Mirror-symmetry violation in bound nuclear ground states.

Conservation laws are deeply related to any symmetry present in a physical system1,2. Analogously to electrons in atoms exhibiting spin symmetries3, it is possible to consider neutrons and protons in the atomic nucleus as projections of a single fermion with an isobaric spin (isospin) of t = 1/2 (ref. 4). Every nuclear state is thus characterized by a total isobaric spin T and a projection Tz-two quantities that are largely conserved in nuclear reactions and decays5,6. A mirror symmetry emerges from this isobaric-spin formalism: nuclei with exchanged numbers of neutrons and protons, known as mirror nuclei, should have an identical set of states7, including their ground state, labelled by their total angular momentum J and parity π. Here we report evidence of mirror-symmetry violation in bound nuclear ground states within the mirror partners strontium-73 and bromine-73. We find that a J π = 5/2- spin assignment is needed to explain the proton-emission pattern observed from the T = 3/2 isobaric-analogue state in rubidium-73, which is identical to the ground state of strontium-73. Therefore the ground state of strontium-73 must differ from its J π = 1/2- mirror bromine-73. This observation offers insights into charge-symmetry-breaking forces acting in atomic nuclei.

Description of the Proton-Decaying 0_{2}

The recent precise experimental determination of the monopole transition form factor from the ground state of ^{4}He to its 0_{2}^{+} resonance via electron scattering has reinvigorated discussions about the nature of this first excited state of the α particle. The 0_{2}^{+} state has been traditionally interpreted in the literature as the isoscalar monopole resonance (breathing mode) or, alternatively, as a particle-hole shell-model excitation. To better understand the nature of this state, which lies only ∼410 keV above the proton emission threshold, we employ the coupled-channel representation of the no-core Gamow shell model. By considering the [^{3}H+p], [^{3}He+n], and [^{2}H+^{2}H] reaction channels, we explain the excitation energy and monopole form factor of the 0_{2}^{+} state. We argue that the continuum coupling strongly impacts the nature of this state, which carries characteristics of the proton decay threshold.

Strong Evidence for

The boundaries of the chart of nuclides contain exotic isotopes that possess extreme proton-to-neutron asymmetries. Here we report on strong evidence of ^{9}N, one of the most exotic proton-rich isotopes where more than one half of its constitute nucleons are unbound. With seven protons and two neutrons, this extremely proton-rich system would represent the first-known example of a ground-state five-proton emitter. The invariant-mass spectrum of its decay products can be fit with two peaks whose energies are consistent with the theoretical predictions of an open-quantum-system approach; however, we cannot rule out the possibility that only a single resonancelike peak is present in the spectrum.

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).

Fermion Pair Dynamics in Open Quantum Systems.

Three-body decay is a rare decay mode observed in a handful of unbound rare isotopes. The angular and energy correlations between emitted nucleons are of particular interest, as they provide invaluable information on the interplay between structure and reaction aspects of the nuclear open quantum system. To study the mechanism of two-nucleon emission, we developed a time-dependent approach that allows us to probe emitted nucleons at long times and large distances. We successfully benchmarked the new method against the Green's function approach and applied it to low-energy two-proton and two-neutron decays. In particular, we studied the interplay between initial-state nucleon-nucleon correlations and final-state interaction. We demonstrated that the time evolution of the two-nucleon wave function is strongly impacted by the diproton/dineutron dynamics and that the correlations between emitted nucleons provide invaluable information on the dinucleon structure in the initial state.

Convenient Location of a Near-Threshold Proton-Emitting Resonance in

The presence of clusterlike narrow resonances in the vicinity of reaction or decay thresholds is a ubiquitous phenomenon with profound consequences. We argue that the continuum coupling, present in the open quantum system description of the atomic nucleus, can profoundly impact the nature of near-threshold states. In this Letter, we discuss the structure of the recently observed near-threshold resonance in ^{11}B, whose very existence explains the puzzling beta-delayed proton emission of the neutron-rich ^{11}Be.

First Observation of Unbound

The structure of the extremely proton-rich nucleus _{8}^{11}O_{3}, the mirror of the two-neutron halo nucleus _{3}^{11}Li_{8}, has been studied experimentally for the first time. Following two-neutron knockout reactions with a ^{13}O beam, the ^{11}O decay products were detected after two-proton emission and used to construct an invariant-mass spectrum. A broad peak of width ∼3.4 MeV was observed. Within the Gamow coupled-channel approach, it was concluded that this peak is a multiplet with contributions from the four lowest ^{11}O resonant states: J^{π}=3/2_{1}^{-}, 3/2_{2}^{-}, 5/2_{1}^{+}, and 5/2_{2}^{+}. The widths and configurations of these states show strong, nonmonotonic dependencies on the depth of the p-^{9}C potential. This unusual behavior is due to the presence of a broad threshold resonant state in ^{10}N, which is an analog of the virtual state in ^{10}Li in the presence of the Coulomb potential. After optimizing the model to the data, only a moderate isospin asymmetry between ground states of ^{11}O and ^{11}Li was found.

