Nonperturbative shell-model interactions from the in-medium similarity renormalization group

Electromagnetic properties of nuclei from first principles: a case for synergies between experiment and theory

One of the overarching goals in nuclear science is to understand how the nuclear chart emerges from the underlying fundamental interactions. The description of the structure of nuclei from first principles, using ab initio methods for the solution of the many-nucleon problem with inputs from chiral effective field theory, has advanced dramatically over the past two decades. We present an overview over the available ab initio tools with a specific emphasis on electromagnetic observables, such as multipole moments and transition strengths. These observables still pose a challenge for ab initio theory and are one of the most exciting domains to exploit synergies with modern experiments. Precise experimental data are vital for the validation of the theory predictions and the refinement of ab initio methods. We discuss some of the past and future experimental efforts highlighting these synergies. This article is part of the theme issue 'The liminal position of Nuclear Physics: from hadrons to neutron stars'.

Impact of Two-Body Currents on Magnetic Dipole Moments of Nuclei

We investigate the effects of two-body currents on magnetic dipole moments of medium-mass and heavy nuclei using the valence-space in-medium similarity renormalization group with chiral effective field theory interactions and currents. Focusing on near doubly magic nuclei from oxygen to bismuth, we have found that the leading two-body currents globally improve the agreement with experimental magnetic moments. Moreover, our results show the importance of multishell effects for ^{41}Ca, which suggest that the Z=N=20 gap in ^{40}Ca is not as robust as in ^{48}Ca. The increasing contribution of two-body currents in heavier systems is explained by the operator structure of the center-of-mass dependent Sachs term.

Ab Initio Uncertainty Quantification of Neutrinoless Double-Beta Decay in ^{76}Ge

The observation of neutrinoless double-beta (0νββ) decay would offer proof of lepton number violation, demonstrating that neutrinos are Majorana particles, while also helping us understand why there is more matter than antimatter in the Universe. If the decay is driven by the exchange of the three known light neutrinos, a discovery would, in addition, link the observed decay rate to the neutrino mass scale through a theoretical quantity known as the nuclear matrix element (NME). Accurate values of the NMEs for all nuclei considered for use in 0νββ experiments are therefore crucial for designing and interpreting those experiments. Here, we report the first comprehensive ab initio uncertainty quantification of the 0νββ-decay NME, in the key nucleus ^{76}Ge. Our method employs nuclear strong and weak interactions derived within chiral effective field theory and recently developed many-body emulators. Our result, with a conservative treatment of uncertainty, is an NME of 2.60_{-1.36}^{+1.28}, which, together with the best-existing half-life sensitivity and phase-space factor, sets an upper limit for effective neutrino mass of 187_{-62}^{+205}  meV. The result is important for designing next-generation germanium detectors aiming to cover the entire inverted hierarchy region of neutrino masses.

First observation of 28O

Subjecting a physical system to extreme conditions is one of the means often used to obtain a better understanding and deeper insight into its organization and structure. In the case of the atomic nucleus, one such approach is to investigate isotopes that have very different neutron-to-proton (N/Z) ratios than in stable nuclei. Light, neutron-rich isotopes exhibit the most asymmetric N/Z ratios and those lying beyond the limits of binding, which undergo spontaneous neutron emission and exist only as very short-lived resonances (about 10-21 s), provide the most stringent tests of modern nuclear-structure theories. Here we report on the first observation of 28O and 27O through their decay into 24O and four and three neutrons, respectively. The 28O nucleus is of particular interest as, with the Z = 8 and N = 20 magic numbers1,2, it is expected in the standard shell-model picture of nuclear structure to be one of a relatively small number of so-called 'doubly magic' nuclei. Both 27O and 28O were found to exist as narrow, low-lying resonances and their decay energies are compared here to the results of sophisticated theoretical modelling, including a large-scale shell-model calculation and a newly developed statistical approach. In both cases, the underlying nuclear interactions were derived from effective field theories of quantum chromodynamics. Finally, it is shown that the cross-section for the production of 28O from a 29F beam is consistent with it not exhibiting a closed N = 20 shell structure.

