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.

First Exploration of Monopole-Driven Shell Evolution above the N=126 Shell Closure: New Millisecond Isomers in

Isomer spectroscopy of heavy neutron-rich nuclei beyond the N=126 closed shell has been performed for the first time at the Radioactive Isotope Beam Factory of the RIKEN Nishina Center. New millisecond isomers have been identified at low excitation energies, 985.3(19) keV in ^{213}Tl and 874(5) keV in ^{215}Tl. The measured half-lives of 1.34(5) ms in ^{213}Tl and 3.0(3) ms in ^{215}Tl suggest spins and parities 11/2^{-} with the single proton-hole configuration πh_{11/2} as leading component. They are populated via E1 transitions by the decay of higher-lying isomeric states with proposed spin and parity 17/2^{+}, interpreted as arising from a single πs_{1/2} proton hole coupled to the 8^{+} seniority isomer in the ^{A+1}Pb cores. The lowering of the 11/2^{-} states is ascribed to an increase of the πh_{11/2} proton effective single-particle energy as the second νg_{9/2} orbital is filled by neutrons, owing to a significant reduction of the proton-neutron monopole interaction between the πh_{11/2} and νg_{9/2} orbitals. The new ms isomers provide the first experimental observation of shell evolution in the almost unexplored N>126 nuclear region below doubly magic ^{208}Pb.

Structure of

Detailed spectroscopy of the neutron-deficient nucleus ^{36}Ca was obtained up to 9 MeV using the ^{37}Ca(p,d)^{36}Ca and the ^{38}Ca(p,t)^{36}Ca transfer reactions. The radioactive nuclei, produced by the LISE spectrometer at GANIL, interacted with the protons of the liquid hydrogen target CRYPTA, to produce light ejectiles (the deuteron d or triton t) that were detected in the MUST2 detector array, in coincidence with the heavy residues identified by a zero-degree detection system. Our main findings are (i) a similar shift in energy for the 1_{1}^{+} and 2_{1}^{+} states by about -250 keV, as compared with the mirror nucleus ^{36}S; (ii) the discovery of an intruder 0_{2}^{+} state at 2.83(13) MeV, which appears below the first 2^{+} state, in contradiction with the situation in ^{36}S; and (iii) a tentative 0_{3}^{+} state at 4.83(17) MeV, proposed to exhibit a bubble structure with two neutron vacancies in the 2s_{1/2} orbit. The inversion between the 0_{2}^{+} and 2_{1}^{+} states is due to the large mirror energy difference (MED) of -516(130) keV for the former. This feature is reproduced by shell model calculations, using the sd-pf valence space, predicting an almost pure intruder nature for the 0_{2}^{+} state, with two protons (neutrons) being excited across the Z=20 magic closure in ^{36}Ca (^{36}S). This mirror system has the largest MEDs ever observed, if one excludes the few cases induced by the effect of the continuum.

Shape Changes in the Mirror Nuclei

We studied the proton-rich T_{z}=-1 nucleus ^{70}Kr through inelastic scattering at intermediate energies in order to extract the reduced transition probability, B(E2;0^{+}→2^{+}). Comparison with the other members of the A=70 isospin triplet, ^{70}Br and ^{70}Se, studied in the same experiment, shows a 3σ deviation from the expected linearity of the electromagnetic matrix elements as a function of T_{z}. At present, no established nuclear structure theory can describe this observed deviation quantitatively. This is the first violation of isospin symmetry at this level observed in the transition matrix elements. A heuristic approach may explain the anomaly by a shape change between the mirror nuclei ^{70}Kr and ^{70}Se contrary to the model predictions.

Sequential Nature of (p,3p) Two-Proton Knockout from Neutron-Rich Nuclei.

