) W.u., respectively. Additionally, E2 matrix elements connecting the 2(1)(+) state with the 4(1)(+) and 2(2)(+) states were determined in Rn-202. No excited 0(+) states were observed in the current data set, possibly owing to a limited population of second-order processes at the currently available beam energies. Conclusions: The results are discussed in terms of collectivity and the deformation of both nuclei studied is deduced to be weak, as expected from the low-lying level-energy schemes. Comparisons are also made to state-of-the-art beyond-mean-field model calculations and the magnitude of the transitional quadrupole moments are well reproduced. (Less)

The deuteron-radius puzzle is alive: A new analysis of nuclear structure uncertainties

To shed light on the deuteron radius puzzle we analyze the theoretical uncertainties of the nuclear structure corrections to the Lamb shift in muonic deuterium. We find that the discrepancy between the calculated two-photon exchange correction and the corresponding experimentally inferred value by Pohl etal. [1] remain. The present result is consistent with our previous estimate, although the discrepancy is reduced from 2.6 sigma about 2 sigma. The error analysis includes statistic as well as systematic uncertainties stemming from the use of nucleon-nucleon interactions derived from chiral effective field theory at various orders. We therefore conclude that nuclear theory uncertainty is more likely not the source of the discrepancy. (c) 2018 The Authors. Published by Elsevier B.V.