The magic nature of 132Sn explored through the single-particle states of 133Sn

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.

^{133}In: A Rosetta Stone for Decays of r-Process Nuclei

The β decays from both the ground state and a long-lived isomer of ^{133}In were studied at the ISOLDE Decay Station (IDS). With a hybrid detection system sensitive to β, γ, and neutron spectroscopy, the comparative partial half-lives (logft) have been measured for all their dominant β-decay channels for the first time, including a low-energy Gamow-Teller transition and several first-forbidden (FF) transitions. Uniquely for such a heavy neutron-rich nucleus, their β decays selectively populate only a few isolated neutron unbound states in ^{133}Sn. Precise energy and branching-ratio measurements of those resonances allow us to benchmark β-decay theories at an unprecedented level in this region of the nuclear chart. The results show good agreement with the newly developed large-scale shell model (LSSM) calculations. The experimental findings establish an archetype for the β decay of neutron-rich nuclei southeast of ^{132}Sn and will serve as a guide for future theoretical development aiming to describe accurately the key β decays in the rapid-neutron capture (r-) process.

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 nucleon^1,2. A microscopic understanding of the extent of this behaviour and its evolution in neutron-rich nuclei remains an open question in nuclear physics^3-5. 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 system^6,7. 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.

Sensitivity of Neutron-Rich Nuclear Isomer Behavior to Uncertainties in Direct Transitions

Nuclear isomers are populated in the rapid neutron capture process (r process) of nucleosynthesis. The r process may cover a wide range of temperatures, potentially starting from several tens of GK (several MeV) and then cooling as material is ejected from the event. As the r-process environment cools, isomers can freeze out of thermal equilibrium or be directly populated as astrophysically metastable isomers (astromers). Astromers can undergo reactions and decays at rates very different from the ground state, so they may need to be treated independently in nucleosythesis simulations. Two key behaviors of astromers—ground state ↔ isomer transition rates and thermalization temperatures—are determined by direct transition rates between pairs of nuclear states. We perform a sensitivity study to constrain the effects of unknown transitions on astromer behavior. Detailed balance ensures that ground → isomer and isomer → ground transitions are symmetric, so unknown transitions are equally impactful in both directions. We also introduce a categorization of astromers that describes their potential effects in hot environments. We provide a table of neutron-rich isomers that includes the astromer type, thermalization temperature, and key unmeasured transition rates.

Early Signal of Emerging Nuclear Collectivity in Neutron-Rich ^{129}Sb

Radioactive ^{129}Sb, which can be treated as a proton plus semimagic ^{128}Sn core within the particle-core coupling scheme, was studied by Coulomb excitation. Reduced electric quadrupole transition probabilities, B(E2), for the 2^{+}⊗πg_{7/2} multiplet members and candidate πd_{5/2} state were measured. The results indicate that the total electric quadrupole strength of ^{129}Sb is a factor of 1.39(11) larger than the ^{128}Sn core, which is in stark contrast to the expectations of the empirically successful particle-core coupling scheme. Shell-model calculations performed with two different sets of nucleon-nucleon interactions suggest that this enhanced collectivity is due to constructive quadrupole coherence in the wave functions stemming from the proton-neutron residual interactions, where adding one nucleon to a core near a double-shell closure can have a pronounced effect. The enhanced electric quadrupole strength is an early signal of the emerging nuclear collectivity that becomes dominant away from the shell closure.

Fragmentation of Single-Particle Strength around the Doubly Magic Nucleus ^{132}Sn and the Position of the 0f_{5/2} Proton-Hole State in ^{131}In

Spectroscopic factors of neutron-hole and proton-hole states in ^{131}Sn and ^{131}In, respectively, were measured using one-nucleon removal reactions from doubly magic ^{132}Sn at relativistic energies. For ^{131}In, a 2910(50)-keV γ ray was observed for the first time and tentatively assigned to a decay from a 5/2^{-} state at 3275(50) keV to the known 1/2^{-} level at 365 keV. The spectroscopic factors determined for this new excited state and three other single-hole states provide first evidence for a strong fragmentation of single-hole strength in ^{131}Sn and ^{131}In. The experimental results are compared to theoretical calculations based on the relativistic particle-vibration coupling model and to experimental information for single-hole states in the stable doubly magic nucleus ^{208}Pb.

Realistic shell model and nuclei around 132Sn

This contribution reports on a shell-model study of nuclei in the 132Sn region employing a realistic effective interaction derived from the CD-Bonn nucleon-nucleon potential renormalized through the use of the Vlow−k approach. We shall focus on some selected results for nuclei with a few valence particles and/or holes with respect to 132Sn, namely Sn isotopes with N > 82 and 130Te, which have, in part, been discussed in previous papers. Results are compared with experiments, and predictions that may provide guidance to future experiments are also discussed. It is the aim of this contribution to underline the importance of studying 132Sn neighbours to acquire a deep understanding of nuclear structure, that may be very useful also in other physics fields, and to show that the realistic shell model is a very effective tool to conduct these studies.

