Nucleus-Dependent Valence-Space Approach to Nuclear Structure

Opportunities for fundamental physics research with radioactive molecules

Molecules containing short-lived, radioactive nuclei are uniquely positioned to enable a wide range of scientific discoveries in the areas of fundamental symmetries, astrophysics, nuclear structure, and chemistry. Recent advances in the ability to create, cool, and control complex molecules down to the quantum level, along with recent and upcoming advances in radioactive species production at several facilities around the world, create a compelling opportunity to coordinate and combine these efforts to bring precision measurement and control to molecules containing extreme nuclei. In this manuscript, we review the scientific case for studying radioactive molecules, discuss recent atomic, molecular, nuclear, astrophysical, and chemical advances which provide the foundation for their study, describe the facilities where these species are and will be produced, and provide an outlook for the future of this nascent field.

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.

Wavefunction matching for solving quantum many-body problems

Ab initio calculations have an essential role in our fundamental understanding of quantum many-body systems across many subfields, from strongly correlated fermions1-3 to quantum chemistry4-6 and from atomic and molecular systems7-9 to nuclear physics10-14. One of the primary challenges is to perform accurate calculations for systems where the interactions may be complicated and difficult for the chosen computational method to handle. Here we address the problem by introducing an approach called wavefunction matching. Wavefunction matching transforms the interaction between particles so that the wavefunctions up to some finite range match that of an easily computable interaction. This allows for calculations of systems that would otherwise be impossible owing to problems such as Monte Carlo sign cancellations. We apply the method to lattice Monte Carlo simulations15,16 of light nuclei, medium-mass nuclei, neutron matter and nuclear matter. We use high-fidelity chiral effective field theory interactions17,18 and find good agreement with empirical data. These results are accompanied by insights on the nuclear interactions that may help to resolve long-standing challenges in accurately reproducing nuclear binding energies, charge radii and nuclear-matter saturation in ab initio calculations19,20.

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.

Nuclear Charge Radii of Silicon Isotopes

The nuclear charge radius of ^{32}Si was determined using collinear laser spectroscopy. The experimental result was confronted with ab initio nuclear lattice effective field theory, valence-space in-medium similarity renormalization group, and mean field calculations, highlighting important achievements and challenges of modern many-body methods. The charge radius of ^{32}Si completes the radii of the mirror pair ^{32}Ar-^{32}Si, whose difference was correlated to the slope L of the symmetry energy in the nuclear equation of state. Our result suggests L≤60  MeV, which agrees with complementary observables.

Precision Mass Measurement of the Proton Dripline Halo Candidate ^{22}Al

We report the first mass measurement of the proton-halo candidate ^{22}Al performed with the low energy beam ion trap facility's 9.4 T Penning trap mass spectrometer at facility for rare isotope beams. This measurement completes the mass information for the lightest remaining proton-dripline nucleus achievable with Penning traps. ^{22}Al has been the subject of recent interest regarding a possible halo structure from the observation of an exceptionally large isospin asymmetry [J. Lee et al., Large isospin asymmetry in Si22/O22 Mirror Gamow-Teller transitions reveals the halo structure of ^{22}Al, Phys. Rev. Lett. 125, 192503 (2020).PRLTAO0031-900710.1103/PhysRevLett.125.192503]. The measured mass excess value of ME=18 092.5(3)  keV, corresponding to an exceptionally small proton separation energy of S_{p}=100.4(8)  keV, is compatible with the suggested halo structure. Our result agrees well with predictions from sd-shell USD Hamiltonians. While USD Hamiltonians predict deformation in the ^{22}Al ground state with minimal 1s_{1/2} occupation in the proton shell, a particle-plus-rotor model in the continuum suggests that a proton halo could form at large quadrupole deformation. These results emphasize the need for a charge radius measurement to conclusively determine the halo nature.

Surprising Charge-Radius Kink in the Sc Isotopes at N=20

Charge radii of neutron deficient ^{40}Sc and ^{41}Sc nuclei were determined using collinear laser spectroscopy. With the new data, the chain of Sc charge radii extends below the neutron magic number N=20 and shows a pronounced kink, generally taken as a signature of a shell closure, but one notably absent in the neighboring Ca, K, and Ar isotopic chains. Theoretical models that explain the trend at N=20 for the Ca isotopes cannot reproduce this puzzling behavior.

Isomeric Excitation Energy for ^{99}In^{m} from Mass Spectrometry Reveals Constant Trend Next to Doubly Magic ^{100}Sn

The excitation energy of the 1/2^{-} isomer in ^{99}In at N=50 is measured to be 671(37) keV and the mass uncertainty of the 9/2^{+} ground state is significantly reduced using the ISOLTRAP mass spectrometer at ISOLDE/CERN. The measurements exploit a major improvement in the resolution of the multireflection time-of-flight mass spectrometer. The results reveal an intriguing constancy of the 1/2^{-} isomer excitation energies in neutron-deficient indium that persists down to the N=50 shell closure, even when all neutrons are removed from the valence shell. This trend is used to test large-scale shell model, ab initio, and density functional theory calculations. The models have difficulties describing both the isomer excitation energies and ground-state electromagnetic moments along the indium chain.

