Ab Initio Uncertainty Quantification of Neutrinoless Double-Beta Decay in

The observation of neutrinoless double-beta (0νßß) 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 0νßß experiments are therefore crucial for designing and interpreting those experiments. Here, we report the first comprehensive ab initio uncertainty quantification of the 0νßß-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 moments of indium isotopes reveal abrupt change at magic number 82.

In spite of the high-density and strongly correlated nature of the atomic nucleus, experimental and theoretical evidence suggests that around particular 'magic' numbers of nucleons, nuclear properties are governed by a single unpaired nucleon1,2. A microscopic understanding of the extent of this behaviour and its evolution in neutron-rich nuclei remains an open question in nuclear physics3-5. The indium isotopes are considered a textbook example of this phenomenon6, in which the constancy of their electromagnetic properties indicated that a single unpaired proton hole can provide the identity of a complex many-nucleon system6,7. Here we present precision laser spectroscopy measurements performed to investigate the validity of this simple single-particle picture. Observation of an abrupt change in the dipole moment at N = 82 indicates that, whereas the single-particle picture indeed dominates at neutron magic number N = 82 (refs. 2,8), it does not for previously studied isotopes. To investigate the microscopic origin of these observations, our work provides a combined effort with developments in two complementary nuclear many-body methods: ab initio valence-space in-medium similarity renormalization group and density functional theory (DFT). We find that the inclusion of time-symmetry-breaking mean fields is essential for a correct description of nuclear magnetic properties, which were previously poorly constrained. These experimental and theoretical findings are key to understanding how seemingly simple single-particle phenomena naturally emerge from complex interactions among protons and neutrons.

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

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).

Ab Initio Neutrinoless Double-Beta Decay Matrix Elements for

We calculate basis-space converged neutrinoless ßß-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 ßß-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 ßß 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.

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.

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

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.

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.

Isomeric Character of the Lowest Observed 4

Previous experiments observed a 4^{+} state in the N=28 nucleus ^{44}S and suggested that this state may exhibit a hindered E2-decay rate, inconsistent with being a member of the collective ground state band. We populate this state via two-proton knockout from a beam of exotic ^{46}Ar projectiles and measure its lifetime using the recoil distance method with the GRETINA γ-ray spectrometer. The result, 76(14)_{stat}(20)_{syst} ps, implies a hindered transition of B(E2;4^{+}→2_{1}^{+})=0.61(19) single-particle or Weisskopf units strength and supports the interpretation of the 4^{+} state as a K=4 isomer, the first example of a high-K isomer in a nucleus of such low mass.

Isospin Symmetry at High Spin Studied via Nucleon Knockout from Isomeric States.

One-neutron knockout reactions have been performed on a beam of radioactive ^{53}Co in a high-spin isomeric state. The analysis is shown to yield a highly selective population of high-spin states in an exotic nucleus with a significant cross section, and hence represents a technique that is applicable to the planned new generation of fragmentation-based radioactive beam facilities. Additionally, the relative cross sections among the excited states can be predicted to a high level of accuracy when reliable shell-model input is available. The work has resulted in a new level scheme, up to the 11^{+} band-termination state, of the proton-rich nucleus ^{52}Co (Z=27, N=25). This has in turn enabled a study of mirror energy differences in the A=52 odd-odd mirror nuclei, interpreted in terms of isospin-nonconserving (INC) forces in nuclei. The analysis demonstrates the importance of using a full set of J-dependent INC terms to explain the experimental observations.

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.

Determining the rp-process flow through 56Ni: resonances in 57Cu(p,γ)58Zn identified with GRETINA.

An approach is presented to experimentally constrain previously unreachable (p, γ) reaction rates on nuclei far from stability in the astrophysical rp process. Energies of all critical resonances in the (57)Cu(p,γ)(58)Zn reaction are deduced by populating states in (58)Zn with a (d, n) reaction in inverse kinematics at 75 MeV/u, and detecting γ-ray-recoil coincidences with the state-of-the-art γ-ray tracking array GRETINA and the S800 spectrograph at the National Superconducting Cyclotron Laboratory. The results reduce the uncertainty in the (57)Cu(p,γ) reaction rate by several orders of magnitude. The effective lifetime of (56)Ni, an important waiting point in the rp process in x-ray bursts, can now be determined entirely from experimentally constrained reaction rates.

ß+ Gamow-Teller transition strengths from 46Ti and stellar electron-capture rates.

The Gamow-Teller strength in the ß(+) direction to (46)Sc was extracted via the (46)Ti(t,(3)He + γ) reaction at 115 MeV/u. The γ-ray coincidences served to precisely measure the very weak Gamow-Teller transition to a final state at 991 keV. Although this transition is weak, it is crucial for accurately estimating electron-capture rates in astrophysical scenarios with relatively low stellar densities and temperatures, such as presupernova stellar evolution. Shell-model calculations with different effective interactions in the pf shell-model space do not reproduce the experimental Gamow-Teller strengths, which is likely due to sd-shell admixtures. Calculations in the quasiparticle random phase approximation that are often used in astrophysical simulations also fail to reproduce the experimental Gamow-Teller strength distribution, leading to strongly overestimated electron-capture rates. Because reliable theoretical predictions of Gamow-Teller strengths are important for providing astrophysical electron-capture reaction rates for a broad set of nuclei in the lower pf shell, we conclude that further theoretical improvements are required to match astrophysical needs.

Nuclear structure towards N = 40 60Ca: in-beam γ-ray spectroscopy of 58,60Ti.

Excited states in the neutron-rich N = 38, 36 nuclei (60)Ti and (58)Ti were populated in nucleon-removal reactions from (61)V projectiles at 90 MeV/nucleon. The γ-ray transitions from such states in these Ti isotopes were detected with the advanced γ-ray tracking array GRETINA and were corrected event by event for large Doppler shifts (v/c ∼ 0.4) using the γ-ray interaction points deduced from online signal decomposition. The new data indicate that a steep decrease in quadrupole collectivity occurs when moving from neutron-rich N = 36, 38 Fe and Cr toward the Ti and Ca isotones. In fact, (58,60)Ti provide some of the most neutron-rich benchmarks accessible today for calculations attempting to determine the structure of the potentially doubly magic nucleus (60)Ca.

Evolution of collectivity in 72Kr: evidence for rapid shape transition.

The transition rates from the yrast 2+ and 4+ states in the self-conjugate 72Kr nucleus were studied via lifetime measurements employing the GRETINA array with a novel application of the recoil-distance method. The large collectivity observed for the 4+→2+ transition suggests a prolate character of the excited states. The reduced collectivity previously reported for the 2+→0+ transition was confirmed. The irregular behavior of collectivity points to the occurrence of a rapid oblate-prolate shape transition in 72Kr, providing stringent tests for advanced theories to describe the shape coexistence and its evolution.

Correlations in intermediate energy two-proton removal reactions.

We report final-state-exclusive measurements of the light charged fragments in coincidence with (26)Ne residual nuclei following the direct two-proton removal from a neutron-rich (28)Mg secondary beam. A Dalitz-plot analysis and comparisons with simulations show that a majority of the triple-coincidence events with two protons display phase-space correlations consistent with the (two-body) kinematics of a spatially correlated pair-removal mechanism. The fraction of such correlated events, 56(12)%, is consistent with the fraction of the calculated cross section, 64%, arising from spin S=0 two-proton configurations in the entrance-channel (shell-model) (28)Mg ground state wave function. This result promises access to an additional and more specific probe of the spin and spatial correlations of valence nucleon pairs in exotic nuclei produced as fast secondary beams.