Twenty-one two-proton knockout (p,3p) cross sections were measured from neutron-rich nuclei at ∼250 MeV/nucleon in inverse kinematics. The angular distribution of the three emitted protons was determined for the first time, demonstrating that the (p,3p) kinematics are consistent with two sequential proton-proton collisions within the projectile nucleus. Ratios of (p,3p) over (p,2p) inclusive cross sections follow the trend of other many-nucleon removal reactions, further reinforcing the sequential nature of (p,3p) in neutron-rich nuclei.

g Factor of the

The gyromagnetic factor of the low-lying E=251.96(9) keV isomeric state of the nucleus ^{99}Zr was measured using the time-dependent perturbed angular distribution technique. This level is assigned a spin and parity of J^{π}=7/2^{+}, with a half-life of T_{1/2}=336(5) ns. The isomer was produced and spin aligned via the abrasion-fission of a ^{238}U primary beam at RIKEN RIBF. A magnetic moment |µ|=2.31(14)µ_{N} was deduced showing that this isomer is not single particle in nature. A comparison of the experimental values with interacting boson-fermion model IBFM-1 results shows that this state is strongly mixed with a main νd_{5/2} composition. Furthermore, it was found that monopole single-particle evolution changes significantly with the appearance of collective modes, likely due to type-II shell evolution.

First Spectroscopy of the Near Drip-line Nucleus

One of the most exotic light neutron-rich nuclei currently accessible for experimental study is ^{40}Mg, which lies at the intersection of the nucleon magic number N=28 and the neutron drip line. Low-lying excited states of ^{40}Mg have been studied for the first time following a one-proton removal reaction from ^{41}Al, performed at the Radioactive Isotope Beam Factory of RIKEN Nishina Center with the DALI2 γ-ray array and the ZeroDegree spectrometer. Two γ-ray transitions were observed, suggesting an excitation spectrum that shows unexpected properties as compared to both the systematics along the Z=12, N≥20 Mg isotopes and available state-of-the-art theoretical model predictions. A possible explanation for the observed structure involves weak-binding effects in the low-lying excitation spectrum.

Proton Shell Evolution below

The ß-delayed γ-ray spectroscopy of neutron-rich ^{123,125}Ag isotopes is investigated at the Radioactive Isotope Beam Factory of RIKEN, and the long-predicted 1/2^{-} ß-emitting isomers in ^{123,125}Ag are identified for the first time. With the new experimental results, the systematic trend of energy spacing between the lowest 9/2^{+} and 1/2^{-} levels is extended in Ag isotopes up to N=78, providing a clear signal for the reduction of the Z=40 subshell gap in Ag towards N=82. Shell-model calculations with the state-of-the-art V_{MU} plus M3Y spin-orbit interaction give a satisfactory description of the low-lying states in ^{123,125}Ag. The tensor force is found to play a crucial role in the evolution of the size of the Z=40 subshell gap. The observed inversion of the single-particle levels around ^{123}Ag can be well interpreted in terms of the monopole shift of the π1g_{9/2} orbitals mainly caused by the increasing occupation of ν1h_{11/2} orbitals.

Prominence of Pairing in Inclusive (p,2p) and (p,pn) Cross Sections from Neutron-Rich Nuclei.

Fifty-five inclusive single nucleon-removal cross sections from medium mass neutron-rich nuclei impinging on a hydrogen target at ∼250 MeV/nucleon are measured at the RIKEN Radioactive Isotope Beam Factory. Systematically higher cross sections are found for proton removal from nuclei with an even number of protons as compared to odd-proton number projectiles for a given neutron separation energy. Neutron removal cross sections display no even-odd splitting, contrary to nuclear cascade model predictions. Both effects are understood through simple considerations of neutron separation energies and bound state level densities originating in pairing correlations in the daughter nuclei. These conclusions are supported by comparison with semimicroscopic model predictions, highlighting the enhanced role of low-lying level densities in nucleon-removal cross sections from loosely bound nuclei.

Erratum: Persistence of the Z=28 Shell Gap Around

This corrects the article DOI: 10.1103/PhysRevLett.119.192501.