Proton Shell Evolution below ^{132}Sn: First Measurement of Low-Lying β-Emitting Isomers in ^{123,125}Ag

The β-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^{-} β-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.

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.

Enhanced Quadrupole and Octupole Strength in Doubly Magic ^{132}Sn

The first 2^{+} and 3^{-} states of the doubly magic nucleus ^{132}Sn are populated via safe Coulomb excitation employing the recently commissioned HIE-ISOLDE accelerator at CERN in conjunction with the highly efficient MINIBALL array. The ^{132}Sn ions are accelerated to an energy of 5.49  MeV/nucleon and impinged on a ^{206}Pb target. Deexciting γ rays from the low-lying excited states of the target and the projectile are recorded in coincidence with scattered particles. The reduced transition strengths are determined for the transitions 0_{g.s.}^{+}→2_{1}^{+}, 0_{g.s.}^{+}→3_{1}^{-}, and 2_{1}^{+}→3_{1}^{-} in ^{132}Sn. The results on these states provide crucial information on cross-shell configurations which are determined within large-scale shell-model and Monte Carlo shell-model calculations as well as from random-phase approximation and relativistic random-phase approximation. The locally enhanced B(E2;0_{g.s.}^{+}→2_{1}^{+}) strength is consistent with the microscopic description of the structure of the respective states within all theoretical approaches. The presented results of experiment and theory can be considered to be the first direct verification of the sphericity and double magicity of ^{132}Sn.

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.

Gamma Decay of Unbound Neutron-Hole States in ^{133}Sn

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 β-decay properties for astrophysical simulations may have to be reconsidered.

Electromagnetic Moments of Radioactive ^{136}Te and the Emergence of Collectivity 2p⊕2n Outside of Double-Magic ^{132}Sn

Radioactive ^{136}Te has two valence protons and two valence neutrons outside of the ^{132}Sn double shell closure, providing a simple laboratory for exploring the emergence of collectivity and nucleon-nucleon interactions. Coulomb excitation of ^{136}Te on a titanium target was utilized to determine an extensive set of electromagnetic moments for the three lowest-lying states, including B(E2;0_{1}^{+}→2_{1}^{+}), Q(2_{1}^{+}), and g(2_{1}^{+}). The results indicate that the first-excited state, 2_{1}^{+}, composed of the simple 2p⊕2n system, is prolate deformed, and its wave function is dominated by excited valence neutron configurations, but not to the extent previously suggested. It is demonstrated that extreme sensitivity of g(2_{1}^{+}) to the proton and neutron contributions to the wave function provides unique insight into the nature of emerging collectivity, and g(2_{1}^{+}) was used to differentiate among several state-of-the-art theoretical calculations. Our results are best described by the most recent shell model calculations.

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.

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.

Double-magic nature of 132Sn and 208Pb through lifetime and cross-section measurements

Single-neutron states in (133)Sn and (209)Pb, which are analogous to single-electron states outside of closed atomic shells in alkali metals, were populated by the ((9)Be, (8)Be) one-neutron transfer reaction in inverse kinematics using particle-γ coincidence spectroscopy. In addition, the s(1/2) single-neutron hole-state candidate in (131)Sn was populated by ((9)Be, (10)Be). Doubly closed-shell (132)Sn (radioactive) and (208)Pb (stable) beams were used at sub-Coulomb barrier energies of 3 MeV per nucleon. Level energies, γ-ray transitions, absolute cross sections, spectroscopic factors, asymptotic normalization coefficients, and excited-state lifetimes are reported and compared with shell-model expectations. The results include a new transition and precise level energy for the 3p(1/2) candidate in (133)Sn, new absolute cross sections for the 1h(9/2) candidate in (133)Sn and 3s(1/2) candidate in (131)Sn, and new lifetimes for excited states in (133)Sn and (209)Pb. This is the first report on excited-state lifetimes of (133)Sn, which allow for a unique test of the nuclear shell model and (132)Sn double-shell closure.

1p3/2 proton-hole state in 132Sn and the shell structure along N = 82

A low-lying state in 131In82, the one-proton hole nucleus with respect to double magic 132Sn, was observed by its γ decay to the Iπ=1/2- β-emitting isomer. We identify the new state at an excitation energy of Ex=1353  keV, which was populated both in the β decay of 131Cd83 and after β-delayed neutron emission from 132Cd84, as the previously unknown πp3/2 single-hole state with respect to the 132Sn core. Exploiting this crucial new experimental information, shell-model calculations were performed to study the structure of experimentally inaccessible N=82 isotones below 132Sn. The results evidence a surprising absence of proton subshell closures along the chain of N=82 isotones. The consequences of this finding for the evolution of the N=82 shell gap along the r-process path are discussed.