Ab Initio Structure Factors for Spin-Dependent Dark Matter Direct Detection

We present converged ab initio calculations of structure factors for elastic spin-dependent WIMP scattering off all nuclei used in dark matter direct-detection searches: ^{19}F, ^{23}Na, ^{27}Al, ^{29}Si, ^{73}Ge, ^{127}I, and ^{129,131}Xe. From a set of established two- and three-nucleon interactions derived within chiral effective field theory, we construct consistent WIMP-nucleon currents at the one-body level, including effects from axial-vector two-body currents. We then apply the in-medium similarity renormalization group to construct effective valence-space Hamiltonians and consistently transformed operators of nuclear responses. Combining the recent advances of natural orbitals with three-nucleon forces expressed in large spaces, we obtain basis-space converged structure factors even in heavy nuclei. Generally results are consistent with previous calculations but large uncertainties in ^{127}I highlight the need for further study.

Nuclear Charge Radii of the Nickel Isotopes ^{58-68,70}Ni

Collinear laser spectroscopy is performed on the nickel isotopes ^{58-68,70}Ni, using a time-resolved photon counting system. From the measured isotope shifts, nuclear charge radii R_{c} are extracted and compared to theoretical results. Three ab initio approaches all employ, among others, the chiral interaction NNLO_{sat}, which allows an assessment of their accuracy. We find agreement with experiment in differential radii δ⟨r_{c}^{2}⟩ for all employed ab initio methods and interactions, while the absolute radii are consistent with data only for NNLO_{sat}. Within nuclear density functional theory, the Skyrme functional SV-min matches experiment more closely than the Fayans functional Fy(Δr,HFB).

Recent Progress in Gamow Shell Model Calculations of Drip Line Nuclei

The Gamow shell model (GSM) is a powerful method for the description of the exotic properties of drip line nuclei. Internucleon correlations are included via a configuration interaction framework. Continuum coupling is directly included at basis level by using the Berggren basis, in which, bound, resonance, and continuum single-particle states are treated on an equal footing in the complex momentum plane. Two different types of Gamow shell models have been developed: its first embodiment is that of the GSM defined with phenomenological nuclear interactions, whereas the GSM using realistic nuclear interactions, called the realistic Gamow shell model, was introduced later. The present review focuses on the recent applications of the GSM to drip line nuclei.

Ab Initio Neutrinoless Double-Beta Decay Matrix Elements for ^{48}Ca, ^{76}Ge, and ^{82}Se

We calculate basis-space converged neutrinoless ββ-decay nuclear matrix elements for the lightest candidates: ^{48}Ca, ^{76}Ge, and ^{82}Se. Starting from initial two- and three-nucleon forces, we apply the ab initio in-medium similarity renormalization group to construct valence-space Hamiltonians and consistently transformed ββ-decay operators. We find that the tensor component is non-negligible in ^{76}Ge and ^{82}Se, and the resulting nuclear matrix elements are overall 25%-45% smaller than those obtained from the phenomenological shell model. While a final matrix element with uncertainties still requires substantial developments, this work nevertheless opens a path toward a true first-principles calculation of neutrinoless ββ decay in all nuclei relevant for ongoing large-scale searches.

Ab Initio Limits of Atomic Nuclei

We predict the limits of existence of atomic nuclei, the proton and neutron drip lines, from the light through medium-mass regions. Starting from a chiral two- and three-nucleon interaction with good saturation properties, we use the valence-space in-medium similarity renormalization group to calculate ground-state and separation energies from helium to iron, nearly 700 isotopes in total. We use the available experimental data to quantify the theoretical uncertainties for our ab initio calculations towards the drip lines. Where the drip lines are known experimentally, our predictions are consistent within the estimated uncertainty. For the neutron-rich sodium to chromium isotopes, we provide predictions to be tested at rare-isotope beam facilities.