Gamma Decay of Unbound Neutron-Hole States in

Excited states in the nucleus ^{133}Sn, with one neutron outside the double magic ^{132}Sn core, were populated following one-neutron knockout from a ^{134}Sn beam on a carbon target at relativistic energies at the Radioactive Isotope Beam Factory at RIKEN. Besides the γ rays emitted in the decay of the known neutron single-particle states in ^{133}Sn additional γ strength in the energy range 3.5-5.5 MeV was observed for the first time. Since the neutron-separation energy of ^{133}Sn is low, S_{n}=2.402(4) MeV, this observation provides direct evidence for the radiative decay of neutron-unbound states in this nucleus. The ability of electromagnetic decay to compete successfully with neutron emission at energies as high as 3 MeV above threshold is attributed to a mismatch between the wave functions of the initial and final states in the latter case. These findings suggest that in the region southeast of ^{132}Sn nuclear structure effects may play a significant role in the neutron versus γ competition in the decay of unbound states. As a consequence, the common neglect of such effects in the evaluation of the neutron-emission probabilities in calculations of global ß-decay properties for astrophysical simulations may have to be reconsidered.

Are There Signatures of Harmonic Oscillator Shells Far from Stability? First Spectroscopy of

The first measurement of the low-lying states of the neutron-rich ^{110}Zr and ^{112}Mo was performed via in-beam γ-ray spectroscopy after one proton removal on hydrogen at ∼200 MeV/nucleon. The 2_{1}^{+} excitation energies were found at 185(11) keV in ^{110}Zr, and 235(7) keV in ^{112}Mo, while the R_{42}=E(4_{1}^{+})/E(2_{1}^{+}) ratios are 3.1(2), close to the rigid rotor value, and 2.7(1), respectively. These results are compared to modern energy density functional based configuration mixing models using Gogny and Skyrme effective interactions. We conclude that first levels of ^{110}Zr exhibit a rotational behavior, in agreement with previous observations of lighter zirconium isotopes as well as with the most advanced Monte Carlo shell model predictions. The data, therefore, do not support a harmonic oscillator shell stabilization scenario at Z=40 and N=70. The present data also invalidate predictions for a tetrahedral ground state symmetry in ^{110}Zr.

Shell Evolution towards

The level structure of the neutron-rich ^{77}Cu nucleus is investigated through ß-delayed γ-ray spectroscopy at the Radioactive Isotope Beam Factory of the RIKEN Nishina Center. Ions of ^{77}Ni are produced by in-flight fission, separated and identified in the BigRIPS fragment separator, and implanted in the WAS3ABi silicon detector array, surrounded by Ge cluster detectors of the EURICA array. A large number of excited states in ^{77}Cu are identified for the first time by correlating γ rays with the ß decay of ^{77}Ni, and a level scheme is constructed by utilizing their coincidence relationships. The good agreement between large-scale Monte Carlo shell model calculations and experimental results allows for the evaluation of the single-particle structure near ^{78}Ni and suggests a single-particle nature for both the 5/2_{1}^{-} and 3/2_{1}^{-} states in ^{77}Cu, leading to doubly magic ^{78}Ni.

Shape Evolution in Neutron-Rich Krypton Isotopes Beyond N=60: First Spectroscopy of

We report on the first γ-ray spectroscopy of low-lying states in neutron-rich ^{98,100}Kr isotopes obtained from ^{99,101}Rb(p,2p) reactions at ∼220 MeV/nucleon. A reduction of the 2_{1}^{+} state energies beyond N=60 demonstrates a significant increase of deformation, shifted in neutron number compared to the sharper transition observed in strontium and zirconium isotopes. State-of-the-art beyond-mean-field calculations using the Gogny D1S interaction predict level energies in good agreement with experimental results. The identification of a low-lying (0_{2}^{+}, 2_{2}^{+}) state in ^{98}Kr provides the first experimental evidence of a competing configuration at low energy in neutron-rich krypton isotopes consistent with the oblate-prolate shape coexistence picture suggested by theory.

