Determination of the N=16 shell closure at the oxygen drip line

High-Precision Spectroscopy of ^{20}O Benchmarking Ab Initio Calculations in Light Nuclei

The excited states of unstable ^{20}O were investigated via γ-ray spectroscopy following the ^{19}O(d,p)^{20}O reaction at 8  AMeV. By exploiting the Doppler shift attenuation method, the lifetimes of the 2_{2}^{+} and 3_{1}^{+} states were firmly established. From the γ-ray branching and E2/M1 mixing ratios for transitions deexciting the 2_{2}^{+} and 3_{1}^{+} states, the B(E2) and B(M1) were determined. Various chiral effective field theory Hamiltonians, describing the nuclear properties beyond ground states, along with a standard USDB interaction, were compared with the experimentally obtained data. Such a comparison for a large set of γ-ray transition probabilities with the valence space in medium similarity renormalization group ab initio calculations was performed for the first time in a nucleus far from stability. It was shown that the ab initio approaches using chiral effective field theory forces are challenged by detailed high-precision spectroscopic properties of nuclei. The reduced transition probabilities were found to be a very constraining test of the performance of the ab initio models.

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.

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.

Pairing Forces Govern Population of Doubly Magic ^{54}Ca from Direct Reactions

Direct proton-knockout reactions of ^{55}Sc at ∼220  MeV/nucleon were studied at the RIKEN Radioactive Isotope Beam Factory. Populated states of ^{54}Ca were investigated through γ-ray and invariant-mass spectroscopy. Level energies were calculated from the nuclear shell model employing a phenomenological internucleon interaction. Theoretical cross sections to states were calculated from distorted-wave impulse approximation estimates multiplied by the shell model spectroscopic factors, which describe the wave function overlap of the ^{55}Sc ground state with states in ^{54}Ca. Despite the calculations showing a significant amplitude of excited neutron configurations in the ground-state of ^{55}Sc, valence proton removals populated predominantly the ground state of ^{54}Ca. This counterintuitive result is attributed to pairing effects leading to a dominance of the ground-state spectroscopic factor. Owing to the ubiquity of the pairing interaction, this argument should be generally applicable to direct knockout reactions from odd-even to even-even nuclei.

Quasifree Neutron Knockout from ^{54}Ca Corroborates Arising N=34 Neutron Magic Number

Exclusive cross sections and momentum distributions have been measured for quasifree one-neutron knockout reactions from a ^{54}Ca beam striking on a liquid hydrogen target at ∼200  MeV/u. A significantly larger cross section to the p_{3/2} state compared to the f_{5/2} state observed in the excitation of ^{53}Ca provides direct evidence for the nature of the N=34 shell closure. This finding corroborates the arising of a new shell closure in neutron-rich calcium isotopes. The distorted-wave impulse approximation reaction formalism with shell model calculations using the effective GXPF1Bs interaction and ab initio calculations concur our experimental findings. Obtained transverse and parallel momentum distributions demonstrate the sensitivity of quasifree one-neutron knockout in inverse kinematics on a thick liquid hydrogen target with the reaction vertex reconstructed to final state spin-parity assignments.

The equation of motion phonon method and its application in the neutron rich oxygen region

An equation of motion phonon method, developed for even-even nuclear systems and extended to odd nuclei, is applied to 22O and to its odd neighbors 23O and 23F. A calculation using the chiral potential NNLOopt is carried out in a space encompassing up to two phonons. The computed dipole cross section in 22O and the spectra of 22O and 23O are in a satisfactory agreement with the experimental data. However, the calculation describes poorly the spectrum of 23F. This discrepancy originates from the strong coupling between the odd proton and the 22O phonons of neutron nature. This coupling pushes down in energy several states enhancing the level density at low energy. We suggest that a viable route for the solution of this problem could be the inclusion of the three-body interaction using the new chiral potential NNLOsat.

Structure of ^{78}Ni from First-Principles Computations

Doubly magic nuclei have a simple structure and are the cornerstones for entire regions of the nuclear chart. Theoretical insights into the supposedly doubly magic ^{78}Ni and its neighbors are challenging because of the extreme neutron-to-proton ratio and the proximity of the continuum. We predict the J^{π}=2_{1}^{+} state in ^{78}Ni from a correlation with the J^{π}=2_{1}^{+} state in ^{48}Ca using chiral nucleon-nucleon and three-nucleon interactions. Our results confirm that ^{78}Ni is doubly magic, and the predicted low-lying states of ^{79,80}Ni open the way for shell-model studies of many more rare isotopes.

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.