Microsecond Isomer at the N=20 Island of Shape Inversion Observed at FRIB

Excited-state spectroscopy from the first experiment at the Facility for Rare Isotope Beams (FRIB) is reported. A 24(2)-μs isomer was observed with the FRIB Decay Station initiator (FDSi) through a cascade of 224- and 401-keV γ rays in coincidence with ^{32}Na nuclei. This is the only known microsecond isomer (1  μs≤T_{1/2}<1  ms) in the region. This nucleus is at the heart of the N=20 island of shape inversion and is at the crossroads of the spherical shell-model, deformed shell-model, and ab initio theories. It can be represented as the coupling of a proton hole and neutron particle to ^{32}Mg, ^{32}Mg+π^{-1}+ν^{+1}. This odd-odd coupling and isomer formation provides a sensitive measure of the underlying shape degrees of freedom of ^{32}Mg, where the onset of spherical-to-deformed shape inversion begins with a low-lying deformed 2^{+} state at 885 keV and a low-lying shape-coexisting 0_{2}^{+} state at 1058 keV. We suggest two possible explanations for the 625-keV isomer in ^{32}Na: a 6^{-} spherical shape isomer that decays by E2 or a 0^{+} deformed spin isomer that decays by M2. The present results and calculations are most consistent with the latter, indicating that the low-lying states are dominated by deformation.

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.

Charge Radii of ^{55,56}Ni Reveal a Surprisingly Similar Behavior at N=28 in Ca and Ni Isotopes

Nuclear charge radii of ^{55,56}Ni were measured by collinear laser spectroscopy. The obtained information completes the behavior of the charge radii at the shell closure of the doubly magic nucleus ^{56}Ni. The trend of charge radii across the shell closures in calcium and nickel is surprisingly similar despite the fact that the ^{56}Ni core is supposed to be much softer than the ^{48}Ca core. The very low magnetic moment μ(^{55}Ni)=-1.108(20)  μ_{N} indicates the impact of M1 excitations between spin-orbit partners across the N,Z=28 shell gaps. Our charge-radii results are compared to ab initio and nuclear density functional theory calculations, showing good agreement within theoretical uncertainties.

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.

Quasifree Neutron Knockout Reaction Reveals a Small s-Orbital Component in the Borromean Nucleus ^{17}B

A kinematically complete quasifree (p,pn) experiment in inverse kinematics was performed to study the structure of the Borromean nucleus ^{17}B, which had long been considered to have a neutron halo. By analyzing the momentum distributions and exclusive cross sections, we obtained the spectroscopic factors for 1s_{1/2} and 0d_{5/2} orbitals, and a surprisingly small percentage of 9(2)% was determined for 1s_{1/2}. Our finding of such a small 1s_{1/2} component and the halo features reported in prior experiments can be explained by the deformed relativistic Hartree-Bogoliubov theory in continuum, revealing a definite but not dominant neutron halo in ^{17}B. The present work gives the smallest s- or p-orbital component among known nuclei exhibiting halo features and implies that the dominant occupation of s or p orbitals is not a prerequisite for the occurrence of a neutron halo.

Precision Mass Measurements of Neutron-Rich Scandium Isotopes Refine the Evolution of N=32 and N=34 Shell Closures

We report high-precision mass measurements of ^{50-55}Sc isotopes performed at the LEBIT facility at NSCL and at the TITAN facility at TRIUMF. Our results provide a substantial reduction of their uncertainties and indicate significant deviations, up to 0.7 MeV, from the previously recommended mass values for ^{53-55}Sc. The results of this work provide an important update to the description of emerging closed-shell phenomena at neutron numbers N=32 and N=34 above proton-magic Z=20. In particular, they finally enable a complete and precise characterization of the trends in ground state binding energies along the N=32 isotone, confirming that the empirical neutron shell gap energies peak at the doubly magic ^{52}Ca. Moreover, our data, combined with other recent measurements, do not support the existence of a closed neutron shell in ^{55}Sc at N=34. The results were compared to predictions from both ab initio and phenomenological nuclear theories, which all had success describing N=32 neutron shell gap energies but were highly disparate in the description of the N=34 isotone.

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 Nuclear Thermodynamics

We propose a new Monte Carlo method called the pinhole trace algorithm for ab initio calculations of the thermodynamics of nuclear systems. For typical simulations of interest, the computational speedup relative to conventional grand-canonical ensemble calculations can be as large as a factor of one thousand. Using a leading-order effective interaction that reproduces the properties of many atomic nuclei and neutron matter to a few percent accuracy, we determine the location of the critical point and the liquid-vapor coexistence line for symmetric nuclear matter with equal numbers of protons and neutrons. We also present the first ab initio study of the density and temperature dependence of nuclear clustering.