Persistence of the Z=28 Shell Gap Around

In-beam γ-ray spectroscopy of ^{79}Cu is performed at the Radioactive Isotope Beam Factory of RIKEN. The nucleus of interest is produced through proton knockout from a ^{80}Zn beam at 270 MeV/nucleon. The level scheme up to 4.6 MeV is established for the first time and the results are compared to Monte Carlo shell-model calculations. We do not observe significant knockout feeding to the excited states below 2.2 MeV, which indicates that the Z=28 gap at N=50 remains large. The results show that the ^{79}Cu nucleus can be described in terms of a valence proton outside a ^{78}Ni core, implying the magic character of the latter.

Pathway for the Production of Neutron-Rich Isotopes around the N=126 Shell Closure.

Absolute cross sections for isotopically identified products formed in multinucleon transfer in the (136)Xe+(198)Pt system at ∼8 MeV/nucleon are reported. The isotopic distributions obtained using a large acceptance spectrometer demonstrated the production of the "hard-to-reach" neutron-rich isotopes for Z<78 around the N=126 shell closure far from stability. The main contribution to the formation of these exotic nuclei is shown to arise in collisions with a small kinetic energy dissipation. The present experimental finding corroborates for the first time recent predictions that multinucleon transfer reactions would be the optimum method to populate and characterize neutron-rich isotopes around N=126 which are crucial for understanding both astrophysically relevant processes and the evolution of "magic" numbers far from stability.

Extension of the N=40 Island of Inversion towards N=50: Spectroscopy of (66)Cr, (70,72)Fe.

We report on the measurement of the first 2(+) and 4(+) states of (66)Cr and (70,72)Fe via in-beam γ-ray spectroscopy. The nuclei of interest were produced by (p,2p) reactions at incident energies of 260 MeV/nucleon. The experiment was performed at the Radioactive Isotope Beam Factory, RIKEN, using the DALI 2γ-ray detector array and the novel MINOS device, a thick liquid hydrogen target combined with a vertex tracker. A low-energy plateau of 2(1)(+) and 4(1)(+) energies as a function of the neutron number was observed for N≥38 and N≥40 for even-even Cr and Fe isotopes, respectively. State-of-the-art shell model calculations with a modified Lenzi-Nowacki-Poves-Sieja (LNPS) interaction in the pfg(9/2)d(5/2) valence space reproduce the observations. Interpretation within the shell model shows an extension of the island of inversion at N=40 for more neutron-rich isotopes towards N=50.

ß-Decay Half-Lives of 110 Neutron-Rich Nuclei across the N=82 Shell Gap: Implications for the Mechanism and Universality of the Astrophysical r Process.

The ß-decay half-lives of 110 neutron-rich isotopes of the elements from _{37}Rb to _{50}Sn were measured at the Radioactive Isotope Beam Factory. The 40 new half-lives follow robust systematics and highlight the persistence of shell effects. The new data have direct implications for r-process calculations and reinforce the notion that the second (A≈130) and the rare-earth-element (A≈160) abundance peaks may result from the freeze-out of an (n,γ)⇄(γ,n) equilibrium. In such an equilibrium, the new half-lives are important factors determining the abundance of rare-earth elements, and allow for a more reliable discussion of the r process universality. It is anticipated that universality may not extend to the elements Sn, Sb, I, and Cs, making the detection of these elements in metal-poor stars of the utmost importance to determine the exact conditions of individual r-process events.

ß-Decay half-lives of 76,77Co, 79,80Ni, and 81Cu: experimental indication of a doubly magic 78Ni.

The half-lives of 20 neutron-rich nuclei with Z=27-30 have been measured at the RIBF, including five new half-lives of (76)Co(21.7(-4.9)(+6.5) ms), (77)Co(13.0(-4.3)(+7.2) ms), (79)Ni(43.0(-7.5)(+8.6) ms), (80)Ni(23.9(-17.2)(+26.0) ms), and (81)Cu(73.2 ± 6.8 ms). In addition, the half-lives of (73-75)Co, (74-78)Ni, (78-80)Cu, and (80-82)Zn were determined with higher precision than previous works. Based on these new results, a systematic study of the ß-decay half-lives has been carried out, which suggests a sizable magicity for both the proton number Z = 28 and the neutron number N=50 in (78)Ni.