The impact of nuclear shape on the emergence of the neutron dripline

Atomic nuclei are composed of a certain number of protons Z and neutrons N. A natural question is how large Z and N can be. The study of superheavy elements explores the large Z limit^1,2, and we are still looking for a comprehensive theoretical explanation of the largest possible N for a given Z-the existence limit for the neutron-rich isotopes of a given atomic species, known as the neutron dripline³. The neutron dripline of oxygen (Z = 8) can be understood theoretically as the result of single nucleons filling single-particle orbits confined by a mean potential, and experiments confirm this interpretation. However, recent experiments on heavier elements are at odds with this description. Here we show that the neutron dripline from fluorine (Z = 9) to magnesium (Z = 12) can be predicted using a mechanism that goes beyond the single-particle picture: as the number of neutrons increases, the nuclear shape assumes an increasingly ellipsoidal deformation, leading to a higher binding energy. The saturation of this effect (when the nucleus cannot be further deformed) yields the neutron dripline: beyond this maximum N, the isotope is unbound and further neutrons 'drip' out when added. Our calculations are based on a recently developed effective nucleon-nucleon interaction⁴, for which large-scale eigenvalue problems are solved using configuration-interaction simulations. The results obtained show good agreement with experiments, even for excitation energies of low-lying states, up to the nucleus of magnesium-40 (which has 28 neutrons). The proposed mechanism for the formation of the neutron dripline has the potential to stimulate further thinking in the field towards explaining nucleosynthesis with neutron-rich nuclei.

Ab Initio Calculations of Low-Energy Nuclear Scattering Using Confining Potential Traps

A recently modified method to enable low-energy nuclear scattering results to be extracted from the discrete energy levels of the target-projectile clusters confined by harmonic potential traps is tested. We report encouraging results for neutron-α and neutron-^{24}O elastic scattering from analyzing the trapped levels computed using two different ab initio nuclear structure methods. The n-α results have also been checked against a direct ab initio reaction calculation. The n-^{24}O results demonstrate the approach's applicability for a large range of systems provided their spectra in traps can be computed by ab initio methods. A key ingredient is a rigorous understanding of the errors in the calculated energy levels caused by inevitable Hilbert-space truncations in the ab initio methods.

First Glimpse of the N=82 Shell Closure below Z=50 from Masses of Neutron-Rich Cadmium Isotopes and Isomers

We probe the N=82 nuclear shell closure by mass measurements of neutron-rich cadmium isotopes with the ISOLTRAP spectrometer at ISOLDE-CERN. The new mass of ^{132}Cd offers the first value of the N=82, two-neutron shell gap below Z=50 and confirms the phenomenon of mutually enhanced magicity at ^{132}Sn. Using the recently implemented phase-imaging ion-cyclotron-resonance method, the ordering of the low-lying isomers in ^{129}Cd and their energies are determined. The new experimental findings are used to test large-scale shell-model, mean-field, and beyond-mean-field calculations, as well as the ab initio valence-space in-medium similarity renormalization group.

Location of the Neutron Dripline at Fluorine and Neon

A search for the heaviest isotopes of fluorine, neon, and sodium was conducted by fragmentation of an intense ^{48}Ca beam at 345  MeV/nucleon with a 20-mm-thick beryllium target and identification of isotopes in the large-acceptance separator BigRIPS at the RIKEN Radioactive Isotope Beam Factory. No events were observed for ^{32,33}F, ^{35,36}Ne, and ^{38}Na and only one event for ^{39}Na after extensive running. Comparison with predicted yields excludes the existence of bound states of these unobserved isotopes with high confidence levels. The present work indicates that ^{31}F and ^{34}Ne are the heaviest bound isotopes of fluorine and neon, respectively. The neutron dripline has thus been experimentally confirmed up to neon for the first time since ^{24}O was confirmed to be the dripline nucleus nearly 20 years ago. These data provide new keys to understanding the nuclear stability at extremely neutron-rich conditions.