Coupled-cluster computations of atomic nuclei

In the past decade, coupled-cluster theory has seen a renaissance in nuclear physics, with computations of neutron-rich and medium-mass nuclei. The method is efficient for nuclei with product-state references, and it describes many aspects of weakly bound and unbound nuclei. This report reviews the technical and conceptual developments of this method in nuclear physics, and the results of coupled-cluster calculations for nucleonic matter, and for exotic isotopes of helium, oxygen, calcium, and some of their neighbors.

Isotopic chains around oxygen from evolved chiral two- and three-nucleon interactions

We extend the formalism of self-consistent Green's function theory to include three-body interactions and apply it to isotopic chains around oxygen for the first time. The third-order algebraic diagrammatic construction equations for two-body Hamiltonians can be exploited upon defining system-dependent one- and two-body interactions coming from the three-body force, and, correspondingly, dropping interaction-reducible diagrams. The Koltun sum rule for the total binding energy acquires a correction due to the added three-body interaction. This formalism is then applied to study chiral two- and three-nucleon forces evolved to low momentum cutoffs. The binding energies of nitrogen, oxygen, and fluorine isotopes are reproduced with good accuracy and demonstrate the predictive power of this approach. Leading order three-nucleon forces consistently bring results close to the experiment for all neutron rich isotopes considered and reproduce the correct driplines for oxygen and nitrogen. The formalism introduced also allows us to calculate form factors for nucleon transfer on doubly magic systems.

Lifetime and fragment correlations for the two-neutron decay of 26O ground state

The structure and decay of 26O are investigated in a three-body 24O+n+n model suitable for studies of the long-lived (including radioactivity time scale) states. We have found extremely strong effects of the subbarrier configuration mixing on the decay width of true 2n emitters due to core recoil and neutron-neutron final state interaction. This effect far exceeds the analogous effect in the true 2p emitters. Our calculations provide reasonably narrow boundaries for the lifetime vs decay energy dependence for the true 2n emission. An upper limit of ∼1  keV for the decay energy of the unbound 26O is inferred based on the recent experimental lifetime value.

Ab Initio calculations of even oxygen isotopes with chiral two-plus-three-nucleon interactions

We formulate the in-medium similarity renormalization group (IM-SRG) for open-shell nuclei using a multireference formalism based on a generalized Wick theorem introduced in quantum chemistry. The resulting multireference IM-SRG (MR-IM-SRG) is used to perform the first ab initio study of all even oxygen isotopes with chiral nucleon-nucleon and three-nucleon interactions, from the proton to the neutron drip lines. We obtain an excellent reproduction of experimental ground-state energies with quantified uncertainties, which is validated by results from the importance-truncated no-core shell model and the coupled cluster method. The agreement between conceptually different many-body approaches and experiment highlights the predictive power of current chiral two- and three-nucleon interactions, and establishes the MR-IM-SRG as a promising new tool for ab initio calculations of medium-mass nuclei far from shell closures.

Spectroscopy of 26F to probe proton-neutron forces close to the drip line

A long-lived J(π) = 4(1)(+) isomer, T(1/2) = 2.2(1) ms, has been discovered at 643.4(1) keV in the weakly bound (9)(26)F nucleus. It was populated at Grand Accélérateur National d'Ions Lourds in the fragmentation of a (36)S beam. It decays by an internal transition to the J(π) = 1(1)(+) ground state [82(14)%], by β decay to (26)Ne, or β-delayed neutron emission to (25)Ne. From the β-decay studies of the J(π) =1(1)(+) and J(π) = 4(1)(+) states, new excited states have been discovered in (25,26)Ne. Gathering the measured binding energies of the J(π) = 1(1)(+) -4(1)(+) multiplet in (9)(26)F, we find that the proton-neutron π0d(5/2)ν0d(3/2) effective force used in shell-model calculations should be reduced to properly account for the weak binding of (9)(26)F. Microscopic coupled cluster theory calculations using interactions derived from chiral effective field theory are in very good agreement with the energy of the low-lying 1(1)(+), 2(1)(+), 4(1)(+) states in (26)F. Including three-body forces and coupling to the continuum effects improve the agreement between experiment and theory as compared to the use of two-body forces only.

N = 16 spherical shell closure in 24O

The unbound excited states of the neutron drip-line isotope 24O have been investigated via the 24O(p,p')23O + n reaction in inverse kinematics at a beam energy of 62  MeV/nucleon. The decay energy spectrum of 24O* was reconstructed from the momenta of 23O and the neutron. The spin parity of the first excited state, observed at E(x) = 4.65±0.14  MeV, was determined to be J(π) = 2+ from the angular distribution of the cross section. Higher-lying states were also observed. The quadrupole transition parameter β2 of the 2(1)+ state was deduced, for the first time, to be 0.15±0.04. The relatively high excitation energy and small β2 value are indicative of the N = 16 shell closure in 24O.