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.

Ab Initio Treatment of Collective Correlations and the Neutrinoless Double Beta Decay of ^{48}Ca

Working with Hamiltonians from chiral effective field theory, we develop a novel framework for describing arbitrary deformed medium-mass nuclei by combining the in-medium similarity renormalization group with the generator coordinate method. The approach leverages the ability of the first method to capture dynamic correlations and the second to include collective correlations without violating symmetries. We use our scheme to compute the matrix element that governs the neutrinoless double beta decay of ^{48}Ca to ^{48}Ti, and find it to have the value 0.61, near or below the predictions of most phenomenological methods. The result opens the door to ab initio calculations of the matrix elements for the decay of heavier nuclei such as ^{76}Ge, ^{130}Te, and ^{136}Xe.

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.

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.

How Robust is the N=34 Subshell Closure? First Spectroscopy of ^{52}Ar

The first γ-ray spectroscopy of ^{52}Ar, with the neutron number N=34, was measured using the ^{53}K(p,2p) one-proton removal reaction at ∼210  MeV/u at the RIBF facility. The 2_{1}^{+} excitation energy is found at 1656(18) keV, the highest among the Ar isotopes with N>20. This result is the first experimental signature of the persistence of the N=34 subshell closure beyond ^{54}Ca, i.e., below the magic proton number Z=20. Shell-model calculations with phenomenological and chiral-effective-field-theory interactions both reproduce the measured 2_{1}^{+} systematics of neutron-rich Ar isotopes, and support a N=34 subshell closure in ^{52}Ar.

Neutron Drip Line in the Ca Region from Bayesian Model Averaging

The region of heavy calcium isotopes forms the frontier of experimental and theoretical nuclear structure research where the basic concepts of nuclear physics are put to stringent test. The recent discovery of the extremely neutron-rich nuclei around ^{60}Ca O. B. Tarasov et al. [Phys. Rev. Lett. 121, 022501 (2018)10.1103/PhysRevLett.121.022501] and the experimental determination of masses for ^{55-57}Ca S. Michimasa et al. [Phys. Rev. Lett. 121, 022506 (2018)10.1103/PhysRevLett.121.022506] provide unique information about the binding energy surface in this region. To assess the impact of these experimental discoveries on the nuclear landscape's extent, we use global mass models and statistical machine learning to make predictions, with quantified levels of certainty, for bound nuclides between Si and Ti. Using a Bayesian model averaging analysis based on Gaussian-process-based extrapolations we introduce the posterior probability p_{ex} for each nucleus to be bound to neutron emission. We find that extrapolations for drip-line locations, at which the nuclear binding ends, are consistent across the global mass models used, in spite of significant variations between their raw predictions. In particular, considering the current experimental information and current global mass models, we predict that ^{68}Ca has an average posterior probability p_{ex}≈76% to be bound to two-neutron emission while the nucleus ^{61}Ca is likely to decay by emitting a neutron (p_{ex}≈46%).

Magic Nature of Neutrons in ^{54}Ca: First Mass Measurements of ^{55-57}Ca

We perform the first direct mass measurements of neutron-rich calcium isotopes beyond neutron number 34 at the RIKEN Radioactive Isotope Beam Factory by using the time-of-flight magnetic-rigidity technique. The atomic mass excesses of ^{55-57}Ca are determined for the first time to be -18650(160), -13510(250), and -7370(990)  keV, respectively. We examine the emergence of neutron magicity at N=34 based on the new atomic masses. The new masses provide experimental evidence for the appearance of a sizable energy gap between the neutron 2p_{1/2} and 1f_{5/2} orbitals in ^{54}Ca, comparable to the gap between the neutron 2p_{3/2} and 2p_{1/2} orbitals in ^{52}Ca. For the ^{56}Ca nucleus, an open-shell property in neutrons is suggested.

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.

Ab initio Calculations of the Isotopic Dependence of Nuclear Clustering

Nuclear clustering describes the appearance of structures resembling smaller nuclei such as alpha particles (^{4}He nuclei) within the interior of a larger nucleus. In this Letter, we present lattice Monte Carlo calculations based on chiral effective field theory for the ground states of helium, beryllium, carbon, and oxygen isotopes. By computing model-independent measures that probe three- and four-nucleon correlations at short distances, we determine the shape of the alpha clusters and the entanglement of nucleons comprising each alpha cluster with the outside medium. We also introduce a new computational approach called the pinhole algorithm, which solves a long-standing deficiency of auxiliary-field Monte Carlo simulations in computing density correlations relative to the center of mass. We use the pinhole algorithm to determine the proton and neutron density distributions and the geometry of cluster correlations in ^{12}C, ^{14}C, and ^{16}C. The structural similarities among the carbon isotopes suggest that ^{14}C and ^{16}C have excitations analogous to the well-known Hoyle state resonance in ^{12}C.

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.