78Ni revealed as a doubly magic stronghold against nuclear deformation

Nuclear magic numbers correspond to fully occupied energy shells of protons or neutrons inside atomic nuclei. Doubly magic nuclei, with magic numbers for both protons and neutrons, are spherical and extremely rare across the nuclear landscape. Although the sequence of magic numbers is well established for stable nuclei, experimental evidence has revealed modifications for nuclei with a large asymmetry between proton and neutron numbers. Here we provide a spectroscopic study of the doubly magic nucleus ⁷⁸Ni, which contains fourteen neutrons more than the heaviest stable nickel isotope. We provide direct evidence of its doubly magic nature, which is also predicted by ab initio calculations based on chiral effective-field theory interactions and the quasi-particle random-phase approximation. Our results also indicate the breakdown of the neutron magic number 50 and proton magic number 28 beyond this stronghold, caused by a competing deformed structure. State-of-the-art phenomenological shell-model calculations reproduce this shape coexistence, predicting a rapid transition from spherical to deformed ground states, with ⁷⁸Ni as the turning point.

Precision Mass Measurements of ^{58-63}Cr: Nuclear Collectivity Towards the N=40 Island of Inversion

The neutron-rich isotopes ^{58-63}Cr were produced for the first time at the ISOLDE facility and their masses were measured with the ISOLTRAP spectrometer. The new values are up to 300 times more precise than those in the literature and indicate significantly different nuclear structure from the new mass-surface trend. A gradual onset of deformation is found in this proton and neutron midshell region, which is a gateway to the second island of inversion around N=40. In addition to comparisons with density-functional theory and large-scale shell-model calculations, we present predictions from the valence-space formulation of the ab initio in-medium similarity renormalization group, the first such results for open-shell chromium isotopes.

Structure of the Lightest Tin Isotopes

We link the structure of nuclei around ^{100}Sn, the heaviest doubly magic nucleus with equal neutron and proton numbers (N=Z=50), to nucleon-nucleon (NN) and three-nucleon (NNN) forces constrained by data of few-nucleon systems. Our results indicate that ^{100}Sn is doubly magic, and we predict its quadrupole collectivity. We present precise computations of ^{101}Sn based on three-particle-two-hole excitations of ^{100}Sn, and we find that one interaction accurately reproduces the small splitting between the lowest J^{π}=7/2^{+} and 5/2^{+} states.

Dawning of the N=32 Shell Closure Seen through Precision Mass Measurements of Neutron-Rich Titanium Isotopes

A precision mass investigation of the neutron-rich titanium isotopes ^{51-55}Ti was performed at TRIUMF's Ion Trap for Atomic and Nuclear science (TITAN). The range of the measurements covers the N=32 shell closure, and the overall uncertainties of the ^{52-55}Ti mass values were significantly reduced. Our results conclusively establish the existence of the weak shell effect at N=32, narrowing down the abrupt onset of this shell closure. Our data were compared with state-of-the-art ab initio shell model calculations which, despite very successfully describing where the N=32 shell gap is strong, overpredict its strength and extent in titanium and heavier isotones. These measurements also represent the first scientific results of TITAN using the newly commissioned multiple-reflection time-of-flight mass spectrometer, substantiated by independent measurements from TITAN's Penning trap mass spectrometer.

Binding Energy of ^{79}Cu: Probing the Structure of the Doubly Magic ^{78}Ni from Only One Proton Away

The masses of the neutron-rich copper isotopes ^{75-79}Cu are determined using the precision mass spectrometer ISOLTRAP at the CERN-ISOLDE facility. The trend from the new data differs significantly from that of previous results, offering a first accurate view of the mass surface adjacent to the Z=28, N=50 nuclide ^{78}Ni and supporting a doubly magic character. The new masses compare very well with large-scale shell-model calculations that predict shape coexistence in a doubly magic ^{78}Ni and a new island of inversion for Z<28. A coherent picture of this important exotic region begins to emerge where excitations across Z=28 and N=50 form a delicate equilibrium with a spherical mean field.