Laser Spectroscopy of Neutron-Rich Tin Isotopes: A Discontinuity in Charge Radii across the N=82 Shell Closure.

The change in mean-square nuclear charge radii δ⟨r^{2}⟩ along the even-A tin isotopic chain ^{108-134}Sn has been investigated by means of collinear laser spectroscopy at ISOLDE/CERN using the atomic transitions 5p^{2} ^{1}S_{0}→5p6 s^{1}P_{1} and 5p^{2} ^{3}P_{0}→5p6s ^{3}P_{1}. With the determination of the charge radius of ^{134}Sn and corrected values for some of the neutron-rich isotopes, the evolution of the charge radii across the N=82 shell closure is established. A clear kink at the doubly magic ^{132}Sn is revealed, similar to what has been observed at N=82 in other isotopic chains with larger proton numbers, and at the N=126 shell closure in doubly magic ^{208}Pb. While most standard nuclear density functional calculations struggle with a consistent explanation of these discontinuities, we demonstrate that a recently developed Fayans energy density functional provides a coherent description of the kinks at both doubly magic nuclei, ^{132}Sn and ^{208}Pb, without sacrificing the overall performance. A multiple correlation analysis leads to the conclusion that both kinks are related to pairing and surface effects.

Puzzling Two-Proton Decay of

Ground-state two-proton (2p) radioactivity is a rare decay mode found in a few very proton-rich isotopes. The 2p decay lifetime and properties of emitted protons carry invaluable information on nuclear structure in the presence of a low-lying proton continuum. The recently measured 2p decay of ^{67}Kr turned out to be unexpectedly fast. Since ^{67}Kr is expected to be a deformed system, we investigate the impact of deformation effects on the 2p radioactivity. We apply the recently developed Gamow coupled-channel framework, which allows for a precise description of three-body systems in the presence of rotational and vibrational couplings. This is the first application of a three-body approach to a two-nucleon decay from a deformed nucleus. We show that deformation couplings significantly increase the 2p decay width of ^{67}Kr; this finding explains the puzzling experimental data. The calculated angular proton-proton correlations reflect a competition between 1p and 2p decay modes in this nucleus.

From Calcium to Cadmium: Testing the Pairing Functional through Charge Radii Measurements of

Differences in mean-square nuclear charge radii of ^{100-130}Cd are extracted from high-resolution collinear laser spectroscopy of the 5s ^{2}S_{1/2}→5p ^{2}P_{3/2} transition of the ion and from the 5s5p ^{3}P_{2}→5s6s ^{3}S_{1} transition in atomic Cd. The radii show a smooth parabolic behavior on top of a linear trend and a regular odd-even staggering across the almost complete sdgh shell. They serve as a first test for a recently established new Fayans functional and show a remarkably good agreement in the trend as well as in the total nuclear charge radius.

Probing Sizes and Shapes of Nobelium Isotopes by Laser Spectroscopy.

Until recently, ground-state nuclear moments of the heaviest nuclei could only be inferred from nuclear spectroscopy, where model assumptions are required. Laser spectroscopy in combination with modern atomic structure calculations is now able to probe these moments directly, in a comprehensive and nuclear-model-independent way. Here we report on unique access to the differential mean-square charge radii of ^{252,253,254}No, and therefore to changes in nuclear size and shape. State-of-the-art nuclear density functional calculations describe well the changes in nuclear charge radii in the region of the heavy actinides, indicating an appreciable central depression in the deformed proton density distribution in ^{252,254}No isotopes. Finally, the hyperfine splitting of ^{253}No was evaluated, enabling a complementary measure of its (quadrupole) deformation, as well as an insight into the neutron single-particle wave function via the nuclear spin and magnetic moment.

Impact of Nuclear Mass Uncertainties on the r Process.

Nuclear masses play a fundamental role in understanding how the heaviest elements in the Universe are created in the r process. We predict r-process nucleosynthesis yields using neutron capture and photodissociation rates that are based on the nuclear density functional theory. Using six Skyrme energy density functionals based on different optimization protocols, we determine for the first time systematic uncertainty bands-related to mass modeling-for r-process abundances in realistic astrophysical scenarios. We find that features of the underlying microphysics make an imprint on abundances especially in the vicinity of neutron shell closures: Abundance peaks and troughs are reflected in trends of neutron separation energy. Further advances in the nuclear theory and experiments, when linked to observations, will help in the understanding of astrophysical conditions in extreme r-process sites.