Constraining the astrophysical origin of the p-nuclei through nuclear physics and meteoritic data

A small number of naturally occurring, proton-rich nuclides (the p-nuclei) cannot be made in the s- and r-processes. Their origin is not well understood. Massive stars can produce p-nuclei through photodisintegration of pre-existing intermediate and heavy nuclei. This so-called γ-process requires high stellar plasma temperatures and occurs mainly in explosive O/Ne burning during a core-collapse supernova. Although the γ-process in massive stars has been successful in producing a large range of p-nuclei, significant deficiencies remain. An increasing number of processes and sites has been studied in recent years in search of viable alternatives replacing or supplementing the massive star models. A large number of unstable nuclei, however, with only theoretically predicted reaction rates are included in the reaction network and thus the nuclear input may also bear considerable uncertainties. The current status of astrophysical models, nuclear input and observational constraints is reviewed. After an overview of currently discussed models, the focus is on the possibility to better constrain those models through different means. Meteoritic data not only provide the actual isotopic abundances of the p-nuclei but can also put constraints on the possible contribution of proton-rich nucleosynthesis. The main part of the review focuses on the nuclear uncertainties involved in the determination of the astrophysical reaction rates required for the extended reaction networks used in nucleosynthesis studies. Experimental approaches are discussed together with their necessary connection to theory, which is especially pronounced for reactions with intermediate and heavy nuclei in explosive nuclear burning, even close to stability.

Neutron single particle structure in 131Sn and direct neutron capture cross sections

Recent calculations suggest that the rate of neutron capture by (130)Sn has a significant impact on late-time nucleosynthesis in the r process. Direct capture into low-lying bound states is expected to be significant in neutron capture near the N=82 closed shell, so r-process reaction rates may be strongly impacted by the properties of neutron single particle states in this region. In order to investigate these properties, the (d,p) reaction has been studied in inverse kinematics using a 630 MeV beam of (130)Sn (4.8 MeV/u) and a (CD(2))(n) target. An array of Si strip detectors, including the Silicon Detector Array and an early implementation of the Oak Ridge Rutgers University Barrel Array, was used to detect reaction products. Results for the (130)Sn(d, p)(131)Sn reaction are found to be very similar to those from the previously reported (132)Sn(d, p)(133)Sn reaction. Direct-semidirect (n,γ) cross section calculations, based for the first time on experimental data, are presented. The uncertainties in these cross sections are thus reduced by orders of magnitude from previous estimates.

Precision mass measurements beyond 132Sn: anomalous behavior of odd-even staggering of binding energies

Atomic masses of the neutron-rich isotopes (121-128)Cd, (129,131)In, (130-135)Sn, (131-136)Sb, and (132-140)Te have been measured with high precision (10 ppb) using the Penning-trap mass spectrometer JYFLTRAP. Among these, the masses of four r-process nuclei (135)Sn, (136)Sb, and (139,140)Te were measured for the first time. An empirical neutron pairing gap expressed as the odd-even staggering of isotopic masses shows a strong quenching across N = 82 for Sn, with a Z dependence that is unexplainable by the current theoretical models.

Calculation of the transition from pairing vibrational to pairing rotational regimes between magic nuclei ¹⁰⁰Sn and ¹³²Sn via two-nucleon transfer reactions

Absolute values of two-particle transfer cross sections along the Sn-isotopic chain are calculated. They agree with measurements within errors and without free parameters. Within this scenario, the predictions concerning the absolute value of the two-particle transfer cross sections associated with the excitation of the pairing vibrational spectrum expected around the recently discovered closed shell nucleus(50)(132)Sn(82) and the very exotic nucleus (50)(100)Sn(50) can be considered quantitative, opening new perspectives in the study of pairing in nuclei.

Quenching of spectroscopic factors for proton removal in oxygen isotopes

We present microscopic coupled-cluster calculations of the spectroscopic factors for proton removal from the closed-shell oxygen isotopes (14,16,22,24,28)O with a chiral nucleon-nucleon interaction at next-to-next-to-next-to-leading order. We include coupling-to-continuum degrees of freedom by using a Hartree-Fock basis built from a Woods-Saxon single-particle basis. This basis treats bound and continuum states on an equal footing. We find a significant quenching of spectroscopic factors in the neutron-rich oxygen isotopes, pointing to enhanced many-body correlations induced by strong coupling to the scattering continuum above the neutron emission thresholds.

Orbital dependent nucleonic pairing in the lightest known isotopes of tin

By studying the (109)Xe→(105)Te→(101)Sn superallowed α-decay chain, we observe low-lying states in (101)Sn, the one-neutron system outside doubly magic (100)Sn. We find that the spins of the ground state (J=7/2) and first excited state (J=5/2) in (101)Sn are reversed with respect to the traditional level ordering postulated for (103)Sn and the heavier tin isotopes. Through simple arguments and state-of-the-art shell-model calculations we explain this unexpected switch in terms of a transition from the single-particle regime to the collective mode in which orbital-dependent pairing correlations dominate.