Ab Initio Description of Open-Shell Nuclei: Merging No-Core Shell Model and In-Medium Similarity Renormalization Group

We merge two successful ab initio nuclear-structure methods, the no-core shell model (NCSM) and the multireference in-medium similarity renormalization group (IM-SRG) to define a new many-body approach for the comprehensive description of ground and excited states of closed and open-shell nuclei. Building on the key advantages of the two methods-the decoupling of excitations at the many-body level in the IM-SRG and the access to arbitrary nuclei, eigenstates, and observables in the NCSM-their combination enables fully converged no-core calculations for an unprecedented range of nuclei and observables at moderate computational cost. We present applications in the carbon and oxygen isotopic chains, where conventional NCSM calculations are still feasible and provide an important benchmark. The efficiency and rapid convergence of the new approach make it ideally suited for ab initio studies of the complete spectroscopy of nuclei up into the medium-mass regime.

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.

Nucleus-Dependent Valence-Space Approach to Nuclear Structure

We present a nucleus-dependent valence-space approach for calculating ground and excited states of nuclei, which generalizes the shell-model in-medium similarity renormalization group to an ensemble reference with fractionally filled orbitals. Because the ensemble is used only as a reference, and not to represent physical states, no symmetry restoration is required. This allows us to capture three-nucleon (3N) forces among valence nucleons with a valence-space Hamiltonian specifically targeted to each nucleus of interest. Predicted ground-state energies from carbon through nickel agree with results of other large-space ab initio methods, generally to the 1% level. In addition, we show that this new approach is required in order to obtain convergence for nuclei in the upper p and sd shells. Finally, we address the 1^{+}/3^{+} inversion problem in ^{22}Na and ^{46}V. This approach extends the reach of ab initio nuclear structure calculations to essentially all light- and medium-mass nuclei.

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

We present a systematic study of both nuclear radii and binding energies in (even) oxygen isotopes from the valley of stability to the neutron drip line. Both charge and matter radii are compared to state-of-the-art ab initio calculations along with binding energy systematics. Experimental matter radii are obtained through a complete evaluation of the available elastic proton scattering data of oxygen isotopes. We show that, in spite of a good reproduction of binding energies, ab initio calculations with conventional nuclear interactions derived within chiral effective field theory fail to provide a realistic description of charge and matter radii. A novel version of two- and three-nucleon forces leads to considerable improvement of the simultaneous description of the three observables for stable isotopes but shows deficiencies for the most neutron-rich systems. Thus, crucial challenges related to the development of nuclear interactions remain.

Nucleus ^{26}O: A Barely Unbound System beyond the Drip Line

The unbound nucleus ^{26}O has been investigated using invariant-mass spectroscopy following one-proton removal reaction from a ^{27}F beam at 201  MeV/nucleon. The decay products, ^{24}O and two neutrons, were detected in coincidence using the newly commissioned SAMURAI spectrometer at the RIKEN Radioactive Isotope Beam Factory. The ^{26}O ground-state resonance was found to lie only 18±3(stat)±4(syst)  keV above threshold. In addition, a higher lying level, which is most likely the first 2^{+} state, was observed for the first time at 1.28_{-0.08}^{+0.11}  MeV above threshold. Comparison with theoretical predictions suggests that three-nucleon forces, pf-shell intruder configurations, and the continuum are key elements to understanding the structure of the most neutron-rich oxygen isotopes beyond the drip line.

Ab initio coupled-cluster effective interactions for the shell model: application to neutron-rich oxygen and carbon isotopes

We derive and compute effective valence-space shell-model interactions from ab initio coupled-cluster theory and apply them to open-shell and neutron-rich oxygen and carbon isotopes. Our shell-model interactions are based on nucleon-nucleon and three-nucleon forces from chiral effective-field theory. We compute the energies of ground and low-lying states, and find good agreement with experiment. In particular, our computed 2(+) states are consistent with N = 14,16 shell closures in (22,24)O, and a weaker N=14 shell closure in (20)C. We find good agreement between our coupled-cluster effective-interaction results with those obtained from standard single-reference coupled-cluster calculations for up to eight valence neutrons.