Charge Radii of Neutron Deficient

Bunched-beam collinear laser spectroscopy is performed on neutron deficient ^{52,53}Fe prepared through in-flight separation followed by a gas stopping. This novel scheme is a major step to reach nuclides far from the stability line in laser spectroscopy. Differential mean-square charge radii δ⟨r^{2}⟩ of ^{52,53}Fe are determined relative to stable ^{56}Fe as δ⟨r^{2}⟩^{56,52}=-0.034(13) fm^{2} and δ⟨r^{2}⟩^{56,53}=-0.218(13) fm^{2}, respectively, from the isotope shift of atomic hyperfine structures. The multiconfiguration Dirac-Fock method is used to calculate atomic factors to deduce δ⟨r^{2}⟩. The values of δ⟨r^{2}⟩ exhibit a minimum at the N=28 neutron shell closure. The nuclear density functional theory with Fayans and Skyrme energy density functionals is used to interpret the data. The trend of δ⟨r^{2}⟩ along the Fe isotopic chain results from an interplay between single-particle shell structure, pairing, and polarization effects and provides important data for understanding the intricate trend in the δ⟨r^{2}⟩ of closed-shell Ca isotopes.

Uncertainty quantification for nuclear density functional theory and information content of new measurements.

Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. The example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.

Landscape of two-proton radioactivity.

Ground-state two-proton (2p) radioactivity is a decay mode found in isotopes of elements with even atomic numbers located beyond the two-proton drip line. So far, this exotic process has been experimentally observed in a few light- and medium-mass nuclides with Z≤30. In this study, using state-of-the-art nuclear density functional theory, we globally analyze 2p radioactivity and for the first time identify 2p-decay candidates in elements heavier than strontium. We predict a few cases where the competition between 2p emission and α decay may be observed. In nuclei above lead, the α-decay mode is found to be dominating and no measurable candidates for the 2p radioactivity are expected.

Optimized chiral nucleon-nucleon interaction at next-to-next-to-leading order.

We optimize the nucleon-nucleon interaction from chiral effective field theory at next-to-next-to-leading order (NNLO). The resulting new chiral force NNLO(opt) yields χ(2)≈1 per degree of freedom for laboratory energies below approximately 125 MeV. In the A=3, 4 nucleon systems, the contributions of three-nucleon forces are smaller than for previous parametrizations of chiral interactions. We use NNLO(opt) to study properties of key nuclei and neutron matter, and we demonstrate that many aspects of nuclear structure can be understood in terms of this nucleon-nucleon interaction, without explicitly invoking three-nucleon forces.

Self-consistent tilted-axis-cranking study of triaxial strongly deformed bands in 158Er at ultrahigh spin.

Stimulated by recent experimental discoveries, triaxial strongly deformed (TSD) states in (158)Er at ultrahigh spins have been studied by means of the Skyrme-Hartree-Fock model and the tilted-axis-cranking method. Restricting the rotational axis to one of the principal axes--as done in previous cranking calculations--two well-defined TSD minima in the total Routhian surface are found for a given configuration: one with positive and another with negative triaxial deformation γ. By allowing the rotational axis to change direction, the higher-energy minimum is shown to be a saddle point. This resolves the long-standing question of the physical interpretation of the two triaxial minima at a very similar quadrupole shape obtained in the principal-axis-cranking approach. Several TSD configurations have been predicted, including a highly deformed band, which is a candidate for the structure observed in experiment.

Microscopic calculations of isospin-breaking corrections to superallowed beta decay.

The superallowed ß-decay rates that provide stringent constraints on physics beyond the standard model of particle physics are affected by nuclear structure effects through isospin-breaking corrections. The self-consistent isospin- and angular-momentum-projected nuclear density functional theory is used for the first time to compute those corrections for a number of Fermi transitions in nuclei from A=10 to A=74. The resulting leading element of the Cabibbo-Kobayashi-Maskawa matrix, |V(ud)|=0.97447(23), agrees well with the recent result of Towner and Hardy [Phys. Rev. C 77, 025501 (2008)].

Shape coexistence and triaxiality in the superheavy nuclei.

Superheavy nuclei represent the limit of nuclear mass and charge; they inhabit the remote corner of the nuclear landscape, whose extent is unknown. The discovery of new elements with atomic numbers Z > or = 110 has brought much excitement to the atomic and nuclear physics communities. The existence of such heavy nuclei hangs on a subtle balance between the attractive nuclear force and the disruptive Coulomb repulsion between protons that favours fission. Here we model the interplay between these forces using self-consistent energy density functional theory; our approach accounts for spontaneous breaking of spherical symmetry through the nuclear Jahn-Teller effect. We predict that the long-lived superheavy elements can exist in a variety of shapes, including spherical, axial and triaxial configurations. In some cases, we anticipate the existence of metastable states and shape isomers that can affect decay properties and hence nuclear half-lives.

Pairing reentrance phenomenon in heated rotating nuclei in the shell-model Monte Carlo approach.

Rotational motion of heated 72Ge is studied within the microscopic shell-model Monte Carlo approach. We investigate the angular momentum alignment and nuclear pairing correlations associated with J^{π} Cooper pairs as a function of the rotational frequency and temperature. The reentrance of pairing correlations with temperature is predicted at high rotational frequencies. It manifests itself through the anomalous behavior of specific heat and level density.