Continuum effects and three-nucleon forces in neutron-rich oxygen isotopes

We employ interactions from chiral effective field theory and compute binding energies, excited states, and radii for isotopes of oxygen with the coupled-cluster method. Our calculation includes the effects of three-nucleon forces and of the particle continuum, both of which are important for the description of neutron-rich isotopes in the vicinity of the nucleus 24O. Our main results are the placement of the neutron drip line at 24O, the assignment of spins, parities and resonance widths for several low-lying states of the drip line nucleus, and an efficient approximation that incorporates the effects of three-body interactions.

Evidence for the ground-state resonance of 26O

Evidence for the ground state of the neutron-unbound nucleus (26)O was observed for the first time in the single proton-knockout reaction from a 82 MeV/u (27)F beam. Neutrons were measured in coincidence with (24)O fragments. (26)O was determined to be unbound by 150(-150)(+50) keV from the observation of low-energy neutrons. This result agrees with recent shell-model calculations based on microscopic two- and three-nucleon forces.

Nuclear structure experiments along the neutron drip line

Invariant mass measurements and breakup reactions of neutron-rich nuclei have been instrumental in the study of nuclear structure effects at the limit of nuclear existence. The measurements of neutron-unbound states rely on the detection of neutrons in coincidence with fragments at energies between 100 and 1000 MeV/u. Charged particle and γ-ray coincidence measurements yield additional information. The production and detection methods for these experiments and examples of results in light nuclei are presented. Future opportunities with new facilities and the development of new detectors are described.

Discovery of the shape coexisting 0+ state in 32 Mg by a two neutron transfer reaction

The "island of inversion" nucleus 32 Mg has been studied by a (t, p) two neutron transfer reaction in inverse kinematics at REX-ISOLDE. The shape coexistent excited 0+ state in 32 Mg has been identified by the characteristic angular distribution of the protons of the Δ L=0 transfer. The excitation energy of 1058 keV is much lower than predicted by any theoretical model. The low γ-ray intensity observed for the decay of this 0+ state indicates a lifetime of more than 10 ns. Deduced spectroscopic amplitudes are compared with occupation numbers from shell-model calculations.

Three-body forces and the limit of oxygen isotopes

The limit of neutron-rich nuclei, the neutron drip line, evolves regularly from light to medium-mass nuclei except for a striking anomaly in the oxygen isotopes. This anomaly is not reproduced in shell-model calculations derived from microscopic two-nucleon forces. Here, we present the first microscopic explanation of the oxygen anomaly based on three-nucleon forces that have been established in few-body systems. This leads to repulsive contributions to the interactions among excess neutrons that change the location of the neutron drip line from (28)O to the experimentally observed (24)O. Since the mechanism is robust and general, our findings impact the prediction of the most neutron-rich nuclei and the synthesis of heavy elements in neutron-rich environments.

Migration of nuclear shell gaps studied in the d(24Ne,pγ)25Ne reaction

The transfer of neutrons onto 24Ne has been measured using a reaccelerated radioactive beam of 24Ne to study the (d,p) reaction in inverse kinematics. The unusual raising of the first 3/2+ level in 25Ne and its significance in terms of the migration of the neutron magic number from N=20 to N=16 is put on a firm footing by confirmation of this state's identity. The raised 3/2+ level is observed simultaneously with the intruder negative parity 7/2- and 3/2- levels, providing evidence for the reduction in the N=20 gap. The coincident gamma-ray decays allowed the assignment of spins as well as the transferred orbital angular momentum. The excitation energy of the 3/2+ state shows that the established USD shell model breaks down well within the sd model space and requires a revised treatment of the proton-neutron monopole interaction.

One-neutron removal measurement reveals 24O as a new doubly magic nucleus

The first measurement of the momentum distribution for one-neutron removal from (24)O at 920A MeV performed at GSI, Darmstadt is reported. The observed distribution has a width (FWHM) of 99 +/- 4 MeV/c in the projectile rest frame and a one-neutron removal cross section of 63 +/- 7 mb. The results are well explained with a nearly pure 2s_{1/2} neutron spectroscopic factor of 1.74 +/- 0.19 within the eikonal model. This large s-wave probability shows a spherical shell closure thereby confirming earlier suggestions that (24)O is a new doubly magic nucleus.